Theory of Surface Forces* 141 



If we put: 



f 'jyW-ft/P, I 2 prdh*= P rV, ( 2 Jh dh*=p s "i? and 



Jl Jl Jl 



Ji 



the expression for H becomes (because ==— = tt*) 



I ? 3 f px-pT p/—p?" Pm'-p,' \ ... (8) 



+ R 2 i 4 + 3 ~~ ~2J 



For the value R=l micron J, = -— (about) for water 



£ 2 

 at ordinary temperature, and so 1^2= 4.10 ~ 6 . If a is a 



quantity of the order p^—p T , we have thus for values of R 

 to the order of the wave-length of light: 



H=fe-^ I )r- f f • (9) 



The equation of Kelvin gives thus: 



Pl Pv R K R K R* V ; 



As R K has a complicate signification, we wish to express 

 pi—fv by means of a formula, where R K is replaced by 



R .r R= li+R?| 



To this end we put the equation (2) into the form: 



(R 1 + h)dpx= — 2(p N — p T )dh, . . . (2 a) 



and integrate with respect to h between and f. In this 

 way we find: 



• p ,- p , = ( p+i*-2i*)g (11) 



In this equation p = ^—^ and p N and p T are resp. the 

 average values of />* and p T ; i. e. : 



1 C 2 1 f 2 



t. j /> N tZ/i and - I /> T dA. 



