OF CAPILLARY ATTRACTION AND THE COHESION OP FLUIDS. 425 



tube, the surface forms itself into a hemisphere, with its vertex down- 

 wards and its base horizontal, in which position it nearly touches the 

 interior surface of the tube ; but when the fluid rises between two 

 planes, the surface assumes a circular form, having for tangents the 

 planes by which it is attracted. 



These experiments and particulars being premised, we shall now 

 proceed to develope the theory of calculation ; and in order that it 

 may be invested with all the interest of which it is susceptible, we 

 deem it advisable to adopt the method of M. le Comte La Place, 

 one of the most profound and sagacious philosophers that have existed 

 in this, or in any preceding age. 



PROBLEM LXVIII. 



533. A cylindrical tube of glass, whose diameter is exceedingly 

 small, has its lower extremity immersed in a vessel of water, 

 and its axis vertical : 



It is required to determine with what force the water rises 

 in the tube, by means of the attractive influence of its surface. 



Let abed represent a vertical section of a vessel, filled with water 

 to the height BC, and let AB be the 

 corresponding section of a small cylin- 

 drical tube immersed in it at the lower 

 extremity, and having its axis perpen- 

 dicular to the surface. 



The fluid rises in the tube above its 

 natural le^vel, a thin film being first 

 raised by the attraction of the inner 

 surface of the glass ; this first film of 

 fluid raises a second, and the second a 

 third, and so on, until the weight of the 



elevated fluid exactly balances all the forces by which it is actuated, 

 viz. the attractive influence of the glass, and the mutual adherence of 

 its own particles. 



Let us now suppose that the inner surface of the tube is produced to 

 E, then carried horizontally to D and vertically to c, and let the sides 

 of this extended tube be conceived to be so extremely thin, as to have 

 no action whatever on the contained fluid, and not to prevent the 

 reciprocal attraction which obtains between the real tube AB and the 

 particles of the fluid ; that is, let the portion BEDC of the tube be so 



