268 FOURTH REPORT — 1834. 



the surface. He shows, moreover, how this uniformity of ten- 

 sion may be a consequence of ulterior principles. 



The course of reasoning Dr. Young pursues in his essay is as 

 follows. He begins with making two assumptions : first, that 

 the tension of the fluid surface is uniform ; secondly, that at the 

 juncture of a fluid surface with the surface of a solid, there is an 

 appropriate angle of contact between the two surfaces. *' This 

 angle," he says, " for glass and water, and in all cases where a 

 solid is perfectly wetted by a fluid, is evanescent : for glass and 

 mercury, it is about 140° for common temperatures, and when 

 the mercury is moderately clean." He shows next that a theory 

 founded on these two hypotheses will explain various capillary 

 phaenomena. And lastly, at the end of the essay, derives the hy- 

 potheses from ulterior physical principles. It is in this last 

 part that Dr. Young's theory contains views not to be found in 

 any previous theory. Following the order which the author 

 adopts, I will endeavour first to exhibit the way in which his 

 theory accounts for phenomena. 



It is known from mechanical principles that if a curve line 

 be uniformly stretched, the normal force it exerts at any point 

 in a direction tending to the centre of curvature is directly as 

 the curvature. The same will be the case with a surface, if it 

 be cylindrical, and therefore curved only in one direction. If 

 the surface be spherical or like that about the vertex of an ellip- 

 tic paraboloid, the curvatures in directions at right angles to 

 each other will have independent effects. Consequently the 

 normal force in this case will vary as the sum of the curvatures : 

 and as, from a known property of curve surfaces, this sum is the 

 same for all perpendicular directions, the normal forcewill bepro- 

 portional to the sum of the greatest and least curvatures. Hence 

 because this force, applied at the surface, is employed in de- 

 pressing the fluid when the surface is convex, and elevating it 

 when concave, (for it is always directed to the centres of curva- 

 ture,) it may be shown in the usual manner, that by reason of 

 the action of gravity, the force at each point is proportional to 

 the distance of that point from the ordinary level of the fluid. 

 By reasoning of this kind. Dr. Young is conducted to the rela- 

 tion between the vertical ordinate and curvature of the surface, 

 which is expressed by the fundamental equation of Laplace's 

 theory. As both theories also admit the constancy of the angle 

 made by the fluid surface with that of a given solid at the junc- 

 ture of the two, it is plain that the explanation of phaenomena 

 must be virtually the same in both. In fact, before the publi- 

 cation of Laplace's theory Dr. Young had accounted for most of 



