THE SCIENTIFIC PAPERS

OF

SIR WILLIAM HERSCHEL

KNT. GUELP., LL.D., F.R.S.

SCIENTIl S

l^

SIR WILLIAM

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INCLUDING EARLY PAP

COLLECTED AND KDI OF A JOINT COMMIT 1 AND THE ROYAL

WITH A BfOGRAPHICAL IKlRi • i-M

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THE

SCIENTIFIC PAPERS

OF

SIR WILLIAM HERSCHEL

,^ KNT. GUELP., LL.D., F.R.S.

INCLUDING EARLY PAPERS HITHERTO UNPUBLISHED

COLLECTED AND EDITED UNDER THE DIRECTION

OF A JOINT COMMITTEE OF THE ROYAL SOCIETY

AND THE ROYAL ASTRONOMICAL SOCIETY

WITH A BIOGRAPHICAL INTRODUCTION COMPILED MAINLY FROM UNPUBLISHED MATERIAL BY J. L. E. DREYER

VOL. II ' ^

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CONTENTS OF VOL. II

PAPERS PUBLISHED IN THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY AND ELSEWHERE

\

40.

41. 42.

43-

:^44 45

On the Discovery of four additional Satellites of the Georgium Sidus (1798)

A Fourth Catalogue of the comparative Brightness of the Stars (1799)

On the Power of penetrating into Space by Telescopes, with a Determination of the

Extent of that Power in natural Vision and in Telescopes (1800) Investigation of the Powers of the prismatic Colours to heat and illuminate Objects,

With an Inquiry into the Method of viewing the Sun advantageously (1800) Experiments on the RefrangibiUty of the invisible Rays of the Sun (1800)

.46.

\47.

48. 49.

50.

51

52.

54- 55- 56. 57-

Parti

(1800)

Experiments on the solar and on the terrestrial Rays that occasion Heat

Part II. (1800)

Observations tending to investigate the Nature of the Sun (1801)

Letter to Bode on the Variation of Solar Heat (1804) Additional Observations on the variable Emission of the Light and Heat of the Sun

with Trials of transmitting the Solar Rays through Liquids (1801) Observations of the two lately discovered celestial Bodies [Ceres and Pallas] (1802) Catalogue of 500 new Nebulae and Clusters ; with Remarks on the Construction of the

Heavens (1802) ......

Notes to the Third Catalogue of Nebulae. By J. L. E. Dreyer Observations of the Transit of Mercury ; Investigation of the Causes which often prevent

the proper Action of Mirrors (1803) Account of the Changes that have happened during the last Twenty-five Years, in

the relative Situation of Double stars (1803) Continuation of an Account of the Changes that have happened in the relative Situation

of double Stars (1804) ..... 53. Experiments for ascertaining how far Telescopes will enable us to determine very small

Angles, and to distinguish real from spurious Diameters ; with an Application

to Observations of Mr. Harding's Star [Juno] (1805) .... On the Direction and Velocity of the Motion of the Sun and Solar System (1805) Observations on the singular Figure of the Planet Saturn (1805) .... On the Quantity and Velocity of the Solar Motion (1806) ..... On the Figure, the Climate, and the Atmosphere of Saturn, and its Ring (1806) .

58. Experiments for investigating the Cause of coloured concentric Rings (1807)

59. Observations on the celestial Body discovered by Dr. Olbers [Vesta] and on the Comet

[1806 II.] (1807) .........

60. Observations of a Comet [1807]. To which is added, an Account of a new Irregularity

in the Figure of Saturn (1808) ....•••

PAGE

I 22

31

53 70

n 98

147 180

181 187

199 234

238 250 277

297

317 332 338 360 368

399 403

CONTENTS

6i.JContinuation of Experiments on coloured concentric Rings (iSog)

Editorial note on the reprint of the Three Papers on this subject 63. SupfJement to the Papers on Coloured Concentric Rings (1810)

63. Astronomical Observations relating to the Construction of the Heavens (i8ii)

64. Observations of a Comet [1811] with Remarks on its Construction (1812)

65. Observations of a Second Comet [i8n II.] with Remarks on its Construction (1812)

66. Astronomical Observations Relating to the Sidereal part of the Heavens and its connection

with the Nebulous part (1814) .....

67. A series of Observations of the Satellites of the Georgian Planet (1815)

68. Astronomical Observations to investigate the Local Arrangement of the Celestial Bodies

in Space and the Milky Way (1817) ....

69. Astronomical Observations for ascertaining the relative Distances of Clusters of Stars and

the Power of Telescopes to Reach into Space (1818)

70. On the Places of 145 new Double Stars (1821) .....

71. Fifth and Sixth Catalogues of the Comparative Brightness of the Stars (Prepared by Col. J

Herschel, 1905) ........

Table of W. Herschel's Observations of Variable Stars

PAGE

414 u''

440 441.

459 498

515

520

542

575

592 614

628 649

APPENDIX

1. Unpublished Observations of Messier's Nebulae and Clusters . . .651

2. Synopsis of all Sir W. Herschel's Measures of Double Stars. By Sir J. F. W. Herschel, Bart. 661

3. Star-Gages from the 358th to the I nth Sweep. Brought together by Caroline Herschel . 699

INDEX

714

PLATES IN VOL. II

Portrait of W. Herschel by Artaud (1819) I. To illustrate Herschel's Theory of Concentric Rings II. Types of Nebulas . . .

III. Types of Nebulae .....

IV. Stars with nebulous Appendages and Clusters Portrait of Caroline Herschel by Tielemann (1829)

Frontispiece To face page 431 480 496 536 651

PAPERS

PUBLISHED IN THE

Thilosophical Transactions of the Royal Society

AND ELSEWHERE

XL.

On the Discovery of four additional Satellites of the Georgium Sidus. The retrograde Motion of its old Satellites announced ; and the Cause of their Disappearance at certain Distances from the Planet explained.

[Phil. Trans., 1798, pp. 47-79.]

Read December 14, 1797.

Having been lately much engaged in improving my tables for calculating the places of the Georgian satellites, I found it necessary to recompute all my observa- tions of them. In looking over the whole series, from the year of the first discovery of the satellites in 1787 to the present time, I found these observations so extensive, especially with regard to a miscellaneous branch of them, that I resolved to make this latter part the subject of a strict examination.

The observations I allude to relate to the discovery of four additional satellites : to surmises of a large and a small ring, at rectangles to each other : to the Ught and size of the satellites : and to their disappearance at certain distances from the planet.

In this undertaking, I was much assisted by a set of short and easy theorems I had laid down for calculating all the particulars respecting the motions of satellites ; such as, finding the longitude of the satellite from the angle of position, or the position from the longitude ; the inclination of the orbit from the angle of position and longitude ; the apogee ; the greatest elongation ; and other particulars. Having moreover calculated tables for reduction ; for the position of the point of

VOL. II, I

2 ON THE DISCOVERY OF FOUR ADDITIONAL

greatest elongation ; and for the distance of the apogee, or opening of the ellipsis ; and also contrived an expeditious application of the globe for checking computa- tions of this sort. I found many former intricacies vanish.

By the help of these tables and theorems, I could examine the miscellaneous observations relating to additional satelUtes, on a supposition that their orbits were in the same plane with the two already known, and that the direction of their motion was also the same with that of the latter.

And here I take an opportunity to announce, that the motion of the Georgian satellites is retrograde.

This seems to be a remarkable instance of the great variety that takes place among the movements of the heavenly bodies. Hitherto, all the planets and satel- lites of the solar system have been found to direct their course according to the order of the signs : even the diurnal or rotatory motions, not only of the primary planets, but also of the sun, and six of their secondaries or satellites, now are known to follow the same direction ; but here we have two considerable celestial bodies completing their revolutions in a retrograde order.

I return to the examination of the miscellaneous observations, the result of which has been of considerable importance, and will be contained in this paper. The existence of four additional satellites of our new planet will be proved. The observations which tend to ascertain the existence of rings not appearing to be satisfactorily supported, it will be proper that surmises of them should either be given up, as ill founded, or at least reserved till superior instruments can be provided, to throw more light upon the subject. A remarkable phaenomenon, of the vanishing of the satellites, will be shewn to take place, and its cause animadverted upon.

I shall now, in the first place, relate the observations on which these con- clusions must rest for support, and afterwards join some short arguments, to shew that my results are fairly deduced from them.

For the sake of perspicuity, I shall arrange the observations under three different heads ; and begin with those which relate to the discovery of additional satellites.

A great number of observations on supposed satellites, that were afterwards found to be stars, or of which it could not be ascertained whether they were stars or satellites, for want of clear weather, will only be related. For, to enter into the particular manner of recording these supposed satellites, or to give the figures which were delineated to point them out, would take up too much time, and be of no considerable service to our present argument. It ought however to be men- tioned, that nearly the same precaution was taken with all the related observations as, it will be found, was used in those that are given in the words of the journals that contain them. The former will be distinguished under the head Reports, the Utter under that of Observations.

SATELLITES OF THE GEORGIUM SIDUS 3

Investigation of additional Satellites ,

Reports.

Feb. 6, 1782. A very faint star was pointed out as probably a satellite, but Feb. 7 and 8 was found remaining in its former situation.

March 4, 1783. A satellite was suspected, but March 8 was found to be a star.

April 5, 1783. A suspected satellite was delineated, but the 6th it was seen remaining in its former place.

Nov. 19, 1783. A supposed satellite was marked down, but no opportunity could be had to account for it afterwards.

Nov. 16, 1784. Supposed ist and 2d satellites were pointed out, but not accounted for afterwards.

Many other fruitless endeavours for the discovery of satellites were made ; but, finding my instrument, in the Newtonian form, not adequate to the under- taking, the pursuit was partly relinquished. The additional light however which I gained, by introducing the Front-view in my telescope, soon after gave me an opportunity of resuming it with more success.

Jan. II, 1787. Three supposed satellites were observed : a first, a second, and a third. Jan. 12, the ist and 2d were gone from the places in which I had marked them, but the 3d was remaining, and therefore was a fixed star.*

Jan. 14. A supposed 3d satellite was delineated, but on the 17th it was found to be a star.

Jan 17. Supposed 3d, 4th, and 5th satelUtes were marked, but were found remaining in their former places on the i8th.

Jan. 24. Supposed 3d and 4th satellites were noted, but the weather proving bad on the succeeding nights, till February 4, they were lost in uncertainty.

Feb. 4. A 3d satellite was marked, but not being afterwards accounted for remains lost.

Feb. 7. A supposed 3d satellite was proved to be a star the gth.

Feb. 10. Supposed 3d and 4th satellites have not been afterwards accounted for.

Feb. 13. Supposed 3d, 4th, and 5th satelUtes proved stars the i6th.

Feb. 16. A 3d satellite proved a star the 17th.

Feb. 19. Supposed 3d and 4th satellites were proved to be stars the same evening, by being left in their places, while the planet was moving on.

Feb. 22. The supposed 3d and 4th of the 19th were seen remaining in their former places ; and new 3d, 4th, and 5th satellites were marked ; but these were lost through bad weather, which lasted till March 4.

March 5. A supposed 3d satellite proved to be a star the 7th.

• It has already been shewn, in a former paper, that the removed satellites were those two which now are sufficiently known.

4 ON THE DISCOVERY OF FOUR ADDITIONAL

March 7. The position of a 3d was taken and a 4th also marked ; but March 8 they were both proved to be fixed stars.

October 20. A very small star was seen near the planet, but lost, for want of opportunity to account for it.

March 13, 1789. The positions of 3d and 4th satellites were taken, but the 14th they were found to be stars.

March 16. Supposed 3d and 4th satellites were well laid down, but March 20 were found to be stars.

March 26. The places of supposed 3d and 4th satellites were ascertained, but no opportunity could be had of deciding whether they were stars or satellites.

Dec. 15. A supposed 3d satellite was accurately delineated, but proved to be a star the i6th.

Observations.

Jan. 18, 1790. 6^ 51'.* A supposed 3d satellite is about 2 diameters of the planet following ; excessively faint, and only seen by glimpses. T"* 57'. I cannot perceive the 3d.

Reports.

Jan. 18, 1790. A supposed 4th satellite Wcis described, but was found to be a star the 19th.

Jan. 20. A 3d satellite was perceived, and its angle of position ascertained ; but was afterwards lost, for want of opportunity to examine its place again.

Observations.

Feb. 9, 1790. 6" 28'. There is a supposed 3d satellite, in a line with the planet and the 2d satellite.

6^ 40'. Configuration of the Georgian planet and satellites. ' ^ ' See fig. I.

Clouds prevent further observations. jf ** Feb. II. The supposed 3d satellite of the gth of February

"7 ^_ I believe is wanting ; at least I cannot see it, though the weather

,«, 6 ^/^^7r is very clear, but windy.

Feb. 12. The supposed 3d satellite of the 9th is not in the place where I saw it that night.

Reports.

Feb. II, 1790. Supposed 3d and 4th sateUites were laid down, but on the 1 2th they were both found remaining in their former places.

Feb. 16. A 3d satellite was delineated, but on the 17th it proved to be a star.

• All the times have been corrected so as to be true, sidereal ; but are only given here to the nearest minute.

SATELLITES OF THE GEORGIUM SIDUS 5

March 5. Supposed 3d and 4th satellites were laid down, but on the 8th were seen remaining in their places.

Feb. 4, 1791. A 3d satellite was marked, but has not been accounted for afterwards.

Feb. 5. Supposed 3d, 4th, and 5th satellites were delineated, but no oppor- tunity could afterwards be found to ascertain their existence.

March 5. Supposed 3d, 4th, and 5th satellites were put down. They could not be seen March 6, but were proved to be smaU stars the 7th.

Feb. 12, 1792. A third satellite was delineated, but was left behind by the planet the same evening, and also seen in its former place the next night.

Feb. 13. A 3d satellite was put down, but proved to be a star the 14th.

Feb. 20. The position of a 3d satellite was taken, but 4 hours after was found to be left behind by the planet. It was also seen in its former place Feb. 21.

Feb. 26. A 3d satellite, between the planet and 2d, was observed ; which, 3'' 37' afterwards, was thought to be left behind, but was so faint as hardly to be perceivable. A fourth was also put down. Neither of them have been accounted for afterwards.

March 8, 1793. The position of a supposed 3d sateUite was taken, but the next day it was found to be a star.

March 9. A supposed 3d satellite was observed, at 5 or 6 times the distance of the 1st, but was not accounted for afterwards.

March 14. Supposed 3d and 4th satellites were observed, but no opportunity could be had afterwards to see them again.

Observations.

Feb. 25, 1794. With 320, there is a small star a, fig. 2, about 15 degrees north preceding the planet ; and another b, about 30 degrees north preceding : also one c, directly preceding. There is a very small fourth star d, making a trapezium with the other three ; and ^-^ iS^y^s.-'j^^- two more e f, preceding this 4th star, are in a line ^^\ a - '''tF/y 6

with it. ^'^\ /^

Feb. 26. The stars, in figure 2, marked/ e d a, are in a line. There is a star g, at rectangles to f e d a : the perpendicular falls upon d : it is towards the south. There is also a star h, north oifed a ; but it is too

faint to admit of a determination of its place : I can only see it now and then by imperfect glimpses.

Feb. 28. 6^ 40'. The stars/ edaoi the 26th are in their places, c is in the place where I have marked it. The star g is in the place where I marked it. I see also the very small star h.

6^ 50'. There is a very small star k, but not so small as h, very near to, and

6 ON THE DISCOVERY OF FOUR ADDITIONAL

north following/, which I did not see on the 26th. It is not quite half way between / and e, but nearer to/ than to e. It makes an obtuse triangle with / and e.

9» 43'. The motion of the planet this evening, since the first observation, is

very visible.

lo" 7'. I cannot perceive the star k. The weather is not so clear as it was.

10^ 21'. I cannot perceive the star k in the place where it was &> 50'.

March 4, 1794. Power 320. 6^ 46'. The stars abcdefgoi Feb. 28, fig. 3, are in their places, but I cannot see the small star k. The evening is not very clear.

g" 51'. I cannot see the star k.

"SfUXas^^^-*

sA{^imA 2

Fig, 3.

Fig. 4.

lo"* 25'. I suppose a, in figure 4, to be the star towards which the planet is moving, cah are in a crooked line, c ef are nearly in a line ; / is a little preceding. cde form a triangle. There is a small star h, preceding d. There is an exceeding small star k, in the line hkg, but a little preceding and nearer b. abc are large stars, deg are also pretty large. / and h are small. Power 157. With 320, there is also a very small star I, near d, forming an isosceles triangle hdl, on the preceding side.

March 5. 7" 39'. Power 320. Thestarsaftc^e/g^^/arein theplaces where they were marked last night.

9" 37'. There is a very small star n, south of g ; another m, preceding g ; and a third 0, south following g.

10" 19'. I suspect a very small star, south following the planet, at one-third of the distance of the ist satellite ; but cannot verify it with 480. With 600, the same suspicion continues.

SATELLITES OF THE GEORGIUM SIDUS 7

March 7. 9" 48'. The stars ahcdefghkl are in their places, nm 0 are in their places. The planet has passed between the stars ef, pretty near to/.

Reports.

March 21 1794. Power 320. A small star was suspected south of the planet, or about 85° south following. It could not be verified with 480, nor with 600 ; and was even supposed to have been a deception ; but the 22d was found remaining in the place where the planet had left it.

Fig. 5.

Ohservations.

March 26, 1794. 9" 35'. With 480, 1 see the ist satellite much better than with 320. I suspected, with 320, a 3d satellite, directly north of the planet, a little farther off than the ist, and this power almost verifies the suspicion. See figure 5.

9^ 44'. With 600, 1 still suspect the same, but cannot satisfy myself of the reality.

ii" 32'. I see the supposed 3d satellite perfectly well now. It is much smaller than the ist, and in a line with the planet and the ist ; so that probably it is a fixed star ; since it preceded the ist, when I saw it before, I think more than the quicker motion of the ist satellite would account for. If it be a fixed star, it makes almost a rectangular triangle with qr, the shorter leg being 3d r ; or it is almost in a line with q and n.

N. B. The lines in the description are truer than in the figure, as the latter is only intended to point out the stars in question.

8 ON THE DISCOVERY OF FOUR ADDITIONAL

March 27. 8» 37'. Power 320. The same small star, observed last night at 11" 32', is gone from the place where I saw it. From its hght last night, compared to r, which to-night is very near the planet, and scarcely visible, I am certain that it must be bright enough to be perceived immediately, if it were in the place pointed out by my description.

io» 20'. The planet is considerably removed from the star r.

11" 41' I had many glimpses of small stars or supposed satellites : one of them in a place agreeing with the 3d satellite of last night, (supposing it to have moved with the planet ;) that is, a little farther off, and after the ist. Another preceding the ist, but nearer. Some others south, at a good distance ; but not one of them could I see for any constancy. They were only lucid gUmpses.

Reports.

March 27, 1794. A supposed 4th satellite was deUneated, but proved to be a star the 28th.

OhservaHons.

March 4, 1796. Configuration of the Georgian planet and fixed stars for lo" 3'. See fig. 6.

March 5. 9" 50'. I suspected a very small star between c and h, which was not

there last night. I had a pretty certain glimpse of it. It is in a Une from the planet

J. towards/: power 320. With 600, I see the satelUte

^y^^^^j^ ^- ^ better than before ; but cannot perceive the suspected

° „ small star.

"* ^ u ^^<Ae iQh 17'. The air is remarkably clear at present,

^ '"4——+ ** »/ but I cannot perceive the suspected star.

-^ * I March 9. 11" 23'. As the probability of other

V satellites is, that they revolve in the same plane with

*' og the ist and 2d, I chiefly look for them in the direction

of their orbits, which is now nearly a straight Une. ^» April 5, 1796. There is no star in the line of the

^'°' ^- transverse, that can be taken for a satellite : the

evening is very beautiful, and I examined that line with 300, at a distance ; and with 600, within the orbits of the two satellites.

March 23, 1797. Three very small stars O P Q, are in the path of the planet ; they form an obtuse triangle.

March 25. 11" 4'. A very bright star S, at almost the distance of the field of view, is a little south of the path of the planet. It has a small north preceding star T, which points to two more V W, towards the north. Between the triangle of March 23d and the four last mentioned stars, is a very small star X. March 28. 10" 52'. I see the stars S T V W X of March 25th.

SATELLITES OF THE GEORGIUM SIDUS g

1 1" 25'. From X towards the triangle O P Q of March 23d, is an exceeding small star Y, about four times the distance of the 2d satellite, and nearly in the line of the greatest elongation. I do not remember to have seen it the 25th.

Ill 41' xhe distance of Y from X is about J of the distance of X from the triangle. It requires much attention to see it ; but I have a very complete view of it, by drawing the planet just out of the field, and the star X almost on the pre- ceding side.

Arguments upon the Reports and Observations.

From the reports of the great number of supposed satellites, compared with the select observations which are given at length, it must be evident that the method of looking for difficult objects, and of marking them down by lines and angles, with every other possible advantage for finding them again, has been completely under- stood and put in practice. So guarded against deceptions, we cannot but allow, that even a single glimpse of a very small star is a considerable argument in favour of its existence. What I call verifying a suspicion, which is generally done with a higher power than that which caused the suspicion, is obtaining a steadier view of the existence of the object in question ; that is, to see it in such a manner as to be able to fix an eye upon it, and to compare it with other surrounding objects ; and thus to be able to ascertain its relative situation with those other objects in a satisfactory manner.

An interior Satellite.

The observation of Jan. 18, 1790 says, " a supposed 3d satellite is about two diameters of the planet following." There is not the least doubt expressed about the existence of the satellite, or object in question, which therefore must be looked upon as ascertained. Now, the angle of the greatest elongation of the Georgian satellites, by my new tables, at the time of observation, was 81° 33' N.F. Therefore, the angle of the apogee was 8° 27' S.F. ; and since, by observation, the satellite was " following," without any mention of degrees being made, we may admit it to have been not far from the parallel ; suppose 11 or 12 degrees S.F. In this case, the sateUite would be in the apogee about the time of the 2d observation, at 7" 57' ; which says, " I cannot perceive the satellite." But it will be shewn hereafter, when I come to treat of the vanishing of the satellites, that it would become invisible in this situation. Indeed, without the supposition of the satellite's coming to the apogee, it might easily happen that the least change in the clearness of the air, during a time of i" 5' which elapsed between the first and second observation, might render an object invisible, which, as the first observation says, was " ex- cessively faint, and could only be seen by glimpses."

From the observed distance, which is put at " 2 diameters of the planet," we may conclude what would be the distance of its greatest elongation. For, 2 dia- meters from the disk of the planet give 2| from the centre. Now, the distance of

VOL. II. 2

10 ON THE DISCOVERY OF FOUR ADDITIONAL

the apogee at this time, by my tables, was -64, supposing that of the greatest

elongation i ; therefore we have the radius of its orbit - t^ — =i6''i

This calculation is not intended to determine precisely the distance of the satellite, but only to shew that its orbit is more contracted than that of the ist, and that consequently it is an interior satellite.

If any doubt should be entertained about the validity of this observation, we have a second, and very striking one, of March 5, 1794 ; where an interior satellite was suspected south following the planet, at one-third of the distance of the ist. March 4, when a description was made of the stars, as in figure 4, this satellite was not in the place where it was observed the 5th. And, by an examination of the same stars March 7, it appears, that even the smallest stars n m 0, of the 5th, were seen in their former places, but not the sateUite. The observation therefore must be looked upon as decisive with regard to its existence. If any doubt should arise, on account of the suspicion not being verified with 480, I must remark, that being used to such imperfect gUmpses, it has generally turned out, even when I have given up as improbable the existence of a supposed sateUite seen in that manner, that it has afterwards nevertheless been discovered that a small star remained in the place where the satellite had been suspected to be situated. An instance of this may be seen in the report of the observations that were made March 21 and 22, 1794. Be- sides, in the present case, it is additionally mentioned, that the same object was examined with a power of 600, which continued the suspicion.

From the assigned place of this satellite, at J of the distance of that of the first, it appears that this observation belongs to the interior satellite of Jan. 18, 1790, which has already been examined. The ist satellite was this evening at its greatest elongation, one-third of which is about 11". The apogee distance of a satellite whose greatest distance is i6"'i would have been 6"*i on the day of our observation ; but, not being come to the apogee, by many degrees, it could not be so near the planet.

For the sake of greater precision, let us admit that the satellite was exactly south following ; that is, 45 degrees from the parallel, and 45 from the meridian ; then, by calculation, a satelUte whose orbit is at i6"-i from the planet, would, in the situation now admitted, have been y"-i from its centre, which might coarsely be rated at | of the distance of the first. But the estimation of 11" is probably more accurate than that in the ist observation, where 2 diameters are given. And, by calculating from this quantity, we find that the greatest elongation distance of the satellite is 2^"-^ ', now, putting 2^ diameters in the first observation, instead of 2, the distance deduced from it will come out ig'-s ; which is certainly an agreement sufficiently near to admit both observations to belong to the same satellite.

March 27, 1794. We find a third observation, which will assist in supporting the two former ones. A glimpse of a satellite is mentioned, which was preceding the ist, but nearer the planet. The position of the ist satellite the same evening

SATELLITES OF THE GEORGIUM SIDUS II

was, by measuring, found to be 62°-i N.F. which is still a considerable way from its greatest elongation ; but our new satellite preceded it, and was therefore more advanced in its orbit, or nearer its greatest distance ; and yet the observation says, that it was not so far from the planet as the ist ; notwithstanding this latter was in a more contracted part of its orbit. It follows therefore that this was also an interior satellite. Now, since we may allow these three observations to belong to the same, we ought not to make a distinction ; but admit, as sufficiently estabhshed, the existence of at least one interior satellite of our new planet.

8!^ An intermediate Satellite.

March 26, 1794. A satellite was suspected, directly north of the planet. At first it could not be verified, but was seen perfectly well afterwards. It was supposed that probably it might be a star, but this was left undecided. The observation of March 27th however removes all doubt upon the subject ; as it fully affirms that the small star observed the 26th, at 11" 32', was gone from the place in which it was the day before. Such strong circumstances are mentioned in confirmation, that we cannot hesitate placing this among the list of existing satelhtes. It was not the interior satellite of Jan. 18, 1790 ; for both the ist and 2d known satellites were in full view March 26th ; see figure 5 ; and the observation places this new one in a line drawn from the planet continued through the ist ; with the remark, that it was a little farther from the planet than the ist. The 2d was then near its greatest southern elongation, and we may see from the figure, as well as from the above description, that the orbit of this new satellite is situated between the orbits of the other two.

We have a second observation of the same satellite March 27, 1794 ; where, among the glimpses of additional satellites at 11'' 41', is mentioned " one in a place probably agreeing with the new satellite of March 26th," which, by its motion, must have been carried forward, so as to be where the observation of the 27th says it was, namely, " a little farther off and after the ist ; " that is, at a little greater distance from the planet than the ist, and not so far advanced in its orbit as that satellite. This amounts not only to an additional proof, but even announces the recognition of the satellite, and its motion in the course of one day.

An exterior Satellite.

Feb. 9, 1790. A new satellite was seen, in a line with the planet and the 2d satellite. See figure i. To convince us that this was not a fixed star, we have the observations of two other nights, the nth and 12th of February, where the removal of it, from the place in which it was Feb. 9, is clearly demonstrated. As it was in a line continued from the planet through the second satellite, its orbit must evidently be of a greater dimension than that of the 2d ; I shall therefore put it down as an exterior satellite.

12 ON THE DISCOVERY OF FOUR ADDITIONAL

Most likely this satellite also was seen among the supposed satellites south of the planet. March 27, 1794 ; where we find mention made of " some others south. at a good distance." In that case, this will make a second observation.

We have a third observation of the same new satellite March 5, 1796 ; when a

very small star was seen, in a place where the evening before there had been none ;

as appears by the configuration of the 5th of March. See figure 6. At the time of

the observation, the planet was come to the longitude of the place where the star

was perceived to be ; which agrees with the idea of its having been brought to that

situation by the planet. It may be objected, that the star could not be verified

with a power of 600 ; but here we have more than a bare suspicion of the satellite.

for the observation says, " I had a pretty certain gUmpse of it ; " and this appears

also from the assigned place of the star at the intersection of two given lines. For,

such a deUneation could not have been made, without having perceived it with a

considerable degree of steady vision. Its distance, to judge by the description.

will agree sufficiently with the two foregoing observations of this new exterior

satellite.

The most distant Satellite.

On Feb. 28, 1794, a star was perceived where on the 26th there was none. This star was larger than a very small star which was observed the 26th, not far from the place of the new supposed satellite ; and a configuration having been made expressly, by way of ascertaining what stars might afterwards come into a situation where they could be mistaken for satellites, our new star or satellite would not have been omitted, when a smaller one very near it was scrupulously recorded. The motion of the planet, in 3 hours and 3 minutes, is mentioned as very visible. The place of the star, which was a new visitor this evening, was very particularly deline- ated, at &> 50'. From its situation, it is evident the motion of the planet must have carried this star, if it was one of its satellites, towards the large star /, figure 3 ; in the light of which a dim satellite would be lost. This accordingly happened ; for at 10* 7' and 10" 21' it was no longer visible. The direction of the planet's motion is plainly pointed out, by the place of the planet March 2d.

With respect to the orbit of this satellite, it appears, from its situation near the apogee, where it was seen, that its distance was to that of the second satellite, which was then near its greatest elongation, as 8 to 5. And, since the apogee distance, on the day of observation, was only -37, we have its greatest elongation as

— to 5 ; that is, as 21-6 to 5, or above 4 to i. From which we may conclude, that

its orbit must lie considerably without the before mentioned exterior satellite of Feb. 9, 1790.

We have a second observation of it March 27, 1794 ; which, though not very strong, yet adds confirmation to the former. For that evening, which was un- commonly fine, other satellites, south, at a good distance, were perceived. This

SATELLITES OF THE GEORGIUM SIDUS

13

must relate principally to our present satellite, which may certainly be said to be at a good distance from the planet, and which, by that time, was probably in the southern part of its orbit, and near its greatest elongation.

There is a third observation, March 28, 1797, which probably also belongs to this satelHte. For the exceedingly small star Y, which is mentioned as not having been seen the 25th, when the delineation of the stars was made, will agree very well with the two former observations ; and, being near the greatest elongation, the distance of this satellite is well pointed out, and agrees remarkably well with the calculation of the first observation of it.

It remains now only to be mentioned, that in such delicate observations as these of the additional satellites, there may possibly arise some doubts with those who are very scrupulous ; but, as I have been much in the habit of seeing very small and dim objects, I have not been detained from publishing these observations sooner, on account of the least uncertainty about the existence of these satellites, but merely because I was in hopes of being able soon to give a better account of them, with regard to their periodical revolutions. It did not appear satisfactory to me to announce a satellite, unless I could, at the same time, have pointed out more precisely the place where it might be found by other astronomers. But, as more time is now already elapsed than I had allowed myself for a completion of the theory of these satellites, I thought it better not to defer the communication any longer.

The arrangement of the four new and the two old satellites together will be thus:

First satellite, the interior one of Jan. 18, 1790.

Second satellite, the nearest old one of Jan. 11, 1787.*

Third satellite, the intermediate one of March 26, 1794.

Fourth sateUite, the farthest old one of Jan. 11, 1787.!

Fifth satellite, the exterior one of Feb. 9, 1790.

Sixth satellite, the most distant one of Feb. 28, 1794.

Observations and Reports tending to the Discovery of one or more Rings of the Georgian Planet, and the flattening of its polar Regions. J

Nov. 13, 1782. 7-feet reflector, power 460. " I perceive no flattening of the polar regions."

April 8, 1783. " I surmise a polar flattening."

Feb. 4, 1787. 20-feet reflector, power 300. " Well defined ; no appearance of any ring ; much daylight."

March 4. "I begin to entertain again a suspicion that the planet is not round. When I see it most distinctly, it appears to have double, opposite points. See figure 7. Perhaps a double ring ; that is, two rings, at rectangles to each other."

♦ [Titania.— Ed.] t [Oberon.— Ed.]

{ The observations are distinguished from the reports by marks of quotation {" ").

14 ON THE DISCOVERY OF FOUR ADDITIONAL

March 5. The Georgian Sidus not being round, the telescope was turned to Jupiter. I viewed that planet with 157, 300, and 480, which showed it perfectly well defined. Returning to the Georgian planet, it was again seen affected with projecting points. Two opposite ones, that were large and blunt, from preceding to following ; and two others, that were small and less blunt, from north to south. See figure 7.

March 7. Position of the great ring R, from 70° S.P. to 70° N.F. Small ring r, from 20° N.P. to 20° N.F. 600 shewed R and r. 800 R and r. 1200 R and r.

March 8. " R and t are probably deceptions."

Nov. g. " The suspicion of a ring returns often when I adjust the focus by one of the sateUites, but yet I think it has no foundation."

Feb. 22, 1789. A ring was suspected.

March 16. 7" 37'. " I have turned my speculum 90° round. A certain appear- ance, owing to a defect which it has contracted by exposure to the air since it was

<0> ^ h Q

Fig. 7. Fig. 8. Fig. 9. Fig. 10.

made, is gone with it ; (see fig. 9 and 10 ;) but the suspected ring remains in the place where I saw it last."

" ^ 50'- Power 471 shews the same appearance rather stronger. Power 589 still shews the same."

" Memorandum. The ring is short, not like that of Saturn. It seems to be as in figure 8 ; and this may account for the great difficulty of verifying it. It is remarkable that the two ansce seem of a colour a little inclined to red. The blur occasioned by the fault of the speculum is, to-night, as represented in figure 9. The other evening it was as in figure 10 ; and the ring is likewise as it was the same evening."

March 20. " 7" 53'. When the satellites are best in focus, the suspicion of a ring is the strongest."

Dec. 15, " The planet is not round, and I have not much doubt but that it has a ring."

Feb. 26, 1792. "6" 34'. My telescope is extremely distinct ; and, when I adjust it upon a very minute double star, which is not far from the planet, I see a very faint ray, like a ring crossing the planet, over the centre. This appearance is of an equ£d length on both sides, so that I strongly suspect it to be a ring. There is, however, a possibility of its being an imperfection in the speculum, owing to some slight scratch : I shall take its position, and afterwards turn the speculum on its axis."

" 8" 39'. Position of the supposed ring 55°-6 from N.P. to S.F."

" 9" 56'. I have turned the speculum one quadrant round ; but the appearance of the very faint ray continues where it was before, so that the defect is not in the

SATELLITES OF THE GEORGIUM SIDUS 15

speculum, nor is it in the eye-glass. But still it is now also pretty evident that it arises from some external cause ; for it is now in the same situation, with regard to the tube, in which it was 3^ hours ago : whereas, the parallel is differently situated, and the ring, of course, ought to be so too."

March 5, 1792. " I viewed the Georgian planet with a newly polished speculum, of an excellent figure. It shewed the planet very well defined, and without any suspicion of a ring. I viewed it successively with 240, 300, 480, 600, 800, 1200, and 2400 ; all which powers my speculum bore with great distinctness. I am pretty well convinced that the disk is flattened." The moon was pretty near the planet.

Dec. 4, 1793. " 7-feet reflector, power 287. The Georgian planet is not so well defined as, from the extraordinary distinctness of my present 7-feet telescope, it ought to be. There is a suspicion of some apparatus about the planet."

Feb. 26, 1794. " 20-feet reflector, power 480. The planet seems to be a little lengthened out, in the direction of the longer axis of the satellites' orbits."

April 21, 1795. " lo-feet reflector, power 400. The telescope adjusted to a neighbouring star, so as to make it perfectly round. The disk of the planet seems to be a little elliptical. With 600, also adjusted upon the neighbouring star, the disk still seems elhptical."

Remarks upon the foregoing Observations.

With regard to the phaenomena which gave rise to the suspicion of one or more rings, it must be noticed, that few specula or object-glasses are so very perfect as not to be affected with some rays or inequalities, when high powers are used, and the object to be viewed is very minute. It seems, however, from the observations of March 16, 1789, and Feb. 26, 1792, that the cause of deception, in this case, must be looked for elsewhere. It has often happened, that the situation of the eye-glass, being on one side of the tube, which brings the observer close to the mouth of it, has occasioned a visible defect in the view of a very minute object, when proper care has not been taken to keep out of the way ; especially when the wind is in such a quarter as to come from the observer across the telescope. The direction of a current of air alone may also affect vision. Without, however, entering further into the discussion of a subject that must be attended with uncertainty, I will only add, that the observation of the 26th seems to be very decisive against the existence of a ring. When the surmises arose at first, I thought it proper to suppose, that a ring might be in such a situation as to render it almost invisible ; and that, conse- quently, observations should not be given up, till a sufficient time had elapsed to obtain a better view of such a supposed ring, by a removal of the planet from its node. This has now sufficiently been obtained in the course of ten years ; for, let the node of the ring have been in any situation whatsoever, provided it kept to the same, we must by this time have had a pretty good view of the ring itself. Placing

l5 ON THE DISCOVERY OF FOUR ADDITIONAL

therefore great confidence on the observation of March 5, 1792, supported by my late views of the planet, I venture to affirm, that it has no ring in the least resembUng that, or rather those, of Saturn.

The flattening of the poles of the planet seems to be sufficiently ascertained by many observations. The 7-feet, the lo-feet, and the 20-feet instruments, equally confirm it ; and the direction pointed out Feb. 26. 1794, seems to be conformable to the analogies that may be drawn from the situation of the equator of Saturn, and

of Jupiter.

This being admitted, we may without hesitation conclude, that the Georgian planet also has a rotation upon its axis, of a considerable degree of velocity.

Reports and Observations relating to the Light and Size of the Georgian Satellites, and to their vanishing at certain Distances from the Planet*

Jan. 14, 1787. A star was put down, as a supposed very faint satellite ; but, on the 17th. the planet being removed, it appeared nearly as bright as two consider- able stars that had also been noted.

Jan. 17. " The ist satelhte is the smallest in appearance."

Jan. 24. " The 2d satellite is brighter than the first."

Feb. 9. 1787. " The ist satellite is larger than the second."

Feb. 10. The planet was supposed to go to a triangle of pretty bright stars. The nth it was between them, and the stars of the triangle were so dim, that, had they not been seen before, they might have been supposed to be satellites.

Sept. 19. 1787. 4" 24'. " I can still see the satellites, though daylight is already very strong : they are fainter than the faintest of Saturn's satellites." f

Feb. 22, 1791. " I cannot perceive the ist satellite, probably owing to its near- ness to the planet."

March 2. 1791. " The ist satellite is hardly to be seen ; I have however had several perfect glimpses of it. It seems to be about the most contracted part of its orbit."

March 6. The supposed 3d and 4th satellites of March 5th were imagined to have been gone from their former places ; but were seen the 7th, with this memor- andum. " I mistook them last night for other stars, they being so large that I did not know them again."

March 9. " The 2d satellite is nearer the planet than the first, and on that account appears smaller."

Dec. 9. 1791. " I do not perceive the 1st satellite."

Feb. 13, 1792. " Gh 16'. The 3d supposed satellite of last night is a considerable star ; not much less than b."

When the supposed third was pointed out the night before, it is said to be

• [In the following, the first and second satellite are respectively Titania and Oberon. — ^Ed.] t Five satellites of Saturn were only known at that time.

SATELLITES OF THE GEORGIUM SIDUS Vf

smaller than the ist and 2d sateUites. By the figure, it did not exceed the distance of the 2d ; and h is called a pretty large star.

Feb. 20, 1792. The 2d satellite, being at a great distance, was mistaken for a pretty large star, till about four hours after, when its motion along with the planet was perceived.

Feb. 21, 1792. " f" 36'. I cannot see the 2d satellite. By calculation, it should be about 8°-6 S.F. and I suspect it to be there, but cannot get the least assurance."

March 15, 1792. " I cannot see the ist satellite with 300 ; nor with 480 ; nor with 600."

March 19. " S*" 35'. I cannot see the 2d satellite with 300. With 480 I see it very well. I see it also with 800 ; and very well with 1200. With 2400 and 4800 the satellite cannot be seen ; but there seems to be a whitish haziness coming on."

March 4, 1794. The ist satellite could not be seen.

March 7. The ist was invisible.

March 17. Both ist and 2d were invisible.

March 21. The ist was invisible, though looked for with all the powers of the instrument.

March 22. The 2d was hardly visible.

March 23. The 2d was not to be seen.

March 26. The ist was but just visible.

March 5, 1796. The 2d was invisible,

April 4, 1796. The ist was invisible.

March 17, 1797. " Power 600. Neither of the satellites are visible to-night ; with 300 I cannot see them. The night is very beautiful, and I have a field bar to hide the planet ; but, notwithstanding this, I cannot see either of the satellites."

March 21. The ist satelUte was invisible.

March 23. The 2d was invisible. The ist could not be seen immediately, but, having been informed where exactly to look for it, according to my calculation of its place, it was perceived ; and with 600 seen very well.

March 25. Both satellites were invisible.

Remarks on the foregoing Observations.

From the observations of Jan. 14, Feb. 10, March 6, 1787, and Feb. 13, 1792, it appears, that all very small stars, when they come near the planet, lose much of their lustre. Indeed, every observation that has been recorded before, of supposed satellites that have been proved to be stars afterwards, has fully confirmed this circumstance ; for they were always found to be considerable stars, and their being mistaken for satellites was owing to their loss of light when near the planet. This would hardly deserve notice, as it is well known that a superior Ught will obstruct an inferior one ; but some circumstances which attend the operation of the affec-

VOL. II. 3

l8 ON THE DISCOVERY OF FOUR ADDITIONAL

tions of light upon the eye, when objects are very faint, are so remarkable, that they must not be passed over in silence.

After having been used to follow up the satellites of Saturn and Jupiter, to the very margin of their planets, so as even to measure the apparent diameter of one of Jupiter's satellites by its entrance on the disk,* I was in hopes that a similar oppor- tunity would soon have offered with the Georgian sateUites : not indeed to measure the satellites, but to measure the planet itself, by means of the passage of the satellite over its disk. I expected also to have settled the epochs of the satellites, from their conjunctions and oppositions, with more accuracy than I have yet been able to do from their various positions in other parts of their orbits. A disappointment of obtaining these capital advantages deserves to have its cause investigated ; but, first of all, let us cast a look upon the observations.

The satellites, we may remark, become regularly invisible, when, after their elongation, they arrive to certain distances from the planet. In order to find what these distances are, we will take the first observation of this kind, as an example.

Feb. 22, 1791, the first satelUte could not be seen. Now, by my lately con- structed tables, its longitude from the apogee, at the time of observation, was 204-5 degrees ; that is, 24*5 degrees from the most contracted part of its orbit, on the side that is turned to us, which, as its opposite is called the apogee, I shall call the perigee. By my tables also for the same day, we have the distance of the apogee from the planet, which is -60 ; supposing the greatest elongation distance to be I. This being given, we may find an easy method of ascertaining the distance of the satellite, when it is near the apogee or perigee : for it will be sufficiently true for our purpose to use the following analogy. Cosine of the distance of the satellite from the apogee or perigee is to the apogee distance from the planet, as the greatest elongation is to the distance of the satellite from the planet. When the ellipsis is very open, this theorem will only hold good in moderate distances from the apogee or perigee ; but, when it is a good deal flattened, it will not be considerably out in more distant situations : and it will also be sufficiently accurate to take the natural cosine from the tables to two places of decimals only. When this is applied to our present instance, we have -91 for the natural cosine of 24-5 degrees ; and the distance

of the satellite from the planet will come out -^^ =2i''-8.

•91

By this method, it appears that the satellite, when it could not be seen, was nearly 22" from the planet.

We must not however conclude, that this is the given distance at which it will always vanish. For instance, the same satellite, though hardly to be seen, was however not quite invisible March 2, 1791. Its distance from the planet, computed

as before, was then only ^^ = iq'^S.

• See Phil. Trans, for 1797, Part II. page 335. [Vol. I. p. 586.]

SATELLITES OF THE GEORGIUM SIDUS

19

The clearness of the atmosphere, and other favourable circumstances, must certainly have great influence in observations of very faint objects ; therefore, a computation of all the observations where the satellites were not seen, as well as a few others where they were seen, when pretty near the apogee or perigee, will be the surest way of settling the fact. The result of these computations is thus.

First sateUite invisible.

Second satellite invisible.

*

1791. Feb. 22 at 218 Dec. 19 at 169

1792. March 15 at 18-4 1794. March 4 at 18-5

March 7 at 12-5 March 17 at 170 March 21 at 15-5 April 4 at 8-5 1797. March 17 at 48 March 21 at 4-6 March 25 at 48

1792. Feb. 21 at 23-3 1794. March 17 at 207 March 23 at 179 1796. March 5 at 9-3 March 17 at 6-3 March 23 at 6-2 March 25 at 87

First satellite visible.

Second satellite visible.

1791. March 2 at 19-8 1794. Feb. 26 at 141

1794. March 22 at 17-5

Thus, having the observations and calculated distances under our inspection, we find that both the satellites became always invisible when they were near the planet : that the ist was generally lost when it came within 18" of the planet, and the 2d at the distance of about 20". In very uncommon and beautiful nights, the ist has once been seen at i3"-8, and the 2d at i7"-3 ; but at no time have they been visible when nearer the planet.

I shall now endeavour to investigate the cause which can render small stars and satellites invisible at so great a distance as 18 or 20".

A dense atmosphere of the planet would account for the defalcation of Ught sufficiently, were it not proved that the satellites are equally lost, whether they are in the nearest half of their orbits, or in that which is farthest from us. But, as a satellite cannot be eclipsed by an atmosphere that is behind it, a surmise of this kind cannot be entertained. Let us then turn our view to light itself, and see whether certain affections between bright and very bright objects, contrasted with others that take place between faint and very faint ones, will not explain the phsenomena of vanishing satellites.

The light of Jupiter or Saturn, for instance, on account of its brilliancy, is

20 ON THE DISCOVERY OF FOUR ADDITIONAL

diffused, almost equally, over a space of several minutes all around these planets. Their satelUtes also, having a great share of brightness, and moving in a sphere that is strongly illuminated, cannot be much affected by their various distances from the planets. The case then is. that they have much Ught to lose, and comparatively lose but little.

The Georgian planet, on the contrary, is very faint ; and the influence of its feeble light cannot extend far, with any degree of equality. This enables us to see the faintest objects, even when they are only a minute or two removed from it. The satellites of this planet are very nearly the dimmest objects that can be seen in the heavens ; so that they cannot bear any considerable diminution of their Ught, by a contrast with a more luminous object, without becoming invisible. If then the sphere of illmnination of our new planet be Umited to i8 or 20", we may fully account for the loss of the satelUtes when they come within its reach ; for they have very Uttle light to lose, and lose it pretty suddenly.

This contrast, therefore, between the condition of the Georgian satellites and those of the brighter planets, seems to be sufficient to account for the phaenomenon of their becoming invisible.

We may avail ourselves of the observations that relate to the distances at which the satelUtes vanish, to determine their relative brightness. The 2d satelUte appears generaUy brighter than the ist ; but, as the former is usuaUy lost farther from the planet than the latter, we may admit the ist satelUte to be rather brighter than the 2d. This seems to be confirmed by the observation of March 9, 1791 ; where the 2d appeared to be smaUer than the ist, though the latter was only 25" from the planet, while the other was so'-S.

The first of the new satellites will hardly ever be seen otherwise than about its greatest elongations, but cannot be much inferior in brightness to the other two ; and, if any more interior satellites should exist, we shall probably not obtain a sight of them ; for the same reason that the inhabitants of the Georgian planet perhaps never can discover the existence of our earth, Venus, and Mercury.

The 2d new or intermediate satelUte is considerably smaUer than the ist and 2d old satelUtes. The two exterior, or 5th and 6th satellites, are the smallest of all, and must chiefly be looked for in their greatest elongations.

Periodical Revolutions of the new Satellites.

It may be some satisfaction to know what time the four additional satelUtes probably employ in revolving round their planet. Now, as this can only be ascer- tained with accuracy by many observations, we must of course remain in suspense, tiU a series of them can be properly instituted. But, in the mean time, we may admit the distance of the interior satellite to be 25"'^, as our calculation of the estimation of March 5, 1794, gives it ; and from this we compute that its periodical revolution wUl be 5 days, 21 hours, 25 minutes.

SATELLITES OF THE GEORGIUM SIDUS 21

If we place the intermediate satellite at an equal distance between the two old ones, or at 38''-57, its period will be lo days, 23 hours, 4 minutes.

By the figure of Feb. 9, 1790, it seems that the nearest exterior satellite is about double the distance of the farthest old one ; hence, its periodical time is found to be 38 days, i hour, 49 minutes.

The most distant satellite, according to the calculation of the observation of Feb. 28, 1794, is full four times as far from the planet as the old 2d satellite ; it will therefore take at least 107 days, 16 hours, 40 minutes, to complete one revolution.

It will hardly be necessary to add, that the accuracy of these periods depends entirely upon the truth of the assmned distances ; some considerable difference, therefore, may be expected, when observations shall furnish us with proper data for more accurate determinations.*

Slough, near Windsor, September i, 1797.

* [Compare paper LXVIL, infra; also Holden's and Lassell's papers in the Monthly Notices R.A.S., XXXV, pp. 16 and 22. — Ed.]

[ 22 ]

XLI.

A Fourth Catalogue of the comparative Brightness of the Stars.

[PhU. Trans., 1799, pp. 121-144.]

Read February 21, 1799.

Lustre of the stars in Auriga.

z

/

5

2.1 4.1

33

S

4

10 7 33 . 8 33 ; 10 Camel

a

g

5.6

4.2,1 2.4

34

0

2

23 . 34 66 Gemin .34 34 ;

23

3

I

4

3-37 5 Arietis - 3 - 44 Persei

23.34

3 . 44 Persei

35

IT

6

35 29 35.46

4

u

5

4.2 2.4.x

36

6

29-36

5

6

5-6

37

e

4

3-37 24 Gemin, 37

6

6

5-6 6-12

38

6.7

39 • 38 . 42

7

t

4

7-10 7 -, 10

39

6.7

39 38

8

i

4

10,8 33,8 10 -.8-, 30

40

6

31 . 40 - 28

9

6.5

7Camelop7 9 11 Camelop , 9 -, la Camelop

41

42

6 6

46-41

38,42.43 47.42.43

10

n

4

7-10,8 10 7 33 7-, 10-8

43

6

42.43

II

M

5

15; 11-20 15711721

44

K

4.5

44 , 136 Tauri 44 - - 49

12

6

6-12

45

6

45 46

13

a

I

13 - - 3 Lyra

46

5

35.46-41 45.46

14

5

i6 , 14 . 19

47

6

47.42

15

X

5

15; II 15 7 11

48

6

49 -. 48 - 53

16

6

16.14

49

5.6

44--49-,48

17

7.6

19 . 17 . 18

50

5.6

50 - 52 50 . 16 Lyncis

18

8

17.18

51

5-6

52-51

19

6

14 . 19 . 17

52

5

50 - 52 - 51

20

P

6

11 - 20 21 . 20

53

6

53 . 28 Gemin 48 - 53 . 54

21

<r

5.6

11 7 21 . 20

54

6

28 Gemin .54-25 Gemin

22

6

26 , 22

53.54

23

y

2

13 Arietis , 23 . 34 34^23 23.34

55

56

5 6

55-58

58 , 56 . 57 16 Lyncis , 56

34

*

5.6

25724

57

6

56.57

25

X

5.6

25726 25724

58

4.5

55 - 58 . 56

26

6

25 7 26 , 22 27 , 26

59

6

62 . 59 . 60

27

0

6

27.26

60

6

59-60

38

7

40-28

61

6

61.62

29

T

5

32,29.31 35 29 -,36

62

6.7

61 . 62 . 59

30

t

6

8 -, 30 42 Camel .30-31 Camel

63

64

4-5 5

63.65 66; 64

31

V

6

29 , 31 . 40

65

5

63 . 65 . 66

32

V

5

32.29

66

5

65 . 66 ; 64

FOURTH CATALOGUE OF THE COMPARATIVE BRIGHTNESS OF THE STARS 23

Lustre of the stars in Draco.

I

2

3 4 5 6

7 8

9

10

II

12

13 14

15 i6

17 i8

19

20 21 22 23

24 25 26 27 28

29

30 31 32 33

34 35 36

37

38

39

I-'

y

3-4 6 6 6

3 6 6 6 6.

5 2

3

3 3

4 5 5 5 5 6

5-4 2

2.3

4 4 6

5 4 6 6

7 3 2

4-5 6 6 6 6 5

1-5

5--2 3;2 3:2

6-4

I.3--2 11-5,13

614

9.7 10-8.9

8.9.7 10-8

II -5

40 Herculis - 12 22 -, 12 27 Here - 12 , 67 Herculis

5.13

I UrsiE min - 14 14 — 22

14 - 23 14 -, 57 15.18 17- 16 17- 16

19,18-, 20 15.18 21.18 19,18 18 -, 20

21 .18 30 , 21 14 - - 22 -, 12 57 7 22

23 , 40 Herculis 14 - 23 23 - 27 Herculis

24.25

24 . 25 - 26 25-26

28 - 27 , 34 27 . 42 31 -28-27

34 - -. 29 30 . 21 31-28

44 -. 32 - 43

7 Ursae min - 33 5 Corona 7 33

55 Ophiu - 33 27.34 35 34--. 29 34-37

35 . 34 35-40+41 42.36

34 - 37 . 38 37.38

45 . 39 • 46

40

41 42

43 44 45 46

47

48

49 50

51 52 53 54 55 56 57 58

59 60 61 62

63

64

65 66 67 68 69 70

71

72

73 74 75 76

77 78

79 80

0

X d

5 5 6

5 4 5 5

4 6 6

4-5

5-6 4-5

5

5

6

6 3-4

4

6

4.5 4-5

6 5.6 5.6

6.5 6

5 6 6 6 6 6 5-6 6 6 5 5 5

7 6

41-40

41 - 40 27 . 42 . 36

32-43

44 -.32

45.39

39 • 46 ; 47

46; 47- -51 47-54

49.48

51 . 49 . 48

52 . 50 7 59 73 .50 55 . 50 52-50

47 - - 51 . 49

60-52 52 . 50 52 - 50

54.53

47 - 54 . 53

61 -.55 55.50

Does not exist.

14 -, 57 7 22

63 -.58 -61 58:67

50 7 59

60-52

58 - 61 -, 55 67 , 61

Does not exist.

63 -. 58

64 -. 65

64-, 65-, 70 65,69 68 . 66 . 71

58 ; 67 f'l

68 . 66 65,69

65 -. 70 66.71

Does not exist.

73.50 73-77 73.78

75 - 74 • 76

75-74

74.76

73-77 78.77

73 . 78 . 77 16 Cephei , 78

80-79

80-79

Lustre of the stars in Lynx.

5.6

4 6

1.5

3--5

8-3.10

6

6

6.7

4.6

2--5-6 1,5 5-6 4-6

A FOURTH CATALOGUE OF

Lustre of the stars in Lynx.

7

6.7

Does not exist.

28

7

36-28

8

6.7

8 , 41 Camelop 8-3

29

5

29 - 56 Camelop 29 , 58 Came-

9

7

11-9

lop 29,30

10

6.7

41 Camelop - 10 3 , 10

30

6

29.30

II

6

14,11-9

31

5

31 -. 27

12

7

15 ; 12 -. 14

32

7

33:32

13

6

13.14

33

6

33:32

14

5

12 -.14 13,14." 19.14-23

34

6

26,34 36,34

15

5

15; 12

35

7

Does not exist.

i6

6

50 Aurigae . 16 , 56 Aurigae

36

6

36,34 37 36 -28

17

7

18 -.17

37

5.6

37 36 37.42

18

6

18 -, 47 Camelop 18 -, 17

38

6

38-40

19

5

24-19.14

39

4

12 Ursae , 39 39 -, 10 Leonis

20

6

21 - - 20

min 39 , 10 Ursae

21

5

22 - 21 - - 20

40

6

38-40

22

6

22-21

41

4

25 Ursae .41-12 Ursae

23

7

14-23

42

6

37 , 42 . 45 15 Leonis min .

24

5

24-19

42 — 14 Leonis min

25

6

26 -, 25

43

6

43-44

26

5

26 -, 25 26 , 34

44

7.6

43-44

27

5

27 - 50 Camelop 31 -, 27

45

5-6

29 Ursae --45 42.45

Lustre of the stars

in Lyra.

I

«c

5

I -, 2 6 - I

II

S^

4-5

12-, II 18,11.9 16,11

2

M

6

1-2

12

s*

4

12 -, II 12 .13 12 - 18 12 - 16

3

a

I

16 Bootis - - 3

13

■K

6

12 .13 20 , 13

4

6

5

6;4-5

14

y

3

6 Cygni 7 14 , 85 Herculis

5

6

4.5

15

X

6

15,9 15.17 15 7 19

6

f

5

6--7 6-1 6;4

16

p

6

12-16, II

7

5

6 — 7

17

6

15.17

8

.-^

6

9.8

18

I

5

12 - 18 , II

9

V*

6

11.9,8 15,9,8

19

6

15719

10

B

3

10 .14 14 7 10 14 -, 10

20

n

6

21 . 20 , 13 20 , 21

14 10 6 + 7J-10

21

e

6

21 .20 20 , 21

Lustre of the stars in

Monoceros.

I

6

3 -. I - 2

10

6

5 -, 10 -, 9 10-7

2

6

1-2,4

II

5

22 0rionis-ii-5 30:11726

3

6

3-1

12

5

13 -, 12 , 14

4

6

2,4.6

13

4

8 - 13 = 7 14 13 -, 12

5

4.5

II -5-, 10 5,8

14

5.6

13 = 7 14 12 , 14

6

6.7

4.6

15

4

8715.17

7

6

10-7

16

6

17-16

8

4

5.8-13 8 7 15 8.18

17

5

15 , 17 - 16

9

5

10-9

18

4

8.18

THE COMPARATIVE BRIGHTNESS OF THE STARS

^5

Lustre of the stars in Monoceros.

19

5

22 - 19 , 20

26

4-5

II 7 26 7 29

20

6

19 , 20 , 25

27

5

29 - 27 28 , 27

21

5

22 -, 21 , 24

28

5

29 , 28 , 27

22

4-5

22 -, 21 22 - 19

29

6

29 - 27 26 7 29 , 28 29 , 31

23

6.7

24.23

30

6

30; II

24

6

21 , 24 , 23

31

4

29.31

25

6

20 , 25

Lustre of the stars in Perseus.

I

6

4.1-3 4-1

31

5.6

29.31

2

g

6

3.2

32

I

6

32 - 30 32 - 36

3

6.7

1-3,2

33

a

2.3

33 - - 26 21 Androm , 33 . 43

4

6

4,1 4-1 4-9

Andromedae

5

6

9-5-7 7-5

34

6

35 - 34 34 - 29

6

A

6

65 Androm , 6 , 63 Androm

35

<r

5

37 . 35 - 34

7

X

7.6

5.7-8 8;7.5

36

6.7

32 - 36 - 30

8

7

7-8 9-.8;7

37

^

5

37.35

9

t

6

4-9-. 8 9-5

38

oi

6

46,38,59 41-38-46

10

7

Does not exist.

39

S

3

45 - - 39 - 25

n

7

27 ; II - 13

40

o«

6

52 , 40 . 42 40 , 42

12

9

6

28 . 12 . 14

41

V

4

25 - 41 , 46 41 - 38

13

d

4

II - 13 , 18 18 7 13

42

n

6

40 .42 40 , 42 54 ; 42 - 55

14

6

12 .14 24 , 14

43

A

5

43.20

15

6

Lost

44

f

3

3 Aurigae - 44 3 Aurigae . 44

16

P'

4

16 , 22 16 - - 20

44,45

17

r

5-6

17,28

45

e

3

44 > 45 - - 39

18

T

5

13 ,18 18 7 13

46

i

5

41 . 46 , 38 38 - 46 46 - 58

19

6

Does not exist

47

\

4

51 • 47 , 53

20

^*

6

16 - - 20 28 - 20 43 , 20

48

c

5

48,51

21

4-5

28.21

49

6.7

50.49

22

IT

4

16 , 22 , 28

50

6.7

52 , 50 , 49

23

y

3

23 . 25 23 -, 4 Trianguh

51

M

4

48 . 51 . 47

24

s

6

28 . 24 , 14

52

/

5

52.50 53-52,40 58-52

25

p

4

23,25-41 39-25

53

d

6

47 . 53 . 52

26

/8

2.3

26 , 25 26 ; 25 26 25

54

6

54; 42

6 Arietis ,26-23

55

6

42 - 55 ; 56

27

K

5-4

27; II

56

7

55:56

28

W

5

22 , 28 . 12 17 , 28 . 24 28 . 21

57

m

6

59-57

28-20

58

e

5

46 - 58 - 52

29

6

34-29.31

59

6

38 , 59 . 57

30

6

32 - 30 36 - 30

Lustre of the s

tars in Sex

tans.

I

5

1-2

4

6

7,4 4-2

2

5

1-2

5

6

3.5

3

6

8-3,5 6.3

6

6

8-6,3

VOL. II.

26

A FOURTH CATALOGUE OF

Lustre of the stars ir

Sextans.

7

6

7.4

25

6

25.26

8

6

8-3 8-6

26

6

24 -, 26 25 .26 23 , 26 -

31

9

6

12 . 9 . 13

27

6

27.28

lO

6

29 Leonis - 7 10 - 11

28

5

29 - 28 . 24 27 , 28 - 32

XI

5.6

10 -II

29

5

30 - 29 - 28

12

6

4-12,9

30

5

32 Hydrae - 30 - 29

13

6

9 13

31

6

26-31

14

6

14.19

32

6

28-32

15

4

35 Hydrae .15-32 Hydrae

33

6

33,24

i6

6

19.16

34

6

35-34.37

17

6

22 , 17 . 18

35

6

35-34

i8

6

17 . 18 - 20

36

6

37 36

19

6

14 . 19 , 16

37

6

55 Leonis -.37. 38 34.37

.36

20

6

18 - 20 . 21

38

6

37.38

21

6

20.21

39

7

41-39 40,39

22

6

22.17

40

6

41 - 40 . 39

23

5

23.26

41

6

41-39 41-40

24

6

28.24-26 33.24

Lustre of the e

>tars in Taurus.

I

0

4

1-2

29

«i

6

29.40

2

^

4

I - 2 . 35

30

e

5

5-30-4 66 , 30 . 46

3

6

Does not exist

31

u*

6

40,31

4

s

6

5 -.4 76 30-4

32

6

53 . 32 . 33

5

/

5

38-5-4 5-30

33

7

32.33

6

/

6

476.12

34

7

39-34

7

6

7 . 66 Arietis

35

X

4

2 , 35 • 38 123 - 35

8

6

Does not exist

36

7

43 ; 36

9

6

Lost

37

A

5

65,37--39 37--43

10

4-5

38 . 10 . 49

38

V

4

35-38-5 38.10

II

6

21 . II . 22

39

6

37--39 51-39 43-39

-34

12

6

6. 12

40

7

29 , 40 , 31 46 ; 40 . 45

13

6

13,14 13-14

41

6

42 ; 41 ; 44

14

6

13.14 13-14

42

^

5

52 . 42 ; 41

15

n

6

Does not exist

43

«»

6

37 — 43-39 43:36

i6

i

7

18 . 16 . 21

44

P

6

41 ; 44 . 59

17

b

5

27 . 17 . 20

45

7

40.45

18

m

7

28 , 18 . 16

46

7

47.46:40 30.46.93

19

e

5

20 . 19 . 23

47

7

49-47.46 47 -60

20

c

6

17 . 20 . 19

48

7

58.48

21

k

6.7

16.21 . II

49

M

4

10,49 49-47 88,49

22

I

7

II , 22 , 26

50

««

6

65 - 50 - 56 50 , 67

23

d

5

19.23-28

51

7

53 . 51 - 39

24

P

7

26.24

52

'P

5

52.42

25

n

3

27 -, 27

53

7

56 . 53 , 51 53 . 32

26

S

7.8

22 . 26 , 24

54

y

3

77T54--58 54761 74

54

27

/

6

25 -. 27 • 17

55

7

63,55

28

A

7.8

23-28.18

56

7

50-56,53

THE COMPARATIVE BRIGHTNESS OF THE STARS

27

Lustre of the stars in Taurus.

57

6.7

58 , 57 • 60

102

(

4

102 = 7 106 102 , 104

58

h

7

54 - - 58 . 48

58 , 57 103

6

103 . 98

73-58-. 76 58. f

iZ 104

m

6

102 , 104 -, 106

59

X

5

44.59

105

6

106 , 105 - 107

60

7

57.60 47 -60

106

/I

6

102 = 7 106 , 105 106 . 109

61

9-

4 .

54 7 61 , 68

104 -, 106 - - 107 106 - 98

62

7

72 - 62 65 ; 62

107

/«

6

105-107 108.107 I06--I07

63

6

64 -. 63 , 55

99 , 107 7 lOI

64

s*

4

68 - 64 -, 63

108

7

109 -, 108 109 , 108 . 107

65

K

5

65-69 65:62 65-5(

3 65,37 109

M

6

114-109-108 106.109,108

66

f

5

66,30

no

7

116 -no. 113 115 -no. 117

67

-C>

5

69 - 67 . 72 50 , 67 ;

72

120 . no

68

s*

6

61 , 68 - 64

III

6.7

III , 116 111,115 119 -III

69

v"

5

65-69-67 94.69

112

^

2

112 -, 24 Orionis

70

7

80-70

"3

6

no . 113

71

7

71; 75

"4

0

5

114-109

72

l/»

6

72-62 67.72 67:72

72-95 "5

7.8

III , 115- no 122 . 115

73

tr

5

73-58 86,73

116

6.7

III , 116-110

74

e

3-4

78 . 74 ; 54

117

7

no . 117

75

7

71 ; 75 . 81

118

6

121 - 118

76

7

58-76 83-76

119

7

119- in

77

0"

5

77 7 54

120

7

120 . no

78

e*

5

78,74

121

6

121 -118

79

b

5

90 - - 79 . 83

122

7

126 - 122 -, 129 122 , 130

80

7

81 , 80 - 70 80-84

80.85

122 . 115

81

7

75 ; 81 , 80

123

t

3

123 7 35 13 Gemin -, 123 , 7

82

7

Does not exist

Gemin

83

7

79.83 58.83-76

124

6.7

Does not exist

84

7

80-84

125

3

132 . 125

85

7

80.85

126

6

126 - 122

86

p

5

86.73

127

6

130 - - 127

87

a

I

58 Orionis--87 i

9 Orionis 128

6

129 , 128

= 7 87 87 - - 78 (

^emin 129

6

122 -, 129 , 128

88

d

5

90 . 88 , 49

130

6

122 , 130 - - 127

89

7

91; 89

131

6

133 . 131 • 132 135 . 131 . 137

90

c»

5

90,88 90 --79 9c

- - 93 132

4

139 , 132 , 125 131 . 132 . 135

91

<ri

6

92 , 91 ; 89

133

6

134 . 133 . 131 134 - 133 . 131

92

(r»

6

92.91

134

6

134.133 134-133

93

c*

6

46.93 90--93

135

6

132. 135-138 135. 131

94

T

5

94.69

136

5

136 '; 139 44 Aurigae , 136

95

6.7

72 -. 95

137

5

135-137 131. 137

96

6

4 Orionis - - 96 97 -

.96 138

6

Does not exist

97

i

6

4 Orionis , 97 -, 96

139

6

I Gemin - 139 , 132 136 • 139 ,

98

k

6

io6 - 98 - 99 103 . 9

8

132

99

6

98 - 99 . 107

140

6

141 . 140

100

6

Lost

141

6

141 . 140

lOI

6

107 7 lOI

28

A FOURTH CATALOGUE OF

Lustre of the stars in Triangulum.

I

i

6

3-1

8

8

5

9-.8-7

a

a

4

4 -, 2 -, 9 31 Androm -, 2

9

y

4

2 -, 9 - 8

2-99 Piscium

10

a

6

6 , 10 ; 12

3

«

6

7-31

II

d

7

12 , II , 13

4

/8

4

6 Arietis - 4 23 Persei -, 4 -, 2 4 =■ 31 Andromedae

12 13

c

6 7

10 ; 12 7 13 12 , II 12 7 13 II , 13

5

7

7-5

14

6

7 ; 14 ; 15

6

1

6

6,7 6 , 10

15

7

14:15

7

1

6

8-7-3 6,7-5 7;i4

16

7

16 , 30 Arietis 33 Arietis -

16

Notes to Auriga.

23 Is 112 Tauri.

30 Is 32 Camelopardali.

45 " Oct. 5, 1798. The time of this star, in the observation of flamsteed, Vol. II. page 189, is marked : : but it cannot be much out, as the star seems to be in the place assigned to it by the British catalogue."

61 The R.A. in the Atlas Calestis requires a correction of - 42'.

Notes to Draco, 10 Is 87 Ursae. 12 and 13 Were never observed by flamsteed, but are in la caille's Catalogue of northern stars.

14 M. de la lande says the star is not to be found. See Mr. bode' s A st. J ahrbuch ior 1795, page 198.

I observed this star in a sweep of the heavens, June 2d, 1788. Its brightness was estimated Sept. II, 1795 ; Sept. 24, 1796 ; Sept. 30, 1796 ; and Dec. 28, 1798 ; so that, if M. de la lande is sure no cloud intervened when he looked for it, we may suspect it to be a changeable star.

15 The British catalogue requires + 30' in R.A.

35 The expression " 35 - 40 + 41 " in my estimation of brightness, means that, with the naked eye, 35 is a very little brighter than 40 and 41 together, taken as one star. For they are so near each other, that the eye alone cannot distinguish them from a single star. The British catalogue gives them 3' farther asunder than they ought to be according to flamsteed's observation, page 463. See also Mr. bode's Ast. Jahrbuch for 1785, page 173.

40 The estimation " 40 -41 " was made with a 7-feet reflector, power 460.

56 Does not exist, flamsteed has no observation of it.* My double star II. 31, called 56 Draconis, is a star situated between 59 and 50, about ij degree from 59 towards 50.^

62 Does not exist, flamsteed has no observation of it ; but, if an error of two hours be supposed in the calculation of one of the observations of 31 Draconis, it will account for the insertion of this star.

72 Does not exist. There is an observation, page 173, which produced it ; but, if we admit an error of 3' in time in that observation, it will then belong to 71. J

Notes to Lynx.

7 Does not exist in the place pointed out by the British catalogue ; but, in flamsteed's observa- tions, page 286, its time is marked : : and there is probably some considerable error.§

* [It is =59 Draconis. — Ed.]

+ When I say Ij degree from 59 towards 50, it is to be understood that I express myself in degrees of a great circle. I have always used the same method of description in my catalogues of double stars ; and, as these objects were pointed out for being viewed with telescopes of great magnifying power, which are generally not fixed, and therefore can give no right ascension, I am rather surprised to find that, in a catal(^ue published not many years ago. the author has taken my degrees of a great circle for degrees of right ascension. For instance, the double star IV. 82, where, in pointing out its place, I say, "above J degree following the 16 Cephei, in a line parallel to 0 and a Cassiopeae," is placed in the zone from 15 to 19° of that author's catalogue, only 2' 47" 5 of time following 16 Cephei, when ilought to have been at least 10' or 11' following.

I take this opportunity to mention that, in general, the same author's account of my double stars is extremely erroneous.

J [72 Draconis is =P. XX. 162, 8-3 mag.— Ed.] § [Flamsteed's Declination is 1° too great.— Ed.]

THE COMPARATIVE BRIGHTNESS OF THE STARS

29

20, 21, 22 The place of these stars in the heavens does not seem to agree with their situation in the Atlas.

30 Is 58 Camelopardali.

35 FLAMSTEED has HO observation of this star ; but, as it is marked 7m in the British catalogue, and has a line allotted to it, my Atlas and stars have been numbered so as to take it in ; and the numbers I have used with double stars and other objects where the stars in Lynx after the 35th are concerned, must be reckoned accordingly.*

37 " Dec. 4, 1796, This star is nearer to 25 than it is marked in the Atlas." The R.A. should be corrected +1°.

Notes to Lyra.

10 This is one of our periodical stars discovered by Mr. goodricke ; its period is about 6 da}'s 9 hours. See Phil. Trans. Vol. LXXVI. page 197. The greatest variation of its light, as far as I have observed, is from " 10 . 14 to 6 + 7 J- 10." The expression 6 + 7 is borrowed from algebra, and is always to be understood as has been explained in the note to 35 Draconis.

16 The British catalogue requires a correction of - 9° in P.D. ; and this star will then agree with 12 Lyrae Hevelii.

19 The British catalogue requires a correction of + 8° in P.D.

Notes to Perseus.

5 FLAMSTEED has no observation of this star ; but there is a star exactly in the place pointed out by the British catalogue.

10 Does not exist, flamsteed never observed it.^

12 " Sept. 5, 1798, This star, which has no time in flamsteed's observations, is placed a little too forward ; or requires about +10' in R.A."

14 " Sept. 4, 1798, The time of this star is marked doubtful by flamsteed, page 214 ; but it seems to be in the situation where the British catalogue places it."

15 Is lost, flamsteed observed it Jan. 17, 1693, page 186 ; but it is not to be seen in the place pointed out by that observation. See bode's Ast. Jahrbuch for 1794, page 97.J

19 Does not exist. There is an observation in page 185, which has produced this star, but it belongs to 18 ; for the star is lettered t, and a memorandum says, " Post transitum." See also bode's Ast. Jahrbuch for 1788, page 172.

24 " Sept. 4, 1798, The place of this star in the British catalogue wants a correction of + 56' in P.D. and - 45' in R.A."

26 Is a periodical star. It has been noticed in the last century as subject to change, by montanari and MARALDi ; but its being periodical was discovered by Mr. goodricke, in 1783, who fixed the time of its change at 2 days 20 hours 48' 56". See Phil. Trans. Vol. LXXIV. page 287. I have seen it when brightest, " 6 Arietis , 26 - 23 ", and when most diminished, " 26 , 25 ".

38 " Sept. 5, 1798, The British catalogue requires nearly + 2° in R.A., and - 13' in P.D. ; at least there is no other star that can be taken for it."

42 " Sept. 4, 1798, The British catalogue requires a correction of + 13 in P.D."

Notes to Sextans.

I Is 10 Leonis. 10 Is 25 Leonis.

II Is 28 Leonis.

12 " March 17, 1797, This star is misplaced in the British catalogue ; the P.D. should be corrected + i°."

28 " March 21, 1797, This star is misplaced in the British catalogue, and requires a correction of + 20' in R.A., and + 1° in P.D." §

29 " March 21, 1797, The P.D. of this star in the British catalogue requires + i°."

• [See Baily's note to 1240.— Ed.] t [See Baily's note to 293.— Ea]

X [It was observed north of the zenith and not south ; =i) Persei.— Ed.] g [See Baily's note to No. i486.— Ed.]

30 A FOURTH CATALOGUE OF THE COMPARATIVE BRIGHTNESS OF THE STARS

Notes to Taurus.

3 Does not exist, flamsteed never observed it.

8 " Jan. 10, 1796, This star does not exist, flamsteed has no observation of it. There is a star about gm not far from the place."

9. " Dec. 28, 1798, This star is lost." M. de tA lande says it is not to be found. See Mr. bode's Asl. Jahrhuch for 1795, page 198. flamsteed has two complete observations of it, page 86, and page 506. We can hardly admit what Mr. bode suggests, that this star, like the rest, has found its way into the British catalogue by some error of writing, or of calculating the observations ; it will therefore be advisable to look for a future re-appearance of it, as it may prove to be a periodical or changeable one.*

15 Does not exist, flamsteed has no observation of it.

34 The estimation " 39 - 34 " belongs to a star very nearly in the place where, according to flam- steed's observation, 34 should be ; but, as we know by calculation that the Georgian planet was about the situation where, the 13 of Dec. 1690, flamsteed observed the supposed 34th, there can be no doubt but that he must have seen it, and taken it for a fixed star. The magnitude, 6m, which he assigned to 34, agrees perfectly well with the lustre of the planet, compared with other stars which the same author has marked 6m ; and, with his telescope, he could not have the most distant suspicion of its being any other object than a fixed star of about the 6th magnitude.

40 " March 4, 1796. The R.A. in the Atlas requires a correction of about + 20'."

55 In the British catalogue, the P.D. requires - 8'.

56 The R.A. in the British catalogue requires - 15'.

82 Does not exist, flamsteed did not observe this star, unless we admit a correction of the British catalogue - 1° 5' in P.D.

99 flamsteed has no observation of this star ; but, as there is one in the heavens, about a degree more north, the British catalogue requires probably a correction of - 1° in P.D.

100 This star is lost, flamsteed settled its place, page 369, and the observation seems to be a very good oncf

103 FLAMSTEED has no observation of this star. How it came to be inserted in the British catalogue does not appear. I have given it as a double star V, 114, and here also estimated its brightness ; but it must be remembered that my estimations do not strictly ascertain the place of objects. If, therefore, 103 does not exist, my double star, as well as the one here estimated, must be some star not far from the place assigned to 103 in the British catalogue.}

112 Is 23 Aurigae.

118 The Atlas should be corrected - 30' in R.A.

124 Does not exist ; unless we admit a correction of + 1° 4' in R.A. of the British catalogue.

138 Does not exist ; but, as there is no time in flamsteed's observation of this star, it is probably misplaced in the British catalogue, for there are several considerable stars in the neighbourhood.§

Notes to Triangulum.

I " Nov. 2, 1798, This star, which has the time and zenith distance in flamsteed's observations doubtful, seems to be nearly in the place where the British catalogue gives it. It should perhaps be a few minutes more north."

Slough, near Windsor, Jan. 28, 1799.

• [D.M. +22*-si8, 7 mag., does not seem to be variable.— Ed.] t [It is B. 686 ; see Peters' Memoir, p. 71.— Ed.]

X [103 Tauri = P. IV. 295 ; see Baily's note to 655.— Ed.] § [See Baily's note to 988.— Ed.]

[ 31 ]

XLII.

On the Power of penetrating into Space by Telescopes ; with a comparative Determina- tion of the Extent of that Power in natural Vision, and in Telescopes of various Sizes and Constructions ; illustrated by select Observations.

[Phil. Trans., 1800, pp. 49-85.]

Read November 21, 1799.

It will not be difficult to shew that the power of penetrating into space by telescopes is very different from magnifying power, and that, in the construction of instru- ments, these two powers ought to be considered separately.

In order to conduct our present inquiry properly, it will be necessary to examine the nature of luminous bodies, and to enter into the method of vision at a distance. Therefore, to prevent the inaccuracy that would unavoidably arise from the use of terms in their common acceptation, I shall have recourse to algebraic symbols, and to such definitions as may be necessary to fix a precise meaning to some ex- pressions which are often used in conversation, without much regard to accuracy.

By luminous bodies I mean, in the following pages, to denote such as throw out light, whatever may be the cause of it : even those that are opaque, when they are in a situation to reflect light, should be understood to be included ; as objects of vision they must throw out light, and become intitled to be called luminous. How- ever, those that shine by their own light may be called self-luminous, when there is an occasion to distinguish them.

The question will arise, whether luminous bodies scatter light in all directions equally ; but, till we are more intimately acquainted with the powers which emit and reflect light, we shall probably remain ignorant on this head. I should remark, that what I mean to say, relates only to the physical points into which we may conceive the surfaces of luminous bodies to be divided ; for, when we take any given luminous body in its whole construction, such as the sun or the moon, the question will assume another form, as will appear hereafter.

That Ught, flame, and luminous gases are penetrable to the rays of Hght, we know from experience ; * it follows therefore, that every part of the sun's disk

• In order to put this to a proof, I placed four candles behind a screen, at f of an inch distance from each other, so that their flames might range exactly in a line. The first of the candles was placed at the same distance from the screen, and just opposite a narrow slit, f of an inch long, and \ broad. On the other side of the screen I fixed up a book, at such a distance from the sht that.

33 ON THE POWER OF

cannot appear equally luminous to an observer in a given situation, on account of the unequal depth of its luminous atmosphere in different places.* This regards only bodies that are self-luminous. But the greatest inequaUties in the brightness of luminous bodies in general will undoubtedly be owing to their natural texture ; which may be extremely various, with regard to their power of throwing out light more or less copiously.

Brightness I ascribe to bodies that throw out light ; and those that throw out most are the brightest.

It will now be necessary to establish certain expressions for brightness in different circumstances.

In the first place, let us suppose a luminous surface throwing out light, and let the whole quantity of light thrown out by it be called L.

Now, since every part of this surface throws out light, let us suppose it divided into a number of luminous physical points, denoted by N.

If the copiousness of the emission of light from every physical point of the luminous surface were equal, it might in general be denoted by c ; but, as that is most probably never the case, I make C stand for the mean copiousness of light thrown out from all the physical points of a luminous object. This may be found in the following manner. Let c express the copiousness of emitting light, of any number of physical points that agree in this respect ; and let the number of these points be n. Let the copiousness of emission of another number of points be c', and their number n' . And if, in the same manner, other degrees of copiousness be called c2, c*, &c. and their numbers be denoted by rfi, «', &c. then will the sum of every set of points, multiplied by their respective copiousness of emitting hght, give us the quantity of light thrown out by the whole luminous body. That is, L=cn +c'n' +c^n^, &c. ; and the mean copiousness of emitting light, of each physical point, wUl be expressed by cn+c'n' +c^n^&c. ^ ^

It is evident that the mean power, or copiousness of throwing out light, of every physical point in the luminous surface, multiplied by the number of points, must give us the whole power of throwing out light, of the luminous body. That is CN=L.

I ought now to answer an objection that may be made to this theory. Light, as has been stated, is transparent ; and, since the light of a point behind the surface of a flame will pass through the surface, ought we not to take in its depth, as well as its superficial dimensions ? In answer to this, I recur to what has been said

when the first of the candles was lighted, the letters might not be sufficiently illuminated to become legible. Then, lighting successively the second, third, and fourth candles, I found the letters gradu- ally more illuminated, so that at last I could read them with great facility ; and, by the arrangement of the screen and candles, the light of the second, third, and fourth, could not reach the book, with- out penetrating the flames of those that were placed before them.

* See the Paper on the Nature and Construction of the Sun, Phil. Trans. 1795. p. 46. [Vol. I. p. 470.]

PENETRATING INTO SPACE BY TELESCOPES ^3

with regard to the different powers of throwing out Ught, of the points of a luminous surface. For, as hght must be finally emitted through the surface, it is but re- ferring all light arising from the emission of points behind the surface, to the surface itself, and the account of emitted light will be equally true. And this will also explain why it has been stated as probable, that different parts of the same luminous surface may throw out different quantities of light.

Since, therefore, the quantity of light thrown out by any luminous body is truly represented by CN, and that an object is bright in consequence of light thrown out, we may say that brightness is truly defined by CN. If, however, there should at any time be occasion for distinction, the brightness arising from the great value of C may be called the intrinsic brightness ; and that arising from the great vdue of N, the aggregate brightness ; but the absolute brightness, in all cases, will still be defined by CN.

Hitherto we have only considered luminous objects, and their condition with regard to throwing out light. We proceed now to find an expression for their appearance at any assigned distance ; and here it will be proper to leave out of the account, every part of CN which is not applied for the purpose of vision. L re- presenting the whole quantity of light thrown out by CN, we shall denote that part of it which is used in vision, either by the eye or by the telescope, /. This will render the conclusions that may be drawn hereafter more unexceptionable ; for, the quantity of Ught / being scattered over a small space in proportion to L, it may reasonably be looked upon as more uniform in its texture ; and no scruples about its inequality will take place. The equation of light, in this present sense, there- fore, is CN = /.

Now, since we know that the density of light decreases in the ratio of the squares of the distances of the luminous objects, the expression for its quantity at

the distance of the observer D, will be j^.

In natural vision, the quantity / undergoes a considerable change, by the opening and contracting of the pupil of the eye. If we call the aperture of the iris a, we find that in different persons it differs considerably. Its changes are not easily to be ascertained ; but we shall not be much out in stating its variations to be chiefly between i and 2 tenths of an inch. Perhaps this may be supposed under- rated ; for the powers of vision, in a room completely darkened, will exert them- selves in a very extraordinary manner. In some experiments on light, made at Bath, in the year 1780, I have often remarked, that after sta3dng some time in a room fitted up for these experiments, where on entering I could not perceive any one object, I was no longer at a loss, in half an hour's time, to find every thing I wanted. It is however probable that the opening of the iris is not the only cause of seeing better after remaining long in the dark ; but that the tranquiUity of the retina, which is not disturbed by foreign objects of vision, may render it fit to receive

VOL. II. 5

34 ON THE POWER OF

impressions such as otherwise would have been too faint to be perceived. This seems to be supported by telescopic vision ; for it has often happened to me, in a fine winter's evening, when, at midnight, and in the absence of the moon, I have taken sweeps of the heavens, of four, five, or six hours duration, that the sensibility of the eye, in consequence of the exclusion of light from surrounding objects, by means of a black hood which I wear upon these occasions, has been very great ; and it is evident, that the opening of the iris would have been of no service in these cases, on account of the diameter of the optic pencil, which, in the 20 feet telescope, at the time of sweeping, was no more than 12 inch. The effect of this increased sensibility was such, that if a star of the 3rd magnitude came towards the field of view, I found it necessary to withdraw the eye before its entrance, in order not to injure the delicacy of vision acquired by long continuance in the dark. The transit of large stars, unless where none of the 6th or 7th magnitude could be had, have generally been declined in my sweeps, even with the 20 feet telescope. And I re- member, that after a considerable sweep with the 40 feet instrument, the appear- ance of Sirius announced itself, at a great distance, like the dawn of the morning, and came on by degrees, increasing in brightness, till this brilliant star at last entered the field of view of the telescope, with all the splendour of the rising sun, and forced me to take the eye from that beautiful sight. Such striking effects are a sufficient proof of the great sensibihty of the eye, acquired by keeping it from the light.

On taking notice, in the beginning of sweeps, of the time that passed, I found that the eye, coming from the light, required near 20', before it could be sufficiently reposed to admit a view of very delicate objects in the telescope ; and that the observation of a transit of a star of the 2d or 3d magnitude, would disorder the eye again, so as to require nearly the same time for the re-estabUshment of its tranquillity.

The difficulty of ascertaining the greatest opening of the eye, arises from the impossibility of measuring it at the time of its extreme dilatation, which can only happen when every thing is completely dark ; but, if the variation of a is not easily to be ascertained, we have, on the other hand, no difficulty to determine the quantity of light admitted through a telescope, which must depend upon the diameter of the object-glass, or mirror ; for, its aperture A may at all times be had by measiurement.

It follows, therefore, that the expression -^s will always be accurate for the

quantity of light admitted by the eye ; and that ^.^ will be sufficiently so for the

telescope. For it must be remembered, that the aperture of the eye is also con- cerned in viewing with telescopes ; and that, consequently, whenever the pencil of light transmitted to the eye by optical instruments exceeds the aperture of the

PENETRATING INTO SPACE BY TELESCOPES 35

pupil, much light must be lost. In that case, the expression A'^ I will fail ; and

therefore, in general, if m be the magnifying power, — ought not to exceed a.

tn

As I have defined the brightness of an object to the eye of an observer at a distance, to be expressed by j^, it will be necessary to answer some objections that

may be made to this theory. Optical writers have proved, that an object is equally bright at all distances. It may, therefore, be maintained against me, that since a wall illuminated by the sun will appear equally bright, at whatsoever distance the observer be placed that views it, the sun also, at the distance of Saturn, or still farther from us, must be as bright as it is in its present situation. Nay, it may be urged, that in a telescope the different distance of stars can be of no account with regard to their brightness, and that we must consequently be able to see stars which are many thousands of times farther than Sirius from us ; in short, that a star must be infinitely distant not to be seen any longer.

Now, objections such as these, which seem to be the immediate consequence of what has been demonstrated by mathematicians, and which yet apparently contradict what I assert in this paper, deserve to be thoroughly answered.

It may be remembered, that I have distinguished brightness into three different sorts.* Two of these, which have been discriminated by intrinsic and absolute brightness, are, in common language, left without distinction. In order to shew that they are so, I might bring a variety of examples from common conversation ; but, taking this for granted, it may be shewn that all the objections I have brought against my theory have their foundation in this ambiguity.

The demonstrations of opticians, with regard to what I call intrinsic bright- ness, will not oppose what I affirm of absolute brightness ; and I shall have nothing farther to do than to shew that what mathematicians have said, must be under- stood to refer entirely to the intrinsic brightness, or illumination of the picture of objects on the retina of the eye : from which it will clearly follow, that their doctrine and mine are perfectly reconcileable ; and that they can be at variance only when the ambiguity of the word brightness is overlooked, and objections, such as I have made, are raised, where the word brightness is used as absolute, when we should have kept it to the only meaning it can bear in the mathematicians' theorem.

The first objection I have mentioned is, that the sun, to an observer on Saturn, must be as bright as it is here on earth. Now by this cannot be meant, that an inhabitant standing on the planet Saturn, and looking at the sun, should absolutely receive as much light from it as one on earth receives when he sees it ; for this would be contrary to the well known decrease of light at various distances. The objection, therefore can only go to assert, that the picture of the sun, on the retina

* See page [33].

36 ON THE POWER OF

of the Satumian observer, is as intensely illuminated as that on the retina of the terrestrial astronomer. To this I perfectly agree. But let those who would go farther, and say that therefore the sun is absolutely as bright to the one as to the other, remember that the sun on Saturn appears to be a hundred times less than on the earth ; and that consequently, though it may there be intrinsically as bright, it must here be absolutely* an hundred times brighter.

The next objection I have to consider, relates to the fixed stars. What has been shewn in the preceding paragraph, with regard to the sun, is so intirely appli- cable to the stars, that it will be very easy to place this point also in its proper light. As I have assented to the demonstration of opticians with regard to the brightness of the sun, when seen at the distance of Saturn, provided the meaning of this word be kept to the intrinsic illumination of the picture on the retina of an observer, I can have no hesitation to allow that the same will hold good with a star placed at any assignable distance. But I must repeat, that the light we can receive

a* I from stars is truly expressed by -j^ ; and that therefore their absolute brightness

must vary in the inverse ratio of the squares of their distances. Hence I am authorised to conclude, and observation abundantly confirms it, that stars cannot be seen by the naked eye, when they are more than seven or eight times farther from us than Sirius ; and that they become, comparatively speaking, very soon invisible with our best instruments. It will be shewn hereafter, that the visibiUty of stars depends on the penetrating power of telescopes, which, I must repeat, falls indeed very short of shewing stars that are many thousands of times farther from us than Sirius ; much less can we ever hope to see stars that are all but infinitely distant.

If now it be admitted that the expressions we have laid down are such as agree with well-known facts, we may proceed to vision at a distance ; and first with respect to the naked eye.

Here the power of penetrating into space is not only confined by nature, but is moreover occasionally Umited by the failure in brightness of luminous objects. Let us see whether astronomical observations, assisted by mathematical reasoning, can give us some idea of the general extent of natural vision. Among the reflecting luminous objects, our penetrating powers are sufficiently ascertained. From the moon we may step to Venus, to Mercury, to Mars, to Jupiter, to Saturn, and last of all to the Georgian planet. An object seen by reflected light at a greater dis- tance than this, it has never been allowed us to perceive ; and it is indeed much to be admired, that we should see borrowed illmnination to the amazing distance of more than i8 hundred millions of miles ; especially when that fight, in coming from the sun to the planet, has to pass through an equal space, before it can be reflected,

* See the definition of absolute brightness, page [33J.

PENETRATING INTO SPACE BY TELESCOPES 37

whereby it must be so enfeebled as to be above 368 times less intense on that planet than it is with us, and when probably not more than one-third part of that light can be thrown back from its disk.*

The range of natural vision with self-luminous objects, is incomparably more extended, but less accurately to be ascertained. From our brightest luminary, the sun, we pass immediately to very distant objects ; for, Sirius, Arcturus, and the rest of the stars of the first magnitude, are probably those that come next ; and what their distance may be, it is well known, can only be calculated imperfectly from the doctrine of parallaxes, which places the nearest of them at least 412530 times farther from us than the sun.

In order to take a second step forwards, we must enter into some preliminary considerations, which cannot but be attended with considerable uncertainty. The general supposition, that stars, at least those which seem to be promiscuously scattered, are probably one with another of a certain magnitude, being admitted, it has already been shewn in a former Paper, f that after a certain number of stars of the first magnitude have been arranged about the sun, a farther distant set will come in for the second place. The situation of these may be taken to be, one with another, at about double the distance of the former from us.

By directing our view to them, and thus penetrating one step farther into space, these stars of the second magnitude furnish us with an experiment that shews what phaenomena will take place, when we receive the illumination of two very remote objects, equally bright in themselves, whereof one is at double the distance of the other. The expression for the brightness of such objects, at all distances, and with any aperture of the iris, according to our foregoing notation, will be

-=^ ; and a method of reducing this to an experimental investigation will be as

follows.

Let us admit that a Cygni, ^ Tauri, and others, are stars of the second magnitude, such as are here to be considered. We know, that in looking at them and the former, the aperture of the iris will probably undergo no change ; since the differ- ence in brightness, between Sirius, Arcturus, a Cygni, and /3 Tauri, does not seem to affect the eye so as to require any alteration in the dimensions of the iris ; a, there- fore becomes a given quantity, and may be left out. Admitting also, that the latter of these stars are probably at double the distance of the former, we have D^ in one case four times that of the other ; and the two expressions for the brightness of the stars, will be / for those of the first magnitude, and J/ for those of the second.

The quantities being thus prepared, what I mean to suggest by an experiment is, that since sensations, by their nature, will not admit of being halved or quar-

* According to Mr. bouguer, the surface of the moon absorbs about two-thirds of the light it receives from the sun. See Traite d'Optique, p. 122.

t Phil. Trans, for the year 1796, p. 166, 167, 168. [Vol. I. p. 530.]

38 ON THE POWER OF

tered, we come thus to know by inspection what phaenomenon will be produced by the fourth part of the light of a star of the first magnitude. In this sense, I think we must take it for granted, that a certain idea of brightness, attached to the stars which are generally denominated to be of the second magnitude, may be added to our experimental knowledge ; for, by this means, we are informed what we are to

understand by the expressions %-^, ^.^. ,, ^ ., .♦ We cannot wonder at

© Sinus I jSTaunr

the immense difference between the brightness of the sun and that of Sirius ; since

the two first expressions, when properly resolved, give us a ratio of brightness of

more than 170 thousand miUions to one ; whereas the two latter, as has been shewn,

give only a ratio of four to one.

What has been said will carry us, with very little addition, to the end of our unassisted power of vision to penetrate into space. We can have no other guide to lead us a third step than the same beforementioned hypothesis ; in consequence of which, however, it must be acknowledged to be sufficiently probable, that the stars of the third magnitude may be placed about three times as far from us as those of the first. It has been seen, by my remarks on the comparative brightness of the stars, that I place no reUance on the classification of them into magnitudes ;t but, in the present instance, where the question is not to ascertain the precise brightness of any one star, it is quite sufficient to know that the number of the stars of the first three different magnitudes, or different brightnesses, answers, in a general way, sufficiently well to a supposed equally distant arrangement of a first, second, and third set of stars about the sun. Our third step forwards into space, may therefore very properly be said to fall on the pole-star, on y Cygni, € Bootis, and all those of the same order.

As the difference between these and the stars of the preceding order is much less striking than that between the stars of the first and second magnitude, we also

find that the expressions ^^ . , , and ^ , . „ , are not in the high ratio of 4 to

/8Taun|' Polaris |*

I, but only as 9 to 4, or 2J to i.

Without tracing the brightness of the stars through any farther steps, I shall

only remark, that the diminution of the ratios of brightness of the stars of the 4th,

5th, 6th, and 7th magnitude, seems to answer to their mathematical expressions,

as well as, from the first steps we have taken, can possibly be imagined. The

calculated ratio, for instance, of the brightness of a star of the 6th magnitude, to

that of one of the 7th, is but Uttle more than i^ to i ; but still we find by experience,

that the eye can very conveniently perceive it. At the same time, the

faintness of the stars of the 7th magnitude, which require the finest nights,

and the best common eyes to be perceived, gives us Uttle room to believe

* The names of the objects 0, Sirius, /3 Tauri, are here used to express their distance from us. t Phil. Trans, for the year 1796, p. 168, 169. [Vol. I. p. 531.]

PENETRATING INTO SPACE BY TELESCOPES m

that we can penetrate much farther into space, with objects of no greater brightness than stars.

But, since it may be justly observed, that in the foregoing estimation of the pro- portional distance of the stars, a considerable uncertainty must remain, we ought to make a proper allowance for it ; and, in order to see to what extent this should go, we must make use of the experimental sensations of the ratios of brightness we have now acquired, in going step by step forward : for, numerical ratios of brightness, and sensations of them, as has been noticed before, are very different things. And since, from the foregoing considerations, it may be concluded, that as far as the 6th, 7th, or 8th magnitude, there ought to be a visible general difference between stars of one order and that of the next following, I think, from the faintness of the stars of the 7th magnitude, we are authorized to conclude, that no star, eight, nine, or at most ten times as far from us as Sirius, can possibly be perceived by the natural eye.

The boundaries of vision, however, are not confined to single stars. Where the light of these falls short, the united lustre of sidereal systems will still be per- ceived. In clear nights, for instance, we may see a whitish patch in the sword- handle of Perseus,* which contains small stars of various sizes, as may be ascer- tained by a telescope of a moderate power of penetrating into space. We easily see the united lustre of them, though the light of no one of the single stars could have affected the unassisted eye.

Considerably beyond the distance of the former must be the cluster discovered by Mr. messier, in 1764 ; north following i Geminorum. It contains stars much smaller than those of the former cluster ; and a telescope should have a consider- able penetrating power, to ascertain their brightness properly, such as my common lo-feet reflector. The night should be clear, in order to see it well with the naked eye, and it will then appear in the shape of a small nebula, j

Still farther from us must be the nebula between ti and ^ Herculis, discovered by Dr. halley, in 1714. The stars of it are so small that it has been called a Nebula ; J and has been regarded as such, till my instruments of high penetrating powers were applied to it. It requires a very clear night, and the absence of the moon, to see it with the natural eye.

Perhaps, among the farthest objects that can make an impression on the eye, when not assisted by telescopes, may be reckoned the nebula in the girdle of Andro- meda, discovered by simon marius, in 1612. It is however not difficult to perceive it, in a clear night, on account of its great extent.

From the powers of penetrating into space by natural vision, we proceed now to that of telescopes.

♦ See the catalogue of a second thousand of new nebulae and clusters of stars, VI. 33, 34, Phil. Trans. Vol. LXXIX. page 251. [Vol. I. p. 361.— Ed.] t [M. 35, N.G.C. 2168.] J In the Connois. d. T. for 1783, No. 13, it is described as a nebula without stars. [N.G.C. 6205.]

4b ON THE POWER OF

It has been shewn, that brightness, or light, is to the naked eye truly repre- sented by -=^ ; in a telescope, therefore, the light admitted will be expressed by

-jy^ . Hence it would follow, that the artificial power of penetrating into space

should be to the natural one as ^ to a. But this proportion must be corrected by the practical deficiency in light reflected by mirrors, or transmitted through glasses ; and it will in a great measure depend on the circumstances of the workmanship, materials, and construction of the telescope, how much loss of light there will be sustained.

In order to come to some determination on this subject, I made many ex- periments with plain mirrors, polished like my large ones, and of the same composi- tion of metal. The method I pursued was that proposed by Mr. bouguer, in his Traits d'Optique, page i6, fig. 3 ; but I brought the mirror, during the trial, as close to the line connecting the two objects as possible, in order to render the reflected rays nearly perpendicular.

The result was, that out of 100 thousand incident rays, 67262 were returned ; and therefore, if a double reflection takes place, only 45242 will be returned.

Before this light can reach the eye, it will suffer some loss in passing through the eye glass ; and the amount of this I ascertained, by taking a highly polished plain glass, of nearly the usual thickness of optical glasses of small focal lengths. Then, by the method of the same author, page 21, fig. 5, I found, that out of 100 thousand incident rays, 94825 were transmitted through the glass. Hence, if two lenses be used, 89918 ; and, with three lenses, 85265 rays will be transmitted to the eye.

Then, by compounding, we shall have, in a telescope of my construction with one reflection, 63796 rays, out of 100 thousand, come to the eye. In the New- tonian form, with a single eye lens, 42901 ; and, with a double eye glass 40681 will remain for vision.

There must always remain a considerable uncertainty in the quantities here assigned ; as a newly polished mirror, or one in high preservation, will give more light than another that has not those advantages. The quahty of metal also will make some difference ; but, if it should appear by experiments, that the metals or glasses in use will yield more or less light than here assigned, it is to be understood that the corrections must be made accordingly.

We proceed now to find a proper expression for the power of penetrating into space, that we may be enabled to compare its effects, in different telescopes, with that of the natural eye.

Since then the brightness of luminous objects is inversely as the squares of the distances, it follows, that the penetrating power must be as the square roots of the light received by the eye.

PENETRATING INTO SPACE BY TELESCOPES 41

In natural vision, therefore, this power is truly expressed by Va*l ; and, since we have now also obtained a proper correction x, we must apply it to the incident light with telescopes.

In the NEWTONIAN and other constructions where two specula are used, there will also be some loss of light on account of the interposition of the small speculum ; therefore, putting h for its diameter, we have A^ -b^ for the real incident light. This being corrected as above, will give the general expression -Jxlx^^P ^^^ the same power in telescopes. But here we are to take notice, that in refractors, and in telescopes with one reflection, b will be=o, and therefore is to be left out.

Then, if we put natural light / = i, and divide by a, we have the general form

'^/x A^ —b"

'- for the penetrating power of all sorts of telescopes, compared to that of

the natural eye as a standard, according to any supposed aperture of the iris, and proportion of light returned by reflection, or transmitted by refraction.

In the following investigation we shall suppose a — 2 tenths of an inch, as being perhaps nearly the general opening of the iris, in star-light nights, when the eye has been some moderate time in the dark. The value of the corrections for loss of light will stand as has been given before.

We may now proceed to determine the powers of the instruments that have been used in my astronomical observations ; but, as this subject will be best explained by a report of the observations themselves, I shall select a series of them for that purpose, and relate them in the order which will be most illustrating.

First, with regard to the eye, it is certain that its power, like all our other faculties, is limited by nature, and is regulated by the permanent brightness of objects ; as has been shewn already, when its extent with reflected light was com- pared to its exertion on self-luminous objects. It is further limited on borrowed light, by the occasional state of illumination ; for, when that becomes defective at any time, the power of the eye will then be contracted into a narrower compass ; an instance of which is the following.

In the year 1776, when I had erected a telescope of 20 feet focal length, of the NEWTONIAN construction, one of its effects by trial was, that when towards evening, on account of darkness, the natural eye could not penetrate far into space, the telescope possessed that power sufficiently to shew, by the dial of a distant church steeple, what o'clock it was, notwithstanding the naked eye could no longer see the steeple itself. Here I only speak of the penetrating power ; for, though it might require magnifying power to see the figures on the dial, it could require none to see the steeple. Now the aperture of the telescope being 12 inches, and the con- struction of the NEWTONIAN form, its penetrating power, when calculated according

VOL. II. 6

42 ON THE POWER OF

to the given formula, will be 4?9 ^ ^^o — ES^^^Sgg. ^4, 6, and a, being all

2

expressed in tenths of an inch.*

From the result of this computation it appears, that the circumstance of seeing so well, in the dusk of the evening, may be easily accounted for, by a power of this telescope to penetrate 39 times farther into space than the natural eye could reach, with objects so faintly illuminated.

This observation completely refutes an objection to telescopic vision, that may be drawn from what has also been demonstrated by optical writers ; namely, that no telescope can shew an object brighter than it is to the naked eye. For, in order to reconcile this optical theory with experience, I have only to say, that the objection is intirely founded on the same ambiguity of the word brightness that has before been detected. It is perfectly true, that the intrinsic illumination of the picture on the retina, which is made by a telescope, cannot exceed that of natural vision ; but the absolute brightness of the magnified picture by which telescopic vision is performed, must exceed that of the picture in natural vision, in the same ratio in which the area of the magnified picture exceeds that of the natural one ; supposing the intrinsic brightness of both pictures to be the same. In our present instance, the steeple and clock-dial were rendered visible by the increased absolute brightness of the object, which in natural vision was 15 hundred times inferior to what it was in the telescope. And this establishes beyond a doubt, that telescopic vision is performed by the absolute brightness of objects ; for, in the present case, I find by computation, that the intrinsic brightness, so far from being equal in the telescope to that of natural vision, was inferior to it in the ratio of three to seven.

The distinction between magnifying power, and a power of penetrating into space, could not but be felt long ago, though its theory has not been inquired into. This undoubtedly gave rise to the invention of those very useful short telescopes called night-glasses. When the darkness of the evening curtails the natural pene- trating power, they come in very seasonably, to the relief of mariners that are on the look out for objects which it is their interest to discover. Night-glasses, such as they are now generally made, will have a power of penetrating six or seven times farther into space than the natural eye. For, by the construction of the double eye-glass, these telescopes will magnify 7 or 8 times ; and the object glass being 2^ inches in diameter, the breadth of the optic pencil will be 3^ or 3f tenths of an inch. As this cannot enter the eye, on a supposition of an opening of the iris of 2 tenths, we are obliged to increase the value of a, in order to make the telescope have its proper effect. Now, whether nature will admit of such an enlargement becomes an object of experiment ; but, at all events, a cannot be assumed less than

♦ I have given the figures, in all the following equations of the calculated penetrating powers, in order to show the constructions of my instruments to those who may wish to be acquainted with them.

PENETRATING INTO SPACE BY TELESCOPES 43

— . Then, if x be taken as has been determined for three refractions, we shall have tn

JS53 X 25' , , ^'-^^ ^ =646 or 739.

Soon after the discovery of the Georgian planet, a very celebrated observer of the heavens, who has added considerably to our number of telescopic comets and nebulae, expressed his wish, in a letter to me, to know by what method I had been led to suspect this object not to be a star, like others of the same appearance. I have no doubt but that the instrument through which this astronomer generally looked out for comets, had a penetrating power much more than sufficient to shew the new planet, since even the natural eye will reach it. But here we have an instance of the great difference in the effect of the two sorts of powers of telescopes ; for, on account of the smallness of the planet, a different sort of power, namely, that of magnifying, was required ; and, about the time of its discovery, I had been remarkably attentive to an improvement of this power, as I happened to be then much in want of it for my very close double stars.*

On examining the nebulae which had been discovered by many celebrated authors, and comparing my observations with the account of them in the Connois- sance des Temps for 1783, I found that most of those which I could not resolve into stars with instruments of a small penetrating power, were easily resolved with telescopes of a higher power of this sort ; and, that the effect was not owing to the magnifying power I used upon these occasions, will fully appear from the observations ; for, when the closeness of the stars was such as to require a considerable degree of magnifying as well as penetrating power, it always appeared plainly, that the instrument which had the highest penetrating power resolved them best, provided it had as much of the other power as was required for the purpose.

Sept. 20, 1783, I viewed the nebula between flamsteed's 99th q.nd 105th Piscium, discovered by Mr. mechain, in 1780. f

" It is not visible in the finder of my 7-feet telescope ; but that of my 20-feet shews it."

Oct. 28, 1784, I viewed the same object with the 7-feet telescope.

" It is extremely faint. With a magnifying power of 120, it seems to be a collection of very small stars : I see many of them."

At the time of these observations, my 7-feet telescope had only a common finder, with an aperture of the object glass of about f of an inch in diameter, and a

single eye-lens; therefore its penetrating power was §9 — 7AL=3-56. The

* Magnifying powers of 460, 625, 932, 1159, 1504, 2010, 2398, 3168, 4294, 5489, 6450, 6652, were used upon e Bootis, y Leonis, a Lyrae, 6-c. See Cat. of double stars, Phil. Trans. Vol. LXXII. page 115, and 147 ; and Vol. LXXV. page 48. [Vol. I. pp. 60, 80, and 172. — Ed.]

t [M. 74 =N.G.C. 628.— Ed.]

44

ON THE POWER OF

finder of the 20-feet instrument, being achromatic, had an object glass 117 inch in diameter; its penetrating power, therefore, was ^ ^ =4'50-

2

Now, that one of them shewed the nebula and not the other, can only be ascribed to space-penetrating power, as both instruments were equal in magnifying power, and that so low as not to require an achromatic object glass to render the image sufficiently distinct.

The 7-feet reflector evidently reached the stars of the nebula ; but its penetrat- ing and magnifying powers are very considerable, as will be shewn presently.

July 30, 1783, I viewed the nebula south preceding flamsteed's 24 Aquarii, discovered by Mr. maraldi, in 1746.*

" In the smzdl sweeper, f this nebula appears like a telescopic comet."

Oct. 27, 1794. The same nebula with a 7-feet reflector.

" I can see that it is a cluster of stars, many of them being visible."

If we compare the penetrating power of the two instruments, we find that we

have in the first ^'41 x 42^-12' ^ ^^^.g^ . ^^^ -^ ^^^ ^^^^^^ v-43 x 63^-12' ^^^.^^

2 2

However, the magnifying power was partly concerned in this instance ; for, in the sweeper it was not sufficient to separate the stars properly.

March 4, 1783. With a 7-feet reflector, I viewed the nebula near the 5th Serpentis, discovered by Mr. messier, in 1764. J

" It has several stars in it ; they are however so small that I can but just per- ceive some, and suspect others."

May 31, 1783. The same nebula with a lo-feet reflector ; penetrating power

i J'4Z X 89* - 16* = 2867.

" With a magnifying power of 250, it is all resolved into stars : they are very close, and the appearance is beautiful. With 600, perfectly resolved. There is a considerable star not far from the middle ; another not far from one side, but out of the cluster ; another pretty bright one ; and a great number of small ones."

Here we have a case where the penetrating power of 20 fell short, when 29 resolved the nebula completely. This object requires also great magnifying power to shew the stars of it well ; but that power had before been tried, in the 7-feet,

• [M. 2 =N.G.C. 7089.]

t The small sweeper is a Newtonian reflector, of 2 feet focal length ; and, with an aperture of 4-2 inches, has only a magnifjong power of 24, and a field of view 2° 12'. Its distinctness is so perfect, that it will shew letters at a moderate distance, with a magnifying power of 2000 ; and its movements are so convenient, that the eye remains at rest while the instrument makes a sweep from the horizon to the zenith. A large one of the same construction has an aperture of 92 inches, with a focal length of 5 feet 3 inches. It is also charged low enough for the eye to take in the whole optic pencil ; and its

penetrating power, with a double eye glass, is '4^ >^9^ -21 =28-57.

2 } [M. 5 =N.G.C. 5904. Compare below, p. 46. — Ed.]

PENETRATING INTO SPACE BY TELESCOPES 45

cis far as 460, without success, and could only give an indication of its being com- posed of stars ; whereas the lower magnifying power of 250, with a greater pene- trating power, in the lo-feet instrument, resolved the whole nebula into stars.

May 3, 1783. I viewed the nebula between 1 and p Ophiuchi, discovered by Mr. MESSIER, in 1764.*

" With a lo-feet reflector, and a magnifying power of 250, I see several stars in it, and make no doubt a higher power, and more light, will resolve it all into stars. This seems to be a good nebula for the purpose of establishing the con- nection between nebulae and clusters of stars in general."

June 18, 1784. The same nebula viewed with a large Newtonian 20-feet

reflector; penetrating power — ^ =6i"i8; and a magnifying power

of 157. " A very large and very bright cluster of excessively compressed stars. The stars are but just visible, and are of unequal magnitudes : the large stars are red ; and the cluster is a miniature of that near flamsteed's 42d Comae Berenices. R.A. 17" 6' 32" ; P.D. 108° 18'."

Here, a penetrating power of 29, with a magnifying power of 250, would barely shew a few stars ; when, in the other instrument, a power 61 of the first sort, and only 157 of the latter, shewed them completely well.

July 4, 1783. I viewed the nebxila between flamsteed's 25 and 26 Sagittarii, discovered by Abraham ihle, in 1665. f

" With a small 20-feet Newtonian telescope, power 200, it is all resolved into stars, that are very small and close. There must be some hundreds of them. With 350, I see the stars very plainly ; but the nebula is too low in this latitude for such a power."

July 12, 1784. I viewed the same nebula with a large 20-feet Newtonian reflector ; power 157. " A most beautiful extensive cluster of stars, of various magnitudes, very compressed in the middle, and about 8' in diameter, besides the scattered ones, which do more than fill the extent of the field of view : % the large stars are red ; the small ones are pale red. R.A. 18'^ 23' 39" ; P.D. 114° 7'."

The penetrating power of the first instrument was 39, that of the latter 61 ; but, from the observations, it is plain how much superior the effect of the latter was to that of the former, notwithstanding the magnifying power was so much in favour of the instrument with the small penetrating power.

July 30, 1783. With a small 20-feet Newtonian reflector, I viewed the nebula in the hand of Serpentarius, discovered by Mr. messier, in 1764. §

" With a power of 200, I see it consists of stars. They are better visible with

* [M. 9=N.G.C. 6333.— Ed.]

t [M. 22 =N.G.C. 6656.— Ed.]

i This field, by the passage of an equatorial star, was 15' 3'.

§ [M. 14 -N.G.C. 6402.— Ed.]

46 ON THE POWER OF

300. With 600, they are too obscure to be distinguished, though the appearance of stars is still preserved. This seems to be one of the most difficult objects to be resolved. With me, there is not a doubt remaining ; but another person, in order to form a judgment, ought previously to go through all the several gradations of nebulae which I have resolved into stars."

May 25, 1791. I viewed the same nebula with a 20- feet reflector of my con- struction, having a penetrating power of i- L=75o8.

" With a magnifying power of 157, it appears extremely bright, round, and easily resolvable. With 300, I can see the stars. It resembles the cluster of stars taken at !&" 43' 40",* which probably would put on the same appearance as this, if it were at a distance half as far again as it is. R.A. 17" 26' 19" ; P.D. 93° 10'."

Here we may compare two observations ; one taken with the penetrating power of 39, the other with 75 ; and, although the former instrument had far the advantage in magnifying power, the latter certainly gave a more complete view of the object.

The 20-feet reflector having been changed from the Newtonian form to my present one, I had a very striking instance of the great advantage of the increased penetrating power, in the discovery of the Georgian satellites. The improvement, by laying aside the small mirror, was from 61 to 75 ; and, whereas the former was not sufficient to reach these faint objects, the latter shewed them perfectly well.

March 14, 1798. I viewed the Georgian planet with a new 25-feet reflector.

Its penetrating power is ^ j^' =95-85 ; and, having just before also viewed

it with my 20-feet instrument, I found, that with an equal magnifying power of 300, the 25-feet telescope had considerably the advantage of the former.

Feb. 24, 1786. I viewed the nebula near flamsteed's 5th Serpentis, which has been mentioned before, with my 20-feet reflector ; magnifying power 157.

" The most beautiful extremely compressed cluster of small stars ; the greatest part of them gathered together into one brilliant nucleus, evidently consisting of stars, surrounded with many detached gathering stars of the same size and colour. R.A. 15" 7' 12" ; P.D. 87° 8'."

May 27, 1791. I viewed the same object with my 40-feet telescope ; penetrating

*/-64 X 480 p r -r .

power -JJ- Jy- — 1=151-69; magnifymg power 370.

" A beautiful cluster of stars. I counted about 200 of them. The middle of it is so compressed that it is impossible to distinguish the stars."

Here it appears, that the superior penetrating power of the 40-feet telescope

* The object referred to is No. 10 of the Connoissance des Temps for 1783, called " Ndbuleuse sans itoiles." My description of it is, " A very beautiful, and extremely compressed, cluster of stars ; the most compressed part about 3 or 4' in diameter. R.A. ib"* 46' 2° ; P.D. 93° 46'." [N.G.C. 6254.— Ed.]

PENETRATING INTO SPACE BY TELESCOPES 47

enabled me even to count the stars of this nebula. It is also to be noticed, that the object did not strike me as uncommonly beautiful ; because, with much more than double the penetrating, and also more than double the magnifjdng power, the stars could not appear so compressed and small as in the 20-feet instrument : this, very naturally, must give it more the resemblance of a coarser cluster of stars, such as I had been in the habit of seeing frequently.

The 40-feet telescope was originally intended to have been of the Newtonian construction ; but, in the year 1787, when I was experimentally assured of the vast importance of a power to penetrate into space, I laid aside the work of the small mirror, which was then in hand, and completed the instrument in its present form.

" Oct. 10, 1791. I saw the 4th satellite and the ring of Saturn, in the 40-feet speculum, without an eye glass."

The magnifying power on that occasion could not exceed 60 or 70 ; but the great penetrating power made full amends for the lowness of the former ; notwith- standing the greatest part of it must have been lost for want of a greater opening of the iris, which could not take in the whole pencil of rays, for this could not be less than 7 or 8 tenths of an inch.

Among other instances of the superior effects of penetration into space, I should mention the discovery of an additional 6th satellite of Saturn, on the 28th of August 1789 ; and of a 7th, on the nth of September, in the same year ; which were first pointed out by this instrument. It is true that both satellites are within the reach of the 20-feet telescope ; but it should be remembered, that when an object is once discovered by a superior power, an inferior one will suflfice to see it afterwards. I need not add, that neither the 7 nor lo-feet telescopes will reach them ; their powers, 20 and 29, are not sufficient to penetrate to such distant objects, when the brightness of them is not more than that of these sateUites. It is also evident, that the failure in these latter instruments arises not from want of magnilying power, as either of them has much more than sufficient for the purpose.

Nov. 5, 1791. I viewed Saturn with the 20 and 40-feet telescopes.

" 20-feet. The 5th sateUite of Saturn is very small. The ist, 2d, 3d, 4th, 5th, and the new 6th satellite, are in their calculated places."

" 40-feet. I see the new 6th satellite much better with this instrument than with the 20-feet. The 5th is also much larger here than in the 20-feet ; in which it was nearly the same size as a small fixed star, but here it is considerably larger than that star."

Here the superior penetrating power of the 40-feet telescope shewed itself on the 6th satellite of Saturn, which is a very faint object ; as it had also a consider- able advantage in magnifying power, the disk of the 5th sateUite appeared larger than in the 20-feet. But the small star, which may be said to be beyond the reach of magnifying power, could only profit by the superiority of the other power.

Nov. 21, 1791. 40-feet reflector; power 370.

48 ON THE POWER OF

" The black division upon the ring is as dark as the heavens about Saturn, and of the same colour."

" The shadow of the body of Saturn is visible upon the ring, on the following side ; its colour is very different from that of the dark division. The 5th satellite is less than the 3d ; it is even less than the 2d."

2o-feet reflector ; power 300.

'' The 3d satellite seems to be smaller than it was the last night but one. The 4th satellite seems to be larger than it was the 19th. This telescope shews the satellites not nearly so well as the 40-feet."

Here, the magnifying power being nearly alike, the superiority of the 40-feet telescope must be ascribed to its penetrating power.

The different nature of the two powers above mentioned being thus evidently established, I must now remark, that, in some respects, they even interfere with each other ; a few instances of which I shall give.

August 24, 1783. I viewed the nebula north preceding flamsteed's i Trianguli, discovered by Mr. messier, in 1764.*

" 7-feet reflector ; power 57. There is a suspicion that the nebula consists of exceedingly small stars. With this low power it has a nebulous appearance ; and it vanishes when I put on the higher magnifying powers of 278 and 460."

Oct. 28, 1794. I viewed the same nebula with a 7-feet reflector.

" It is large, but very faint. With 120, it seems to be composed of stars, and I think I see several of them ; but it will bear no magnifying power."

In this experiment, magnifying power was evidently injurious to penetrating power. I do not account for this upon the principle that by magnifying we make an object less bright ; for, when opticians have also demonstrated that brightness is diminished by magnifying, it must again be understood as relating only to the intrinsic brightness of the magnified picture ; its absolute brightness, which is the only one that concerns us at present, must always remain the same.f The real explanation of the fact, I take to be, that while the light collected is employed in magnifying the object, it cannot be exerted in giving penetrating power.

• [M. 33 =N.G.C. 598-— Ed.]

f This may be proved thus. The mean intrinsic brightness, or rather illumination, of a point of the picture on the retina, will be all the light that falls on the picture, divided by the number of its

I points ; or C =-^. Now, since with a greater magnifying power m, the number of points N increases

/ as the squares of the power, the expression for the intrinsic brightness -^, will decrease in the same

/ I

ratio ; and it will consequently be in general N a m*, and -jrr- or C oc — - ; that is, by compounding

Li tn'

CN <x — - =/ =1 ; or absolute brightness a given quantity. M. bouguer has carefully distinguished tn

intrinsic and absolute brightness, when he speaks of the quantity of light reflected from a wall, at

different distances. Traiti d'Optique, page 39 and 40.

PENETRATING INTO SPACE BY TELESCOPES 49

June 18, 1799. I viewed the planet Venus with a lo-feet reflector.

" Its light is so vivid that it does not require, nor will it bear, a penetrating power of 29, neither with a low nor with a high magnifying power."

This is not owing to the least imperfection in the mirror, which is truly para- bolical, and shews, with all its aperture open, and a magnifying power of 600, the double star 7 Leonis in the greatest perfection.

" It shewed Venus, perfectly well defined, with a penetrating power as low as 14, and a magnifying power of 400, or 600 "

Here, penetrating power was injurious to magnifying power ; and that it necessarily must be so, when carried to a high pitch, is evident ; for, by enlarging the aperture of the telescope, we increase the evil that attends magnifying, which is, that we cannot magnify the object without magnifying the medium. Now, since the air is very seldom of so homogeneous a disposition as to admit to be magni- fied highly, it follows that we must meet with impurities and obstructions, in pro- portion to its quantity. But the contents of the columns of air through which we look at the heavens by telescopes, being of equal lengths, must be as their bases, that is, as the squares of the apertures of the telescopes ; and this is in a much higher ratio than that of the increase of the power of penetrating into space. From my long experience in these matters, I am led to apprehend, that the highest power of magnifying may possibly not exceed the reach of a 20 or 25-feet telescope ; or may even lie in a less compass than either. However, in beautiful nights, when the outside of our telescopes is dropping with moisture discharged from the atmo- sphere, there are now and then favourable hours, in which it is hardly possible to put a limit to magnifying power. But such valuable opportunities are extremely scarce ; and, with large instruments, it will always be lost labour to observe at other times.

As I have hinted at the natural limits of magnifying power, I shall venture also to extend my surmises to those of penetrating power. There seems to be room for a considerable increase in this branch of the telescope ; and, as the penetrating power of my 40-feet reflector already goes to 191-69, there can hardly be any doubt but that it might be carried to 500, and probably not much farther. The natural limit seems to be an equation between the faintest star that can be made visible, by any means, and the united brilliancy of star-Ught. For, as the light of the heavens, in clear nights, is already very considerable in my large telescope, it must in the end be so increased, by enlarging the penetrating power, as to become a balance to the light of all objects that are so remote as not to exceed in brightness the general light of the heavens Now, if P be put for penetrating power, we

= A=io feet 5-2 inches for the aperture of a reflector, on my con- struction, that would have such a power of 500.

But, to return to our subject ; from what has been said before, we may con- voi. II. 7

50 ON THE POWER OF

elude, that objects are viewed in their greatest perfection, when, in penetrating space, the magnifying power is so low as only to be sufficient to shew the object well ; and when, in magnifying objects, by way of examining them minutely, the space-penetrating power is no higher than what will suffice for the purpose ; for, in the use of either power, the injudicious overcharge of the other will prove hurt- ful to perfect vision.

It is remarkable that, from very different principles, I have formerly deter- mined the length of the visual ray of my 20-feet telescope upon the stars of the milky way, so as to agree nearly with the calculations that have been given.* The extent of what I then figuratively cadled my sounding line, and what now appears to answer to the power of penetrating into space, was shewn to be not less than 415, 461, and 497 times the distance of Sirius from the sun. We now have calculated that my telescope, in the Newtonian form, at the time when the paper on the Construction of the Heavens was written, possessed a power of penetration, which exceeded that of natural vision 61 18 times ; and, as we have also shewn, that stars at 8, 9, or at most 10 times the distance of Sirius, must become invisible to the eye, we may safely conclude, that no single star, above 489-551, or at most 612 times as far as Sirius, can any longer be seen in this telescope. Now, the greatest length of the former visual ray, 497, agrees nearly with the lowest of these present numbers, 489 ; and the higher ones are all in favour of the former com- putation ; for that ray, though taken from what was perhaps not far from its greatest extent, might possibly have reached to some distance beyond the apparent bounds of the milky way ; but, if there had been any considerable difference in these determinations, we should remember that some of the data by which I have now calculated are only assumed. For instance, if the opening of the iris, when we look at a star of the 7th magnitude, should be only one-tenth of an inch and a half, instead of two, then a, in our formula, will be = i-5 ; which, when resolved, will give a penetrating power of 8158 ; and therefore, on this supposition, our telescope would easily have shewn stars 571 times as far from us as Sirius ; and only those at 653, 734, or 816 times the same distance, would have been beyond its reach. My reason for fixing upon two-tenths, rather than a lower quantity, was, that I might not run a risk of over-rating the powers of my instruments. I have it however in contemplation, to determine this quantity experimentally, and perceive already, that the difficulties which attend this subject may be overcome.

It now only remains to shew, how far the penetrating power, 192, of my large reflector, will really reach into space. Then, since this number has been calculated to be in proportion to the standard of natural vision, it follows, that if we admit a star of the 7th magnitude to be visible to the unassisted eye, this telescope will shew stars of the one thousand three hundred and forty-second magnitude. * Phil. Trans. Vol. LXXV. p. 247, 248. [Vol. I. pp. 247 248.]

PENETRATING INTO SPACE BY TELESCOPES 51

But, as we did not stop at the single stars above mentioned, when the pene- tration of the natural eye was to be ascertained, so we must now also call the united lustre of sidereal systems to our aid in stretching forwards into space. Suppose therefore, a cluster of 50,000 stars to be at one of those immense distances to which only a 40-feet reflector can reach, and our formula will give us the means of cal- culating what that may be. For, putting S for the number of stars in the cluster,

and D for its distance, we have ^ =D ;* which, on computation, comes

out to be above iif millions of millions of millions of miles ! A number which exceeds the distance of the nearest fixed star, at least three hundred thousand times.

From the above considerations it follows, that the range for observing, with a telescope such as my 40-feet reflector, is indeed very extensive. We have the inside of a sphere to examine, the radius of which is the immense distance just now assigned to be within the reach of the penetration of our instruments, and of which all the celestial objects visible to the eye, put together, form as it were but the kernel, while all the immensity of its thick shell is reserved for the telescope.

It follows, in the next place, that much time must be required for going through so extensive a range. The method of examining the heavens, by sweeping over space, instead of looking merely at places that are known to contain objects, is the only one that can be useful for discoveries.

In order therefore to calculate how long a time it must take to sweep the heavens, as far as they are within the reach of my 40-feet telescope, charged with a magnifying power of 1000, I have had recourse to my journals, to find how many favourable hours we may annually hope for in this climate. It is to be noticed, that the nights must be very clear ; the moon absent ; no twilight ; no haziness ; no violent wind ; and no sudden change of temperature ; then also, short intervals for filling up broken sweeps will occasion delays ; and, under all these circum- stances, it appears that a year which will afford 90, or at most 100 hours, is to be called very productive.

In the equator, with my 20-feet telescope, I have swept over zones of two degrees, with a power of 157 ; but, an allowance of 10 minutes in polar distance must be made, for lapping the sweeps over one another where they join.

As the breadth of the zones may be increased towards the poles, the northern hemisphere may be swept in about 40 zones : to these we must add 19 southern zones ; then, 59 zones, which, on account of the sweeps lapping over one another about 5' of time in right ascension, we must reckon of 25 hours each, will give 1475 hours. And, allowing 100 hours per year, we find that, with the 20-feet telescope, the heavens may be swept in about 14 years and f .

* £» =11765475948678678679 miles.

52 ON THE POWER OF PENETRATING INTO SPACE BY TELESCOPES

Now, the time of sweeping with different magnifying powers will be as the squares of the powers ; and, putting p and / for the power and time in the 20-feet

telescope, and P = 1000 for the power in the 40, we shall have p^ :t: : F" : -r^ =

P

59840. Then, making the same allowance of 100 hours per year, it appears that it will require not less than 598 years, to look with the 40-feet reflector, charged with the abovementioned power, only one single moment into each part of space ; and, even then, so much of the southern hemisphere will remain unexplored, as will take up 213 years more to examine.

Slough, near Windsor, Jxine 20, 1799.

[ 53 ]

XLIII.

Investigation of the Powers of the prismatic Colours to heat and illuminate Objects ; with Remarks, that prove the different Refrangibility of radiant Heat. To which is added, an Inquiry into the Method of viewing the Sun advantageously, with Telescopes of large Apertures and high magnifying Powers.

[Phil. Trans., 1800, pp. 255-283.]

Read March 27, 1800.

It is sometimes of great use in natural philosophy, to doubt of things that are commonly taken for granted ; especially as the means of resolving any doubt, when once it is entertained, are often within our reach. We may therefore say, that any experiment which leads us to investigate the truth of what was before admitted upon trust, may become of great utility to natural knowledge. Thus, for instance, when we see the effect of the condensation of the sun's rays in the focus of a burning lens, it seems to be natural to suppose, that every one of the united rays contri- butes its proportional share to the intensity of the heat which is produced ; and we should probably think it highly absurd, if it were asserted that many of them had but Uttle concern in the combustion, or vitrification, which follows, when an object is put into that focus. It will therefore not be amiss to mention what gave rise to a surmise, that the power of heating and illuminating objects might not be equally distributed among the variously coloured rays.

In a variety of experiments I have occasionally made, relating to the method of viewing the sun, with large telescopes, to the best advantage, I used various combinations of differently -coloured darkening glasses. What appeared remark- able was, that when I used some of them, I felt a sensation of heat, though I had but httle light ; while others gave me much light, with scarce any sensation of heat. Now, as in these different combinations the sun's image was also differently coloured, it occurred to me, that the prismatic rays might have the power of heating bodies very unequally distributed among them ; and, as I judged it right in this respect to entertain a doubt, it appeared equally proper to admit the same with regard to light. If certain colours should be more apt to occasion heat, others might, on the contrary, be more fit for vision, by possessing a superior illuminating power. At all events, it would be proper to recvu: to experiments for a decision.

54

INVESTIGATION OF THE POWERS OF

Experiments on the heating Power of coloured Rays.

I fixed a piece of pasteboard, AB [fig. i], in a frame, mounted upon a stand, CD, and moveable upon two centres. In the pasteboard, I cut an opening, tnn, a little larger than the ball of a thermometer, and of a sufficient length to let the whole extent of one of the prismatic colours pass through. I then placed three thermometers upon small inclined planes, EF : their balls were blacked with

Fig. I.

japan ink. That of No. i was rather too large for great sensibility. No. 2 and 3 were two excellent thermometers, which my highly esteemed friend Dr. wilson, late Professor of Astronomy at Glasgow, had lent me for the purpose : their balls being very small, made them of exquisite sensibility. The scales of all were properly disengaged from the balls.

I now placed the stand, with the framed pasteboard and the thermometers, upon a small plain board, GH ; that I might be at liberty to move the whole apparatus together, without deranging the relative situation of the different parts.

This being done, I set a prism, moveable on its axis, into the upper part of an open window, at right angles to the solar ray, and turned it about till its refracted

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 55

coloured spectrum became stationary, upon a table placed at a proper distance from the window.

The board containing the apparatus was now put on the table, and set in such a manner as to let the rays of one colour pass through the opening in the paste- board. The moveable frame was then adjusted to be perpendicular to the rays coming from the prism ; and the incUned planes carrying the three thermometers, with their balls arranged in a line, were set so near the opening, that any one of them might easily be advanced far enough to receive the irradiation of the colour which passed through the opening, while the rest remained close by, under the shade of the pasteboard.

By repeated trials, I found that Dr. Wilson's No. 2 and mine always agreed in shewing the temperature of the place where I examined them, when the change was not very sudden ; but that mine would require ten minutes to take a change, which the other would shew in five. No. 3 never differed much from No. 2.

1st Experiment. Having arranged the three thermometers in the place pre- pared for the experiment, I waited till they were stationary. Then, advancing No. I to the red rays, and leaving the other two close by, in the shade, I marked down what they shewed, at different times.

No. I .

. 43i

48

49i

49i

50

No. 2 .

■ 43i

43i

43i

43i

43i

N0.3 . .

■ 43J

43i

43i

43*

43J

This, in about 8 or 10 minutes, gave 6f degrees, for the rising produced in my thermometer, by the red rays, compared to the two standard thermometers.

2d Experiment. As soon as my thermometer was restored to the temperature of the room, which I hastened, by applying it to a large piece of metal that had been kept in the same place, I exposed it again to the red rays, and registered its march, along with No. 2 as a standard, which was as follows.

No. 1 .

.

. 45

48

51

51

51

No. 2 .

•

• 45

45

45

44i

44

Hence, in 10 minutes, the red rays made the thermometer rise 7 degrees.

^d Experiment. Proceeding in the same manner as before, in the green rays I had.

No. I . . ,43 45J 46 46 46

No. 2 . . .43 43 43 42J 42i

Therefore, in ten minutes, the green rays occasioned a rise of 3J degrees. 4/A Experiment. I now exposed my thermometer to the violet rays, and compared it with No. 2.

No. I ... 44 44 44| 45

No. 2 ... 44 44 43J 43

Here we have a rising of 2 degrees, in ten minutes, for the violet rays.

56 INVESTIGATION OF THE POWERS OF

5<A Experiment. I now exposed Dr. Wilson's thermometer No. 2 to the red rays, and compared its progress with No. 3.

No. 2 .

• 44

46

46i

46I

No. 3 .

• 44

44

431

43f

Here the thermometer, exposed to red, rose in five minutes 2f degrees. 6th Experiment. In red rays again.

No. 2 .

• 44

46

46*

47

47

No. 3 .

• 44

44

43i

43t

43

And here the thermometer, exposed to red, rose in five minutes 4 degrees, yth Experiment. In green rays.

No. 2 . . . 43J 44i 44i

No. 3 . . . 43i 43J 43

This made the thermometer rise, in the green rays, i\ degree. %th Experiment. Again in green rays.

No. 2 . . .43 44J 44|

No. 3 . . .43 42I 42!

Here the rising, by the green rays, was 2 degrees.

From these experiments, we are authorised to draw the following results. In the red rays, my thermometer gave 6f degrees in the ist, and 7 degrees in the 2d, for the rising of the quicksilver : a mean of both is 6|. In the 3d experiment, we had 3^^ degrees, for the rising occasioned by the green rays ; from which we obtain the proportion of 55 to 26, for the power of heating in red to that in green. The 4th experiment gave 2 degrees for the violet rays ; and therefore we have the rising of the quicksilver in red to that in violet, as 55 to 16.

A sufficient proof of the accuracy of this determination we have, in the result of the four last experiments. The rising for red rays in the 5th, is 2f ; and in the 6th, 4 degrees : a mean of both is 3|. In the 7th experiment, we have i\, and in the 8th, 2 degrees, for the rising in green : a mean of these is if. Therefore, we have the proportion of the rising in red to that in green, as 27 to 11, or as 55 to 224.

We may take a mean of the result of both thermometers, which will be 55 to 24-2, or more than 2J to i, in red to green ; and about 3I to i, in red to violet.

It appears remarkable, that the most sensible thermometer should give the least alteration, from the exposure to the coloured rays. But since, in these cir- cumstances, there are two causes constantly acting different ways ; the one to raise the thermometer, the other to bring it down to the temperature of the room, I suppose, that on account of the smallness of the ball in Dr. Wilson's No. 2, which is but little more than \ of an inch, the cooling causes must have a stronger effect on the mercury it contains than they can have on mine, the ball of which is half an inch.

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 57

More accuracy may hereafter be obtained, by attending to the circumstances of blacking the balls of the thermometers, and their exposure to a more steady and powerful light of the sun, at greater altitudes than it can be had at present ; but the experiments which have been related are quite sufficient for my present purpose ; which only goes to prove, that the heating power of the prismatic colours is very far from being equally divided, and that the red rays are chiefly eminent in that respect.

Experiments on the illuminating Power of coloured Rays.

In the following examination of the illuminating power of differently-coloured rays, I had two ends in view. The first was, with regard to the illumination itself ; and the next, with respect to the aptness of the rays for giving distinct vision ; and, though there did not seem to be any particular reason why these two should not go together, I judged it right to attend to both.

The microscope offered itself as the most convenient instrument for this in- vestigation ; and I thought it expedient to view only opaque objects, as these would give me an opportunity to use a direct prismatic ray, without running the risk of any bias that might be given to it, in its transmission through the colouring particles of transparent objects.

1st Experiment. I placed an object that had very minute parts, under a double microscope ; and, having set a prism in the window, so as to make the coloured image of the sun stationary upon the table where the microscope was placed, I caused the differently-coloured rays to fall successively on the object, by advancing the microscope into their light. The magnifying power was 27 times.

In changing the illumination, by admitting a different colour, it always be- comes necessary to re-adjust the instrument. It is well known, that the different refrangibility of the rays will sensibly affect the focal length of object-glasses; but, in compound vision, such as in a microscope, where a very small lens is made to cast a lengthened secondary focus, this difference becomes still more considerable.

By an attentive and repeated inspection, I found that my object was very well seen in red ; better in orjange, and still better in yellow ; full as well in green ; but to less advantage in blue ; indifferently well in indigo, and with more imper- fection in violet.

This trial was made upon one of the microscopic objects which are generally prepared for transparent vision ; but, as I used it in the opaque way, I thought that others might be chosen which would answer the purpose better ; and, in order to give some variety to my experiments, and to see the effect differently coloured substances might have on the rays of light, I provided the following materials to be viewed. Red paper ; green paper ; a piece of brass ; a nail ; a guinea ; black paper. Having also found that a higher power might be used, with

VOL. II. 8

58 INVESTIGATION OF THE POWERS OF

sufficient convenience for the rays of light to come from the prism to the object, I made the microscope magnify 42 times.

The appearance of the nail in the microscope, is so beautiful, that it deserves to be noticed ; and the more so, as it is accompanied with circumstances that are very favourable for an investigation, such as that which is under our present con- sideration. I had chosen it on account of its solidity and blackness, as being most likely to give an impartial result, of the modifications arising from an illumination by differently-coloured rays ; but, on viewing it, I was struck with the sight of a bright constellation of thousands of luminous points, scattered over its whole extent, as far as the field of the microscope could take it in. Their light was that of the illuminating colour, but differed considerably in brightness ; some of the f>oints being dim and faint, while others were luminous and brilliant. The brightest of them also admitted of a little variation in their colour, or rather in the intensity of the same colour ; for, in the centre of some of the most brilliant of these lucid appearances, their light had more vivacity, and seemed to deviate from the illuminating tint towards whiteness, while on and near the circumference it appeared to take a deeper hue.

An object so well divided by nature, into very minute and differently-arranged points, on which the attention might be fixed, in order to ascertain whether they would be equally distinct in all colours, and whether their number would be in- creased or diminished by different degrees of illumination, was exactly what I wanted ; nor could I think it less remarkable, that all the other objects I had fixed upon, besides many more which have been examined, such as copper, tin, silver, &c., presented themselves nearly with the same appearance. In the brass, which had been turned in a lathe, the luminous points were arranged in furrows ; and in tin they were remarkably beautiful. The result of the examination of my objects was as follows.

2d Experiment. Red paper.

In the red rays, I view a bright point near an accidental black spot in the paper, which serves me as a mark ; and I notice the space between the point and the spot : it contains several faint points.

In the orange rays, I see better. The bright point, I now perceive, is double.

In the yellow rays, I see the object still better.

In the green rays, full as well as before.

In the blue rays, very well.

In the indigo rays, not quite so well as in the blue.

In the violet rays, very imperfectly.

3«f Experiment. Green paper.

Red. I fix my attention on many faint points, in a space between two bright double points.

Orange. I see those faint points better,

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 59

YeUow. Still better.

Green. As well as before. I see remarkably well. Blue. Less bright, but very distinct. Indigo. Not well. Violet. Bad.

4ih Experiment. A piece of very clean turned brass.

R. I remark several faint luminous points between two bright ones. The colour of the brass makes the red rays appear like orange.

0. I see better, but the orange colour is likewise different from what it ought to be ; however, this is not, at present, the object of my investigation.

Y. I see still better.

G. I see full as well as before.

B. I do not see so well now.

1. I cannot see well. V. Bad.

^th Experiment. A nail.

R. I remark two bright points, and some faint ones.

0. Brighter than before ; and more points visible. Very distinct.

Y. Much brighter than before ; and more points and lines visible. Very distinct.

G. Full as bright ; and as many points visible. Very distinct. B. Much less bright. Very distinct.

1. Still less bright. Very distinct.

V. Much less bright again. Very distinct.

6th Experiment. I viewed a guinea, at 9 feet 6 inches from the prism ; and adjusted the place of the object in the several rays, by the shadow of the guinea. If this be not done, deceptions will take place.

R. Four remarkable points. Very distinct.

0. Better illuminated. Very distinct.

Y. Still better illuminated. Very distinct. The points all over the field of view are coloured ; some green ; some red ; some yellow ; and some white, en- circled with black about them.

Between yellow and green is the maximum of illumination. Extremely distinct.

G. As well illuminated as the yellow. Very distinct.

B. Much inferior in illumination. Very distinct.

1. Badly illuminated. Distinct.

V. Very badly illuminated I can hardly see the object at all. yth Experiment. The nail again, at 8 feet from the prism. R. I attended to two bright points, with faint ones between them. Almost all the points in the field of view are red. Very distinct.

60 INVESTIGATION OF THE POWERS OF

0. I see all the points better : they are red, green, yellow, and whitish, with black about them. Very distinct.

Y. I see better. More bright points, and more faint ones : the points are of various colours. Very distinct.

G. I see as well. The points are mostly green, and brightish-green, inclining to white. Very distinct.

B. Much worse illuminated. Very distinct.

1. Badly illuminated. Very distinct. V. There is hardly any illumination.

Sih Experiment. The nail again, at 9 feet 6 inches from the prism, by way of having the rays better separated.

R. Badly illuminated. The bright points are very distinct.

0. Much better illuminated. The bright points very distinct. Y. Still better illuminated. All points extremely distinct.

G. As well illuminated, and equally distinct.

B. Badly illuminated. The bright points are distinct ; but the others are not so.

1. Very badly illuminated. I do not see distinctly ; but I believe it to be for want of Ught.

V. So badly illuminated that I cannot see the object ; or at least but barely perceive that it exists.

gth Experiment. Black paper, at 8 feet from the prism.

R. The object is hardly visible. I can only see a few faint points.

O. I see several bright points, and many faint ones.

Y. Numberless bright and small faint points.

Between yellow and green, is the maximum of illumination.

G. The same as the yellow.

B. Very indifferently illuminated ; but not so bad as in the red rays.

L I cannot see the object.

V. Totally invisible.

From these observations, which agree uncommonly well, with respect to the illuminating power assigned to each colour, we may conclude, that the red-making rays are very far from having it in any eminent degree. The orange possess more of it than the red ; and the yellow rays illuminate objects still more perfectly. The maximum of illumination lies in the brightest yellow, or palest green. The green itself is nearly equally bright with the yellow ; but, from the full deep green, the illuminating power decreases very sensibly. That of the blue is nearly upon a par with that of the red ; the indigo has much less than the blue ; and the violet is very deficient.

With regard to the principle of distinctness, there appears to be no deficiency in any one of the colours. In the violet rays, for instance, some of the experiments

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 6l

mention that I saw badly ; but this is to be understood only with respect to the number of small objects that could be perceived ; for, although I saw fewer of the points, those which remained visible were always as distinct as, in so feeble an illumination, could be expected. It must indeed be evident, that by removing the great obstacle to distinct vision, which is the different refrangibility of the rays of light, a microscope will be capable of a much higher degree of distinctness than it can be under the usual circumstances. A celebrated optical writer has formerly remarked, that a fly, illuminated by red rays, appeared uncommonly distinct, and that all its minute parts might be seen in great perfection ; and, from the experi- ments which have been related, it appears that every other colour is possessed of the same advantage.

I am well aware that the results I have drawn from the foregoing experiments, both with regard to the heating and illuminating powers of differently-coloured rays, must be affected by some little inaccuracies. The prism, under the circum- stances in which I have used it, could not effect a complete separation of the colours, on account of the apparent diameter of the sun, and the considerable breadth of the prism itself, through which the rays were transmitted.

Perhaps an arrangement like that in Fig. i6, of the Newtonian experiments, might be employed ; if instruments of sufficient sensibility, such as air thermo- meters, can be procured, that may be affected by the enfeebled illumination of rays that have undergone four transmissions, and eight refractions ; and especially when their incipient quantity has been so greatly reduced, in their limited passage through a small hole at the first incidence.

But it appeared most expedient for me, at present, to neglect all further refine- ments, which may be attempted hereafter at leisure. It may even be presumed that, had there not been some small admixture of the red rays in the other colours, the result would have been still more decisive, with regard to the power of heating vested in the red rays. And it is hkewise evident, that at least the red hght of the prismatic spectrum, was much less adulterated than any of the other colours ; their refractions tending all to throw them from the red. That the same rays which occasion the greatest heat, have not the power of illumination in any strong degree, stands on as good a foundation. For, since here also they have undergone the fairest trial, as being most free from other colours, it is equally proved that they illuminate objects but imperfectly. There is some probability that a ray, purified in the Newtonian manner above quoted, especially in a well darkened room, may remain bright enough to serve the purpose of microscopic illumination, in which case, more precision can easily be obtained.

The greatest cause for a mixture of colours, however, which is, the breadth of the prism, I saw might easily be removed ; therefore, on account of the coloured points, which have been mentioned in the 6th and 7th experiments, I was willing to try whether they proceeded from this mixture ; and therefore covered the

63 INVESTIGATION OF THE POWERS OF

prism in front with a piece of pasteboard, having a sUt in it of about ^V o^ ^^ inch broad.

loth Experiment. The nail, at 9 feet 2 inches from the prism.

R. I fix my attention on two shining, red points ; they are pretty bright.

0. I see many more points. The object is better illuminated than in the red. The points are surrounded by black ; but are orange-coloured.

Y. The points now are yellow, and white surrounded by black. The object is better illuminated than in orange.

The maximum of illumination is in the brightest yellow, or palest green.

G. The points are green and white, as before surrounded by black. Better illuminated than in orange.

B. The illumination is nearly equal to red.

1. Very indifferently illuminated. V. Very badly illuminated.

The phaenomena of the differently-coloured points being now completely resolved, since they were plainly owing to the former admixture of colours, and the illimiinating power remaining ascertained as before, I attempted also to repeat the experiments upon the thermometer, with the prism covered in the same manner ; but I found the effect of the coloured rays too much enfeebled to give a decisive result.

I might now proceed to my next subject ; but it may be pardonable if I digress for a moment, and remark, that the foregoing researches ought to lead us on to others. May not the chemical properties of the prismatic colours be as different as those which relate to light and heat ? Adequate methods for an investigation of them may easily be found ; and we cannot too minutely enter into an analysis of light, which is the most subtle of all the active principles that are concerned in the mechanism of the operations of nature. A better acquaintance with it may enable us to account for various facts that fall under our daily observation, but which have hitherto remained unexplained. If the power of heating, as we now see, be chiefly lodged in the red-making rays, it accounts for the comfortable warmth that is thrown out from a fire, when it is in the state of a red glow ; and for the heat which is given by charcoal, coke, and balls of small-coal mixed up with clay, used in hot-houses ; all which, it is well known, throw out red light. It also explains the reason why the yellow, green, blue, and purple flames of burning spirits mixed with salt, occasion so httle heat that a hand is not materially injured, when passed through their coruscations. If the chemical properties of colours also, when ascertained, should be such that an acid principle, for instance, which has been ascribed to light in general, on account of its changing the complexion of various substances exposed to it, may reside only in one of the colours, while others may prove to be differently invested, it will follow, that bodies may be variously affected by light, according as they imbibe and retain, or transmit and reflect, the different colours of which it is composed.

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 63

Radiant Heat is of different Refrangihility.

I must now remark, that my foregoing experiments ascertain beyond a doubt, that radiant heat, as well as light, whether they be the same or different agents, is not only refrangible, but is also subject to the laws of the dispersion arising from its different refrangihility ; and, as this subject is new, I may be permitted to dwell a few moments upon it. The prism refracts radiant heat, so as to separate that which is less efficacious, from that which is more so. The whole quantity of radiant beat contained in a sun-beam, if this different refrangihility did not exist, must inevitably fall uniformly on a space equal to the area of the prism ; and, if radiant heat were not refrangible at all, it would fall upon an equal space, in the place where the shadow of the prism, when covered, may be seen. But, neither of these events taking place, it is evident that radiant heat is subject to the laws of refraction, and also to those of the different refrangibihty of light. May not this lead us to surmise, that radiant heat consists of particles of light of a certain range of momenta, and which range may extend a little farther, on each side of refrangi- hility, than that of light ? We have shewn, that in a gradual exposure of the thermometer to the rays of the prismatic spectrum, beginning from the violet, we come to the maximum of light, long before we come to that of heat, which lies at the other extreme. By several experiments, which time will not allow me now to report, it appears that the maximum of illumination has little more than half the heat of the full red rays ; and, from other experiments, I Ukewise conclude, that the full red falls still short of the maximum of heat ; which perhaps lies even a little beyond visible refraction. In this case, radiant heat will at least partly, if not chiefly, consist, if I may be permitted the expression, of invisible light ; that is to say, of rays coming from the sun, that have such a momentum as to be unfit for vision. And, admitting, as is highly probable, that the organs of sight are only adapted to receive impressions from particles of a certain momentum, it explains why the maximum of illumination should be in the middle of the refrangible rays ; as those which have greater or less momenta, are likely to become equally unfit for impressions of sight. Whereas, in radiant heat, there may be no such limitation to the momentum of its particles. From the powerful effects of a burning lens, how- ever, we gather the information, that the momentum of terrestrial radiant heat is not likely to exceed that of the sun ; and that, consequently, the refrangihility of calorific rays cannot extend much beyond that of colourific light. Hence we may also infer, that the invisible heat of red-hot iron, gradually cooled till it ceases to shine, has the momentum of the invisible rays which, in the solar spectrum viewed by day-light, go to the confines of red ; and this will afford an easy solution of the reflection of invisible heat by concave mirrors.

64 INVESTIGATION OF THE POWERS OF

Application of the Result of the foregoing Observations, to the Method of viewing the Sun advantageously, with Telescopes of large Apertures and high magnifying Powers.

Some time before the late transit of Mercury over the disk of the sun, I pre- pared my 7-feet telescope, in order to see it to the best advantage. As I wished to keep the whole aperture of the mirror open, I soon cracked every one of the darkening sUps of wedged glasses, which are generally used with achromatic tele- scopes : none of them could withstand the accumulated heat in the focus of pencils, where these glasses are generally placed. Being thus left without resource, I made use of red glasses ; but was by no means satisfied with their performance. My not being better prepared, as it happened, was of no consequence ; the weather proving totally unfavourable for viewing the sun at the time of the transit. However, as I was fully aware of the necessity of providing an apparatus for this purpose, since no method that was in use could be applied to my telescopes, I took the first oppor- tunity of beginning my trials.

The instrument I wished to adapt for solar inspection, was a Newtonian reflector, with 9 inches aperture ; and my aim was, to use the whole of it open.

I began with a red glass ; and, not finding it to stop light enough, took two of them together. These intercepted full as much light as was necessary ; but I soon found that the eye could not bear the irritation, from a sensation of heat, which it appeared these glasses did not stop.

I now took two green glasses ; but found that they did not intercept light enough. I therefore smoked one of them ; and it appeared that, notwithstanding they now still transmitted considerably more light than the red glasses, they remedied the former inconvenience of an irritation arising from heat. Repeating these trials several times, I constantly found the same result ; and, the sun in the first case being of a deep red colour, I surmised that the red-making rays, transmitted through red glasses, were more efficacious in raising a sensation of heat, than those which passed through green, and which caused the sun to look greenish. In con- sequence of this surmise, I undertook the investigations which have been delivered under the two first heads.

As soon as I was convinced that the red light of the sun ought to be inter- cepted, on account of the heat it occasions, and that it might also be safely set aside, since it was now proved that pale green light excels in illumination, the method which ought to be pursued in the construction of a darkening appar- atus was sufficiently pointed out ; and nothing remained but to find such matericds as would give us the colour of the sun, viewed in a telescope, of a pale green light, sufficiently tempered for the eye to bear its lustre.

To determine what glasses would most effectually stop the red rays, I procured some of all colours, and tried them in the following manner.

THE PRISMATIC COLOURS TO HEAT AND ILLUMINATE OBJECTS 65

I placed a prism in the upper part of a window, and received its coloured spectrum upon a sheet of white paper. Then I intercepted the colours, just before they came to the paper, successively, by the glasses, and found the result as follows.

A deep red glass intercepted all the rays.

A paler red did the same.

From this, we ought not to conclude that red glasses will stop the red rays ; but rather, that none of the sun's light, after its dispersion by the prism, remains intense enough to pass through red glasses, in sufficient quantity to be perceptible, when it comes to the paper. By looking through them directly at the sun, or even at day objects, it is sufficiently evident that they transmit chiefly red rays.

An orange glass transmitted nearly all the red, the orange, and the yellow. It intercepted some of the green ; much of the blue ; and very little of the indigo and violet.

A yellow glass intercepted hardly any light, of any one of the colours.

A dark green glass intercepted nearly all the red, and partly also the orange and yellow. It transmitted the green ; intercepted much of the blue ; but none of the indigo and violet.

A darker green glass intercepted nearly all the red ; much of the orange ; and a little of the yellow. It transmitted the green ; stopped some of the blue ; but transmitted the indigo and violet.

A blue glass intercepted much of the red and orange ; some of the yellow ; hardly any of the green ; none of the blue, indigo, or violet.

A purple glass transmitted some of the red ; a very little of the orange and yellow : it also transmitted a little of the green and blue ; but more of the indigo and violet.

From these experiments we see, that dark green glasses are most efficacious for intercepting red light, and will therefore answer one of the intended purposes ; but since, in viewing the sun, we have also its splendour to contend with, I pro- ceeded to the following additional trials.

White glass, lightly smoked, apparently intercepted an equal share of all the colours ; and, when the smoke was laid on thicker, it permitted none of them to pass.

Hard pitch, melted between two white glasses, intercepted much light ; and, when put on sufficiently thick, transmitted none.

Many differently-coloured fluids, that were also tried, I found were not suffi- ciently pure to be used, when dense enough to stop light.

Now, red glasses, and the two last-mentioned resources of smoke, and pitch, any one of which, it has been seen, will stop as much light as may be required, had still a remaining trial to undergo, relating to distinctness ; but this I was convinced could only be decided by actual observations of the sun.

As an easy way of smoking glasses uniformly is of some consequence to distinct

VOL. II. 9

66 INVESTIGATION OF THE POWERS OF

vision, it may be of service here to give the proper directions, how to proceed in the o{)eration.

With a pair of warm pHers, take hold of the glass, and place it over a candle, at a sufficient distance not to contract smoke. When it is heated, but no more than still to permit a finger to touch the edges of it, bring down the glass, at the side of the flame, as low as the wick will permit, which must not be touched. Then, with a quick vibratory motion, agitate it in the flame from side to side ; at the same time advancing and retiring it gently all the while. By this method, you may proceed to lay on smoke to any required darkness. It ought to be viewed from time to time, not only to see whether it be sufficiently dark, but whether any inequality may be perceived ; for, if that should happen, it will not be proper to go on.