§11 OF ARTS AND SCIENCES. 403 



(6") of each surface must be overcome through the dis- 

 tance of one centimetre, requiring an expenditure of en- 

 ergy equal numerically to twice this tension; the density 

 of the film being D and the thickness /, the weight will be 

 ID and the equivalent of the internal latent heat JLID, 

 about two-thirds of which is required to laminate the 

 liquid in this w^ay. Equating the two expressions for the 



work, we have '534 7 —. 2 S, whence 



(19.740) K 



7 _ 3-1 5 J^S .. 



a formula by which the absolute thickness of a molecular 

 film may be calculated according to the theory.* 



If we could regard the cohesive pressure across a 

 square centimetre of surface as the sum of the contractile 

 forces of a suflicient number of films of thickness /, and 

 cutting the surface at right-angles, we should at once 

 obtain an expression for the cohesive pressure; but we 

 must remember to take into account the eflfect of oblique 

 action, and the accumulative attraction of successive 

 shells, which will increase the results in the ratio of the 

 two series, (i) and (2), 



(1) I + (i-)' + (ly + (1)^ + etc. 



+ a)' + (i)' + (i)' + etc. 



+ {.ly + (Ay + etc. 



+ (i)^ + etc. 

 -|- etc. 



(2) I + (1)' + ay + (i)' + etc. 



+ («' + iiy + i\y + etc. 



+ (i)' + etc. 

 + etc. 



* The usual expression for this thickness, / = -—- — , entirely disregards the fact that the 



JLD 



liquid is only partly volatilized when reduced to a thin film. For the results of another method 



of calculating the molecular diameter, see Riihlmann, Volume IL.page 237. 



