344 Mr. A. M. Worthington on the 



be the repulsive reaction between (B) and the third layer; 

 and this exceeds the repulsive reaction [(1) (2)] between A 

 and the second layer by the amount 



F 2 + F 3 + F 4 + + F W . 



Again, the total attraction downwards on every molecule C 

 of the third layer is SF. The repulsive pressure downwards 

 is 22F — F l7 and the upward attraction is F x -f F 2 . Therefore 

 the total resultant action downwards is 



3SF-2F 1 -F S = F 1 + 2F 2 + 3F 8 + 3F 4 + + 3F„; 



and to maintain equilibrium this must therefore be the repul- 

 sive reaction [(3) (4)] between each molecule C and the 

 fourth layer ; and this exceeds the repulsive reaction [(2) (3)] 

 by the amount F 3 + F 4 + . . . . + F». 



Similarly, the repulsive action [(4) (5)] between the fifth 

 layer and a molecule of the fourth will exceed the reaction 

 ](3) (4)] by the amount F 4 + F 5 + . . . , +F„, and that 

 between the n + lth. layer and a molecule of the nth will 

 exceed that between the nth. layer and a molecule of the 

 (n — l)th by the amount F», after which the excess will be 

 zero. It is thus seen that, in order to maintain the equili- 

 brium, the repulsive reaction between consecutive layers 

 must increase with the distance from the surface till a depth 

 equal to the radius of the molecular action is attained, after 

 which a constant value is required. 



7. Now let us assign to the liquid such a temperature as shall 

 maintain the molecules in the interior at the distance apart at 

 which we have placed them. 



The repulsive reaction is now too great to maintain the 

 equilibrium of the molecules near the surface. If left to 

 themselves, these molecules will recede from one another, and 

 those at the surface will recede furthest. In other words, the 

 density of the liquid will diminish as we rise to the surface; 

 and it is evident that such a condition is one of stable equi- 

 librium, and therefore permanent. For by the increase of 

 distance the repulsive heat-force diminishes, as we have 

 seen, more rapidly than the force of cohesive attraction. 



We may either suppose the readjustment of the mole- 

 cules near the surface to involve only an increase in distances 

 parallel to the Surface, while the distance between adjacent 

 layers measured normally to the surface remains the §ame 

 as in the interior of the liquid ; or, on the other hand, the 

 adjustment may involve an increase in molecular distances 

 both parallel and perpendicular to the surface. The latter 

 supposition is the more general, and, as we shall see later, is 



