REPORT ON CAPILLiARY ATTRACTIOX. 273 



solved in the direction of the solid surface, will give k g cos i, 

 which is counteracted hy k §' — k {§ — §'), the difference of the 

 other two forces. Hence it follows that 



g' = f cos«— . 



When Q = 90°, 2 §' = §, as Clairaut found. The preceding 

 theory is deficient in not informing us how the other resolved 

 portion of the tension of the fluid, viz. k g sin 3, is counteracted. 



The essay of Dr. Young, as it appears in the second volume 

 of his Natural Philosophy^ contains by way of appendix some 

 remarks and strictures on Laplace's theory, the results of which 

 are shown to be readily derivable from his own theory ; but an 

 objection is raised against its principles on the ground that no 

 account is taken of a repulsive molecular force. We have al- 

 ready seen in what way this objection may be obviated without 

 affecting the results of Laplace's theory, or materially altering 

 the analysis. Another objection urged by him, to which allu.sion 

 has been made before (p. 266), lies against the reasoning, and not 

 the principles, of Laplace's theory. In determining the conditions 

 of equilibrium of a fluid particle situated at the angle of contact, 

 Laplace takes account only of the attractions of the solid and 

 fluid upon it, omitting the consideration of the variation oi pres- 

 sure occasioned by these forces as well near the free surface of 

 the fluid as near that in contact with the solid. The error to 

 which this omission leads will be understood by reverting to 

 the reasoning by which it was shown (p. 258), according to Clai- 

 raut's method, that when the attractive force of the fluid is double 

 that of the solid, the capillary surface will be horizontal. The 

 same kind of reasoning as that employed to show that the hori- 

 zontal attractions in this case counterbalance each other, would 

 also prove that the particle at the angle of contact is urged ver- 

 tically downwards, by only half the force with which another 

 particle at the fluid surface situated beyond the sphere of the 

 attraction of the solid, is urged in the same direction. The 

 horizontality of the fluid surface may nevertheless be maintained 

 if we consider that the variation of pressure near the surface, 

 due to the molecular attractions, will not be the same at the sur- 

 face in contact with the soUd as at the free surface, by reason of 

 the solid's attraction. Had Laplace taken account of this cir- 

 cumstance, as the principles of his theory required him to do, 

 notwithstanding the supposition of incompressibility, he would 

 have obtained an equation equivalent to that which expresses 

 above the relation between g' and g, instead of the faulty equation 

 of art. 12 of his treatise. In fact, M. Gauss and M. Poisson, as 



1834. T 



