210 Mb POWER'S THEORY OF 



It is convenient to give a name to the quantity H \ we will call 

 it the capillary affinity between the two materials of which the tube 

 and fluid are composed. 



It is easy to see that the quantity H will remain unchanged if we 

 conceive the tube and the fluid to exchange their materials; for, by 

 the equality of action and reaction, the elementary attractions, of which 



cH 



—— is the sum, will be equal in the two hypotheses. The tube may 



be regarded either as solid or fluid, and this fluid may be either the 

 same as that which fills its interior or a different one. 



If we conceive the density of the inner fluid to be diminished in 

 any ratio, all the elementary attractions, and therefore H, will be 

 diminished in the same ratio ; and if, further, the density of the tube 

 be diminished in any ratio, H will be diminished in the compound 

 ratio. 



10. Next, let u and v be the original quantities by volume of two 

 vmmixed fluids. Then, if no penetration of dimensions takes place, 

 u + v will be their volume after mixture. If we regard the fluids after 

 mixture as coexisting, each with a diminished density, within the same 

 volume u + v, calling r, and pi these diminished or partial densities, 

 (r) and {p) the densities of the unmixed fluids, we shall have 



,^ J and 7— , 



{r) u + v \p) u + v 



whence 



^ +-^ =1 



{r) ^ (p) 



Again, 



ri + pi = r, 



r being the total or ordinary density of the mixture. The two last 

 equations serve to express ri and pi in terms of /•, (;•) and {p). 



