ART. IX. A Letter from M. Gay-Lussac to Mr. Daniell,

on the Expansion of Gases by Vapour.

"Mon cher Monsieur,

Paris, 2 Nov., 1825.

"J'ai reçu la lettre que vous m'avez fait l'honneur de m'écrire, pour me donner le renseignement que j'avois pris la liberté de vous demander:-je vous prie d'en recevoir mes sincères remer cimens.

"Je profite de cette occasion pour vous prévenir que dans le dernier No. du Journal de Science, &c., p. 74, que je reçois à l'instant, vous donnez une formule pour l'expansion d'un gaz en contact avec un liquide fournissant indéfiniment de la vapeur, p

qui ne me semble pas exacte, et que c'est bien réellement

p-f

qui est l'expression du volume que doit prendre le gaz en se saturant de vapeur dont la force élastique est ƒ, sous la pression p. de

l'atmosphère.

"En effet, dans un vase inextensible, le gaz en contact avec le liquide qui fournit la vapeur a une force élastique égale à p+f; et si on suppose que le vase devienne extensible, il se dilatera jusqu'à ce que la pression intérieure devienne égale à la pression extérieure; or, comme ƒ est constant, le gaz se dilatera jusqu'à ee que sa force élastique soit égale à p-f: et les volumes étant en raison inverse des poids comprimans, on a

volume de l'air avant son mélange avec la vapeur, est à V, volume après le mélange, comme p-f est à p: c'est à-dire

"Le volume V devient infini lorsque fp, et cela doit être ; car alors la vapeur fait seule équilibre au poids de l'atmosphère, et la force élastique du gaz doit être infiniment petite, ou son volume infiniment grand.

Mr. Herschel on Reflecting Telescopes.

293

whose position and distance are stated at 45° 27′ sf and 1".957

respectively, while Mr. South's recent measures, which appear entitled to preference, being the results of 19 measures of angle and 10 of distance taken on 4 different nights, and agreeing well together, make the mean result as follows.

Position 33° 14' sf; Distance 1".447; Epoch 1825.59. It seems certain therefore that an error of 10° must have been committed in the reading off of the printed angles. Granting this, the remaining error of 20° 13′ would be pardonable in so very close a

single set of measures.

make

on that

star as the result of a In the remarks I have thought it necessary to part of Mr. Fraunhofer's memoir which refers to the action of reflecting telescopes, I should be very sorry to have expressed myself in any way capable of being construed in a controversial sense, or as intended to give the slightest personal offence to its celebrated author, who as an artist must surely be ever regarded as a benefactor to astronomy, while optical science is no less indebted to him as a philosopher, for his beautifully delicate experiments on the constitution of the prismatic spectrum, which have given a degree of precision to optical determinations hitherto unheard of, and shewn the practicability of placing the construction of telescopes on purely scientific grounds, while they have unfolded phenomena of the highest interest in a speculative point of view. Nor can I help feeling that I should ill requite his liberal and friendly reception during a visit to Munich, which I shall ever recollect with pleasure, and in which I had ample opportunity to admire both the resources of his genius and the simplicity of his manners, by a word calculated to give pain or excite unpleasant feelings,

quod vitium procul abfore chartis

Atque animo prius, ut si quid promittere de me

Possum aliud, vere promitto.

J. F. W. HERSCHEL.

292

Mr. Herschel on Reflecting Telescopes.

A reflector of 18 inches aperture would be equivalent to an achromatic of 151, and one of 48 inches to an achromatic of 41 in aperture, a size we cannot suppose (from any thing we have yet seen) that it is possible the latter should ever attain. Reflectors of 18 or 20 inches are perfectly manageable, and, I ap prehend, quite within the power of any good artist to execute, and (if intended only for use, and not at all for show) at no very ruinous expense. That which I habitually use, of the former dimension, is my own workmanship, (en amateur), and though inferior in distinctness to the exquisite one used by my father in his sweeps, is by no means an instrument to be despised. Indeed, from the experience I have had of these telescopes, I am satisfied of their applicability even to the more exact purposes of astronomy, and that great improvements in their construction and mechanism remain to be made.

Having referred to the paper on double stars, published by Mr. South and myself, permit me (with his concurrence) to rectify some errors into which we have there fallen, and which have been' recognised by him in the course of his observations at Passy in continuation of the same subject, the results of which, I hope, will, ere long, be before the public, and will afford a convincing proof of his zeal and indefatigable industry.-The first of these errors is in the case of the small star accompanying 36 Ophiuchi.

It is stated in the work referred to (as the result of a single measure, probably a hasty one, or affected by an accidental derangement of the micrometer head, as having its position 19° 5′ np) and distance 3'0".735. There is no memorandum of which of the close stars the position was measured from, but it must have been from the most southern, as Mr. South, by a mean of 10 measures, finds 17° 41' np for its angle of position with respect to this star. The difference (1° 24') is not very important, but the distance is greatly in error. Mr. S. has determined the distance

of the small star from the more southern of the close stars (by a mean of 19 measures) at 3'′15′′.252, and from the more northern (by a mean of 21) at 3' 13.689.

The next correction I have to notice is in the case of 'Aquilæ,

F

Mr. Herschel on Reflecting Telescopes.

291

was in

Fraunhofer concludes that the power of the telescope sufficient to resolve it, and must therefore have been inferior to that of an achromatic in the hands of Mr. Bessel, with which it was recognised by that eminent astronomer as double. It will be seen on reference to the Memoir on double stars lately published in the Philosophical Transactions by Mr. South and myself, that this star had been long since ascertained to be double, not only by Mr. Bessel, but by Messrs. Struve, Pond, and South, and, what is more to the present purpose, by Sir William Herschel himself, It was only by oversight that we omitted to refer in that work to his account of it, which is published in his paper "On the places of 145 new double Stars," in the first volume of the Transactions of the Astronomical Society, page 178. Which paper was read on June 8, 1821. It will not be amiss if we extract the account verbatim.

"(114). Journal, April 5, 1796.-7 feet reflector power 460 (Bootis double 1st class.. Very nearly in contact; I can, however, see a small division. A little unequal, the preceding is the smallest."

"Rev. Aug. 6, 1796. Bootis. double. Position 2 Rev.14.5 parts + 1.1 for Zero=41° 59′.1 np. With 460 a division is but barely visible of S. Both w. A little or pretty unequal."

"Rev. July 12. 1807. Bootis. They are fine, equal, whitish stars: the interval between their apparent discs with 460 is of } the diameter of either."

To these observations I will only add, that with the same telescope, but with a mirror much tarnished, and now used only for the most ordinary observations, I last night saw this star, as well as • Coronæ and ʼn Coronæ, distinctly double.

n

The argument, then, from the omission of this star, is untenable. Orionis would have furnished a case much more in point. The very singular history of this star will be found in the Memoir on double Stars already mentioned.

In large reflectors, in which only one metallic mirror is used, the disadvantage in point of light under which they labour, in comparison with refractors, is however much less formidable.

290

Mr. Herschel on Reflecting Telescopes. by metallic reflection, are, I think, somewhat too strong. He observes that, "the most perfect metallic mirror reflects only a small part of the incident light, and that the greater part is absorbed;" and that, "in conséquence, the intensity of the light entering the eye of the observer is always very small" (ist immer sehr gering.) A metallic mirror, however, reflects 0.673 of the incident light, or more than two-thirds, and absorbs less than onethird of the whole. Mr. Fraunhofer appears rather to have had in view the Newtonian construction, where two metallic mirrors

are used, and where the whole effective quantity

of

light is only 0.452 of the incident rays. No one who has been half blinded by the entrance of Sirius or a Lyræ into one of my father's 20 feet reflectors, will say that the intensity of its light is small, nor, to take a less extreme case, will any one who uses one of M. Amici's Newtonian reflectors of 12 inches aperture (a perfectly convenient and manageable size, and of which he has constructed several,) be disposed to complain of its want of light. The ordinary reflector used by my father in his reviews of the Heavens was a Newtonian, of 7 feet focus, and barely six inches in aperture, and consequently equal (cæteris paribus) to an achromatic of 4 (4.254) English, or 3.99 Paris inches, and therefore by no means proper to be put in competition with Mr. Fraunhofer's chefd'œuvres of 7 and 9 inches. Yet it will be recollected, that with this telescope, and with a magnifying power of 460, Leonis was discovered to be double and distinctly separated, and its angle of position measured.

In order to demonstrate the superiority of refracting over reflecting telescopes, Mr. Fraunhofer has selected the star Bootis, which my father has described as a double star of the 6th class (No. 104) in his second catalogue of double stars, but without mentioning the division of the large star into two, as a double star of the first class. It might, however, be very easily overlooked in a review in indifferent weather. It is at least as difficult to resolve as Coronæ, more so than σ, either of which, with any scope, be its goodness what it may, requires a favourable atmosphere for its separation. From this omission, however, Mr.

tele