OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 433 



but since d is conceived to be very small in comparison with b, the 







horizontal breadth of the plates, the fraction may be considered as 



evanescent, and then we get 



The solidity of the fluid parallelopipedon corresponding to the 

 mean altitude, is expressed by bdh'i but this is equal to the whole 

 quantity of fluid raised ; therefore we have 



bdh'=bd{h + Jd(l J*0}, 

 from which, by casting out the common terms, we get 



A'= A +Jrf(l TT); (318). 



Now, (1 |TT) is a constant quantity ; hence it appears, that the 

 mean altitude varies inversely as the distance between the planes. 



547. Let the symbol for the mean altitude, be substituted in 

 equation (317), instead of its analytical value as expressed in equation 

 (318), and we shall obtain 



where the value of the constant quantity is the same as before ; hence 

 we have 



rfA'=.0214. (319). 



The practical rule which this equation supplies, may be expressed 

 in words, in the following manner. 



RULE. Divide the constant number 0. 021 4 by the perpen- 

 dicular distance between the planes, and the product will 

 give the mean altitude to which the fluid rises. 



548. EXAMPLE. The parallel distance between two very smooth plates 

 of glass, is 0.06 of an inch ; now, supposing the lower edges of the 

 plates to be immersed in a vessel of water ; what is the mean altitude 

 to which the fluid ascends ? 



Here, by operating as the rule directs, we have 

 h' = 0.0214 -f. 0.06 0.356 of an inch. 



In this example, the distance between the planes is the same as the 

 diameter of the tube in the preceding case, but the mean altitude of 

 the fluid is only one half of its former quantity ; hence it appears, 

 that if the tube and the planes are of the same nature and substance, 

 and the radius of the one the same as the distance between the 



VOL. i. 2 F 



