CapUlary Attraction. 71 



of such lubes 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 the same whatever the diameter of the 

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

 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 witli 

 these distances; and that the internal curvature \w 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 «= the quantity of fluid raised in any ver- 

 tical capillary tube; iv^= the weight of a portion of tlie fluid whose 

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

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



internal perimeter of the tube, then nm=p of n=^~' Now au? 



lit 



aw 

 the effect of all the laminae .*- — = tlie effect of one of them (since- 



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



mo awm aw r \ c^ 



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



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

 angle, d; and that a^= the quantity of fluid raised; w^ when resolved 

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



plane,) becomes sin^w;.". as before^ -=c (2). 



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

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



D'HP 



tube being supposed to be vertical) then a= ~";i — '' ^::=DP.'-. 



, ^ aw DHiP ^^^ ^^ 



by (1) — =--7— =r, or DH=— 



1 



con- 



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



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

 \ ever*?, maybe: this result, together with (1) and (2) have been 



I 



obtained by La Place in his theory of capillary attraction. 



