Capillary Attraction. 71 



of such tubes to be composed of an indefinite number of laminae, 

 of uniform and equal width, which are parallel to the axes of the 

 tubes. My object is to find the effect of one of these laminae, and 

 to show, that it is always tlie same whatever the diameter of the 

 tube may be. It has been proved abundantly by experiment, that 

 the attraction between the fluid and tubes extends to imperceptible 

 distances. I hence infer, that the diameter of any capillary tube 

 may be regarded without sensible error as infinite in comparison with 

 these distances ; and that the internal curvature in cylindrical tubes, 

 and the angles in those of a prismatic form do not sensibly affect the 

 attraction between the fluid and tubes, nor the attraction of the par- 

 ticles of the fluid to each other. From these principles it is evident 

 that the effect of one of the laminae is the same as if it was detach- 

 ed from the tube, and inserted by itself in the fluid, which effect is 

 manifestly constant. Let a= the quantity of fluid raised in any ver- 

 tical capillary tube; w= the weight of a portion of the fluid whose 

 mass is denoted by unity; then aw= the weight of a ; put m= the 

 width of one of the laminae, and n=- the number of them ; p=- the 



P 

 internal perimeter of the tube, then nm=p or n=--- Now aw = 



the effect of all the laminae .'. — = the effect of one of them (since 



they evidently produce equal effects ;) hence by what has been shown 



cnv awm . aw 



— =^ = const, or (since m=const.) — — const. =c. (1). Sup- 



n p ^ ^ p \/f 



posing now that the axis of the tube is inclined to the horizon, at the 



angle, ^; and that «'= the quantity of fluid raised; w, when resolved 



in the direction of the axis of the tube (by the theory of the inclined 



plane,) becomes sin^w.'. as before -_ =c (2). 



Let the internal surface of the tube be C3dindrical, D= the diam- 

 eter, H= the mean height of the fluid; 3.14159 etc.=:P; (the 



, , . D--HP 



tube bemg supposed to be vertical) then a= — ^^ — j p=DP.', 



aw DHmj 4c 



by (1)— ■= — -^ — =c, or DH=— =const. (since c and w are con- 



1 



stant)or H is as -j^- It is evident by (1) and (2) that the vertical 



height of the fluid in the same tube is constantly the same, what- 

 ever &, may be : this result, together with (1) and (2) have been 

 obtained by La Place in his theory of capillary attraction. 



