RBPOHT ON CAPILLARY ATTRACTION. 26\ 



body will consequently be repelled from the other. More ex- 

 act explanations of these phaenomena have since been given by 

 Young, Laplace, and Poisson, but not materially differing in 

 principle from the above. 



We ought now to notice the labours of Dr. Young in the theory 

 of capillary attraction, as being next in order of time j but as his 

 paper on this subject was published only a short interval (some- 

 thing more than a year) before the " Treatise on Capillary Ac- 

 tion" by Laplace, and as it contains an idea which is not in 

 Laplace's theory, and which may be considered an additional 

 step towards the complete explanation of the phsenomena, it 

 will be convenient to deviate from the historical order for the 

 purpose of exhibiting more clearly the progressive steps by which 

 the theory of capillary attraction has arrived at its existing state. 

 I will, therefore, now endeavour to give some notion of the prin- 

 ciples of Laplace's theory, and of the extent to which they will 

 explain phsenomena. 



This essay was pubUshed in 1806, as a supplement to the 

 tenth book of the M^canique Celeste. It contains explanations 

 more exact than had hitherto been given of the several facts we 

 have had occasion to mention in the foregoing part of the Report, 

 and of others in addition to these : and the explanations are sus- 

 tained throughout by mathematical calculations. The hypotheses 

 of the theory are, that the fluid is perfectly incompressible ; that 

 there is as well an attraction of the particles of the fluid for each 

 other, as a mutual attraction between the particles of the fluid 

 and the particles of the tube, and that these forces are sensible 

 only at insensible distances from the attractive centres. From 

 these principles a fundamental equation relative to the upper 

 surface of fluid raised by capillary action, is derived by a process 

 of the following nature. 



Conceive an infinitely slender canal, of uniform transverse 

 section, to be drawn from any point of the fluid surface, sup- 

 posed to be concave by reason of the capillary action, to a point 

 of the horizontal surface which is unafiiected by the same cause. 

 Let the canal be everywhere beyond the sphere of the attraction 

 of the solid from which the capillary action proceeds. Suppose 

 its two ends to terminate perpendicularly to the surfaces, and to 

 be rectilinear for a distance from each of them not less than a 

 certain small quantity A, the extent of the sphere of activity of 

 the fluid's attraction : it is proposed to determine the condition 

 of equilibrium of this canal. It is plain that any point of it 

 distant by more than A from its extremities will be attracted 

 equally in all directions. The case is different with all points 

 situated within the distance A from either of the extremities. 



