360 PROCEEDINGS OF THE AMERICAN ACADEMY § 2 



particles may be situated with respect to the common line of 

 resolution; and hence the resultant force of cohesion, per- 

 pendicular to any surface, due to the action of all particles 

 on one side of that surface upon all particles on the other, 

 will also vary as the Ath power, inversely, of the ratio of 

 expansion, while the area of the surface separating a given 

 number of molecules will vary inversely as the square of the 

 ratio of expansion. It follows that the resultant cohesion 

 /^", measured in dynes per square centimetre of surface, 

 will vary inversely as the x -\- 2^ power of the ratio of 

 linear expansion. 



Denoting, therefore, by P^' the value of the cohesive 

 pressure when the volume is V^ and the average molecular 

 distance /, we shall have 



X -\-2 



P" L'^' V. 3 



o ' o 



o 



also, taking logarithms, 



3 log / — 3 log 4 = log V— log f; 



whence, by differentiation, 



dl _ dV 

 ^ I V 



Now it is established in thermod3aiamics that the work 

 hW done in the (small) expansion SF against the press- 

 ure P IS 



hW=P"hV, 



hence the total work necessary to overcome the cohesive 

 forces in expanding from a volume F, to a volume V^ will 

 be 



I 



