E = — A3^— 2-^' 



400 PROCEEDINGS OF THE AMERICAN ACADEMY § lO 



Substituting this value in the equation 



2A - 



-J -yj -\- 2 P" = o, we have 



P' 

 -—jj- = 1.228, nearly, whence 



—= 0.228, nearly. 



6, 7^ \6 



Substituting for P'' its value, P/' -^ = P,'' f^j f-L\ 



6 



p' = 0.09566 (^A) p;^ IV. 



7^=. 0.01776 (^-^)V/ V. 



The last expression was obtained by taking the differ- 

 ence of two very nearly equal values, and is therefore not 

 very reliable. If the atoms are spherical, the appar- 

 ent molecular diameter (or shortening of the free path) 

 will be less, the further the molecules are apart; in a 

 linear expansion, therefore, of from forty to fifty per 

 cent., we must on this account look for a greater free 

 path, and consequently a less kinetic pressure; further- 

 more, since for great distances the law of variation of the 

 magnetic attraction is inversely as some power much 

 greater than the fourth, and we have supposed that the aver- 

 age power is the fourth, it follows that at short distances 

 the attraction, according to the analogy, cannot vary quite 

 so rapidly. Both these causes combined would tend to 

 diminish the external pressure, the first by lessening the 

 frequency of impact of the molecules (or atoms), the 

 second by holding them more closely together; the result 

 is that we must expect to find that the external pressure, 

 calculated in this way, is considerably too great. 



