red, yellow, green, and blue media, which are absolutely incapable of reflecting or transmitting certain definite rays of the same colour with themselves.

The true cause of the colours of natural bodies may be thus stated: When light enters any body, and is either reflected or transmitted to the eye, a certain portion of it, of various refrangibilities, is lost within the body; and the colour of the body, which evidently arises from the loss of part of the intromitted light, is that which is composed of all the rays which are not lost; or, what is the same thing, the colour of the body is that which, when combined with that of all the rays which are lost, compose the original light. Whether the lost rays are reflected, or detained by a specific affinity for the material atoms of the body, has not been rigorously demonstrated. In some cases of opalescence, they are either partly or wholly reflected; but it seems almost certain, that in all transparent bodies, and in that great variety of substances in which no reflected tints can be seen, the rays are detained by absorption*.

LXXX. On the Proposition that a Function of and can be developed in ONLY ONE Series of Laplace's Coefficients; the Function being supposed not to become infinite between the limits o and of and 。 and 2 of 4. By the Rev. J. H. PRATT, B.A.†

THIS important proposition is, in fact, not proved, but assumed, by Laplace in the Mécanique Céleste, III. ii. § 12. Professor Airy pointed out this defect, and gave a proof of the proposition in the Cambridge Philosophical Transactions: but this labours under the restriction of supposing the number of terms in the series finite. M. Poisson has considered this among numerous other important questions in a paper in the Connoisance des Tems for 1829, and also in his Théorie Mathématique de la Chaleur, chap. viii. But I confess it appears to me that the proposition is not proved even in these places; though by a slight addition to the reasoning the objection to the proof may be removed.

M. Poisson shows that if p = cos cos ' + sin sin e' cos (V), and also if (1-2 a p+ a)− = 1+a P2+a2 P2+.... + a2 P; +......

1 าร 2

then

ƒ (0, 4) = = =SS2* {1+ 3 × P ̧ + ... + (2 i + 1 ) a1P ̧ +...}

f(0', ') sin e' de' dv.

α

(1.)

• The views on this subject of Sir John Herschel will be found in a paper by that philosopher in Lond. and Edinb. Phil. Mag., vol. iii. p. 401.—EDIT. + Communicated by the Author.

He then says,

that since

JJ6*. P.f(,4) sin ở để đó

is of the form of Laplace's coefficients, we may put it

and hence f(0, 4) = Yo + Y1 + ...... + Y; +......

1

the accents denoting that ' and are put for and V.

2i+1

2 T

Hence Y1 = 24+ *** P,ƒ (6', V') sin &' de' d↓ by

42. P, Y', sin'ded by the

4 π

nature of Laplace's Coefficients. All so far is clear enough. But in order to show that f(0, 4) cannot be developed in another series Vo+V1+

possible we should have

2i+1 าร

V1 = 24+2*. P, V/ sin 0' d 0' d↓

V;

4 π

0

by what has preceded; and then easily deduces the result desired. But surely this is no less than begging the question. All we learn from it is that if we proceed to develop, as above, we shall arrive at a series of determinate terms; but it does not follow that another method of development cannot be discovered which would lead to another series. The following demonstration appears to be free from objection.

In the formula (1.) we may evidently interchange and ', and since P, P are the same functions of 0,4 and, V. Hence from that formula we learn that the definite integral of the product of any given function of and ↓, and the function (1 + 3 a P1 + + (2 i + 1) a P; + ....) sin does not vanish between the limits specified above.

....

Now, suppose f (0, 4) can be expanded in the two distinct series Qo+Q+...... + Qi +..... and Ro+R, +......R; +.... Then by hypothesis Q-R, does not vanish; and consequently,

2.

P;

SS2* (1+3× P1 + ..... + (2 i + 1) aa P., + ......) sin ♦

does not vanish.

··SS**· P, · sin 0 (Q,— R,) dê d↓ does not vanish, since

all the other terms do vanish by the nature of Laplace's Coefficients.

...

Again, (Q-Ro) + (Q1−R1)+ +(Qi−R1) + Multiply by P, sin and integrate; then we have

= 0.

but we showed that this does not vanish if Q, and R, are different functions. Hence that hypothesis is not true, and therefore Q, R, and the expansions off (4, 4) are identical.

=

Caius College, Cambridge, Feb. 18, 1836.

LXXXI. On a supposed new Sulphate and Oxide of Antimony. By MICHAEL FARADAY, D.C.L., F.R.S., &c. &c.

To the Editors of the Philosophical Magazine and Journal. GENTLEMEN,

N my Experimental Researches, paragraphs 693. 694. 695. 696.*, I have, in relation to antimony, described what I considered to be a new sulphuret, and expressed my belief that a new and true protoxide existed consisting of single proportions, "but could not stop to ascertain this matter strictly by analysis." Professor Rose when in London informed me that Berzelius objected to my new sulphuret, and I was induced to make more accurate experiments on that point, which showed me my error, and accorded generally with what Rose had described to me. I intended to publish these results in the first electric paper which I might have to put forth; but my friend Mr. Solly has put into my hands a translation of Berzelius's paper, and it is so clear and accurate as to the facts that I now prefer asking you to publish it, adding merely that my experiments quite agree with those described in it, as regards the sulphuret. With respect to the supposed chloride and oxide, I have not anywhere implied that I had made quantitative experiments on them.

On Faraday's supposed Sulphuret of Antimony and Oxide of Antimony: by J. J. BERZELIUS.-From his "Jahresbericht,"

No. 15.

"Faraday has stated, that when sulphuret of antimony is beated with more metallic antimony, a new sulphuret of antimony is formed, which when in the fused state is distinguish• See Lond. and Edinb. Phil. Mag., vol. v. p. 170.-Edit.

able from the common sulphuret. According to a few experiments, this sulphuret of antimony is composed of Sb S, or one atom of each element. When this sulphuret is dissolved in muriatic acid, sulphuretted hydrogen is evolved, and although a little antimony is separated, yet there remains in solution a combination with chlorine Sb Cl, which when decomposed with carbonate of soda furnishes a new oxide. The mixing of this with the common oxide is said to have given rise to the contradictory views of its composition, and also to the appearance that the fused oxide of antimony is decomposed to a certain extent by the electric current only until the new oxide is reduced.

"Faraday appears convinced of the truth of this statement, but adds that he has not confirmed by analysis the composition of this oxide, because he should thereby have interrupted the course of his main experiments.

"This appeared to me to deserve a nearer investigation, as well for itself as for the importance of its influence on Faraday's electro-chemical views. I have therefore repeated the above-described experiments of Faraday on the three new combinations of antimony with sulphur, chlorine, and oxygen, and I have found that even if they do exist they cannot possibly be formed by the means which he has described, and they are therefore still to be discovered.

"The following is the substance of my examination. I mixed together very carefully and intimately sulphuret of antimony and metallic antimony in the proportions that, through melting, the combination Sb+ S must be formed: the mixture was then put into a glass tube; this was drawn out to a capillary end; the air was then expelled by heat, and the tube was hermetically sealed. The tube was then placed in a vessel covered with sand, heated to a full red-heat, and then suffered to cool slowly. When the mass was taken out there was at the bottom a regulus, which contained 63 per cent. of the antimony which had been added after it had been separated from some adhering portions of sulphuret of antimony by boiling with a little muriatic acid.

“This had all the properties of pure antimony. Rubbed to powder and boiled with muriatic acid, it still evolved however a little sulphuretted hydrogen and gave some antimony to the acid. The powder when thus boiled had lost 6 per

cent.

"From all this it is evident that though the resulting sulphuret of antimony contained more antimony after than before the process, it is not the combination which Faraday thought it was. Even in the cleavage it had not the appear

ance of a pure sulphuret of antimony. The upper portions had the same radiated structure as the common sulphuret of antimony, and a few larger crystals had shot up into the upper surface of the regulus, where they were surrounded with an irregular mass of a lighter colour. The upper and the lower portions of this so-formed antimony were each separately analysed, in such a manner that a weighed portion was put into muriatic acid and digested in it in the water-bath. The solution went on rapidly. From the lowermost portion crystals fell off one after another, upon which the acid did not act. The same happened likewise with the uppermost portion, only they were smaller and fewer in number. These insoluble parts when well boiled and washed were from the lowermost 15 and from the uppermost 10 per cent. It proved to be pure metallic antimony formed in feathery crystals, and shows, therefore, the interesting fact that sulphuret of antimony can dissolve at a high temperature 13 per cent. of metallic antimony, which when the solution is suffered to cool sufficiently slowly crystallizes out of the yet fluid sulphuret of antimony before this latter solidifies. By a more rapid cooling the whole mass congeals together, and the cleavage is then quite similar throughout.

"From what has been said it is quite evident that the muriatic acid takes up nothing but the common chloride of antimony. I have examined this behaviour further in detail, and thereby found, that by this method neither with water nor alkali is it possible to obtain any other oxide.

"The above-mentioned experiment of Faraday, that melted oxide of antimony is decomposed by the electric current, clearly proves that the law proposed by him that similar quantities of electricity always evolve equal chemical proportions, only holds good so long as the comparison is made between, combinations of proportional composition.

"As for the cause of the appearance, that the decomposition of the oxide of antimony becomes gradually weaker and weaker, and at last ceases, it is evident that Faraday has overlooked the circumstance that the oxide is decomposed into metal at the negative conductor and antimonious acid at the positive conductor, which then soon becomes encrusted with a solid substance, after which the electricity could not have any further action."

With respect to Berzelius's objection in the last paragraph but one of his paper, I will ask you to reprint paragraph 821.* of my series. All these facts combine into, I think, an irresistible mass of evidence, proving the truth of the important * See Lond. and Edinb. Phil. Mag., vol. v. p. 344.-EDIT.