258 FOURTH REPORT — 1834. 



dent in the fluid. Yet Clairaut was the first to see the ne- 

 cessity of taking account of the action of the fluid on itself; 

 and this addition to the tlieory of capillary attraction is the princi- 

 pal feature of the propositions on this subject introduced, in rather 

 a cursory manner and beside his main purpose, into his cele- 

 brated treatise on the Figure of the Earth*. After stating the 

 insufficiency of the method of Jurin, he proceeds to a careful 

 consideration of all the forces concerned in raising the fluid, 

 both those due to the tube and those due to the fluid, as well at 

 the upper part of the column raised, as at the lower extremity 

 of the tube. His method of considering the forces, which is 

 stated clearly and illustrated by good diagrams, has been for 

 the most part followed in succeeding treatises on the same sub- 

 ject. But although Clairaut asserts that the forces concerned in 

 this problem are sensible only at very small distances, he does 

 not seem to be aware that the distances must be considered alto- 

 gether insensible. This is not a necessary condition in his view 

 of the mode in which the forces act ; respecting the law of the 

 variation of which, as the distances increase, he makes no other 

 hypothesis than that the function which expresses it is the same 

 both for the tube and the fluid. He is consequently unable to 

 prove that the height at which the fluid stands in a capillary 

 tube is inversely proportional to the diameter. 



By reasoning on the hypothesis just named, Clairaut arrives 

 at the following conclusion : " If the attraction of the capillary 

 tube should be of less intensity than that of the water, provided 

 it be not so small as half the other, the water will still rise." 

 This he confirms in another method, the principle of which will 

 be exhibited by showing as follows, that if the attraction of the 

 fluid for itself were exactly double that of the tube for the fluid, 

 the surface of the fluid within the tube would be horizontal, and 

 consequently on a level with the surface without. Let us sup- 

 pose the fluid surface to be everywhere horizontal, and consider 

 the equilibrium of a particle in contact with the vertical surface 

 of the solid, which we will suppose to be plane. Now as the 

 resultant of the forces acting on the particle must be perpendi- 

 cular to the fluid surface, and therefore vertical, the horizontal 

 attractions destroy each other. Therefore the horizontal attrac- 

 tion of the solid, which is its total action, is equal to the hori- 

 zontal attraction of the fluid, which is only half what it would 

 be if the fluid were continued above the particle as it is below, 

 and consequently placed under the same circumstances of at- 



* T/ii'orie de la Figure de la Terre. Paris, 1808, pp. 105—128. 



