Law of Molecular Force. 311 



of the surface-layer, namely 2Ta/R. We see that this tension, 

 or the energy per unit surface, is 



N/2(l-sin6') + sin6'- — ^(l-sin6>)^ 



a = 7rp2Ae< 3—1 + ; r-; , \ 



'^ Uos6' l-sin^+N/2(l-sin6') J 



This equation is founded on the assumption that the capillary 

 tube is so small that the meniscus-surface may be considered 

 to be a portion of a sphere. When this is not close enough 

 to the truth we shall require a more extended investigation of 

 the necessary form of the meniscus, but for present purposes 

 the above will suffice. It gives us an important relation 

 between the parameter A and the surface-tension, but one 

 involving the unknown average density p of the surface-film, 

 and the angle 6 which is difficult to determine. But, however, 

 as 6, if not zero for all ordinary liquids, is small, we will 

 assume it to be zero, so that the bracketed expression above 



reduces to ~. And as in the first case we desire only 



2 + V2 -^ 



relative values of A for a number of substances, we cannot go 



far wrong in assuming that, at their boiling-points, the ratios 



of the mean density of the surface-film of different liquids to 



the ordinary densities are approximately the same ; we will 



therefore write p Cf-p, and reduce our equation above to the 



form a. crAp^e. 



Now it is natural to suppose that, in different liquids, e is 



proportional to the mean distance apart of the molecules in 



the surface-film, that is to the cube root of the molecular 



domain (usually called the molecular volume) ; 



.*. ^ cc ^m/p oc Vm/p : 



so that finally l-Ap^mi = u, where k\sa constant approximately 

 the same for all liquids if the tension a is measured at the 

 boiling-point ; but the strict equation for any one substance is 



Ap^mi a a. 



Eotvos's result is that 



d 



dt I "Vp 



for most liquids, which, according to our equation above, gives 



|(Mmp) = -227 



Mm^ = -227 

 dt 



{.{ff}=-m 



