Liquid Spheres — Molecular Diameters. 885 



coalescence of large spheres to the coalescence of small spheres 

 down to the molecules themselves. The method of obtaining 

 it embodies in its essence discontinuity, involving from the 

 beginning to the end no fewer than p distinct acts of 



N 

 coalescence where 2 P = — , so that p = 75. 



At first thought it would seem that in the latter stages of 

 condensation, where large spheres coalesce, the decrease in T 

 on account of the heat motion of the molecules next the 

 surface would greatly modify our value of N. Whatever 

 effect this would have, however, must necessarily be very 

 slight. For, suppose the first act of coalescence is to form 

 the molecules into pairs, so that the resulting spheres would 

 each contain two molecules. Then, if we consider only a 

 gram mass, the first act of coalescence may be proved to 

 cause a transference of potential energy into heat amounting 

 to L(l — 2~*) calories; the second act a transference of 

 L(l-2-*)(2-*) calories; the third act of L(l- 2"*)(2-*) 2 

 calories ; and so on, the ^th act of L(l — 2"*)(2"3)2- 1 calories. 

 These results are calculated in the table below. 



Table I. 



q. Energy transferred. 



1 lC2-6c. 



2 81-4 c. 



3 64-6 c. 



4 51-2c. 



5 40-7c. 



21 10c. 



75 (final) 0-00000385 c. 



At the completion of the fifth act the spheres each consist 

 of 32 molecules, but the gram mass has suffered a change of 

 potential surface energy into heat amounting to 340*5 calories, 

 or of 68 per cent, of the whole. After the 21st act, which 

 causes a change of only 1 calorie, the total surface energy 

 remaining is only 3*91 calories, or considerably less than 

 1 per cent. Thus we see that the change in T on account o^ 

 the heat motion in the large spheres towards the latter part 

 of the process of condensation would not affect the value of X 

 materially, causing only a slight increase. 



Since the formula obtained above gives the value oi' X so 



