I take the length of an undulation of the yellow rays, which are the most brilliant of the spectrum, and of which the dark and light stripes consequently coincide with the darkest and brightest stripes of the fringes produced by white light, which is commonly employed in these experiments, both because of its greater brightness, and because of the more marked character which it gives to the central stripe, so as to prevent any other from being mistaken for it.

It was an apparatus of this kind that Mr. ARAGO and myself employed for measuring the difference of the refractive powers of dry air, and of air saturated with moisture at 80° F., which is so small, that it would escape every other method of observation, because the greater refractive power of aqueous vapour is almost exactly compensated by the less specific gravity of moist air. But, in the generality of cases, the slightest mixture of one vapour or gas with another produces a considerable displacement in the fringes: and if we had a series of experiments of this kind, made with care, the apparatus might become a valuable instrument of chemical analysis.

[To be continued.]

iii. Remarks on the Action of CORPUSCULAR FORCES. In a Letter to Mr. POISSON. [◊]

My dear Sir,

I AM very glad to see that you have been applying your analytical powers to the investigation of the acustical effects of corpuscular forces, and that, among many more refined determinations, you, have confirmed several of the results relating to sounding bodies, which were published twenty years ago in my Lectures on Natural Philosophy: though they were generally such as might have been derived from the calculations of Bernoulli and Euler; which I attempted in some [p449] measure to simplify by the introduction of the element which I called the Modulus of Elasticity of each substance. You have very properly observed that it is often difficult to represent the combination of these corpuscular forces by an integral, since in many practical cases the integral must vanish, where it would naturally be applied to the phenomena: and, from similar considerations, I trust you will be prepared to admit the objections that I made long ago, to the reasoning of your great predecessor, Mr. Laplace, to whose station in the mathematical world you appear so eminently qualified to succeed.

The equation, which may be called final, in Mr. Laplace’s Supplement to the Xth Book, p. 47, is Q cos. (ω−θ) = (2ς−ς′) K sin. θ. Now this, in my opinion, is a perfect reductio ad absurdum: for Q must always be incomparably less than K; the attraction of the particles lying between a cylinder and its tangent plane being always infinitely less than that of the particles in an angular or prismatic edge: or if this were denied in general, it would obviously become true when the cylinder itself becomes a plane, and Q vanishes altogether; which will always be the state of the problem, when the surface of the solid is so inclined to the horizon, that the surface of the fluid may remain horizontal, the appropriate angle of contact being unaltered in these circumstances, as it is easy to show by making the experiment with mercury.

I entreat you to consider this objection with patient attention, and to tell me if you can find any arguments to supersede it. I would also presume to ask your opinion of my own method of deducing the force of capillarity from the elementary attractions and repulsions of bodies, at the end of my Illustrations of the Celestial Mechanics, Art. 382; Appendix A, p. 329 to 337. The volume is in the Library of the Academy; or I should have taken the liberty of sending you a copy, as an inadequate return for so many valuable communications with which you have had the kindness to favour me.

Believe me always, dear Sir,

Very truly yours,