Astronomical and Nautical Collections, 449 



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 re- 

 present 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 pheno- 

 mena: 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 emi- 

 nently qualified to succeed. 



The equation, which may be called final, in Mr. Laplace's 

 Supplement to the Xth Book, p. 47, is Q cos. (^ — 6) = 

 (2§ — §') K sin. 0. Now this, in my opinion, is a perfect 

 reductio ad absurdum : for Q must always be incoirvparahly 

 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 va- 

 nishes 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 experi- 

 ment with mercury. 



I entreat you to consider this objection with patient atten- 

 tion, 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 elemen- 

 tary 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 Aca- 

 demy ; or I should have taken the liberty of sending you a 

 copy, as an inadequate return for so many valuable communi- 

 cations with which you have had the kindness to favour me. 



Believe me always, dear Sir, 

 Very truly yours, 

 London,\%Nov.\%21. # * # * 



