792 Dr. R. D. Kleeman on the Nature of the 



The work done in moving the molecules lying on a line at 

 right angles to AB to infinity is 





F.dn. 



Therefore the work done in removing a cylinder one cm. 2 in 

 cross-section standing on the plane AB is 



-I rc = aof»°° 



4^(2c«) 2 2 F.dn 



I 71 = 00 /~'°° V=<K> U = co W = ao (" ~\ 



= Utc a Y t 2 2 2 *-UV{(»+w)'+«'+i>*U 



«^a ?i=l »/ w v=-oo m= — oo w=0 ^ J 



(n + w) . dn 

 X V{(» + w) s, + M a + t^} 



/ p \ 1/3 

 Since &'« = (— I 



this gives X=1Q"-GS«J»*4Q, 



where Q is a function of x a . We have seen that a*Q or k" 

 is the same for all liquids at corresponding states (equation 2). 

 This is realized if <j>(z) is taken to be of the form 



where x c is the distance between the molecules at the critical 

 temperature. The surface-tension is then given by 



*=\$c a yM=(pJ(tc a yM, 



where M is a function of — , and this is the same for all 

 liquids at corresponding states since — = ~ } and — has the 



&C Pc Pc 



same value at corresponding states. 



The preceding investigation gave that <f>(z) must be of the 

 form <£(c, a, /3), when the matter is evenly distributed in 

 space. The result just obtained shows that </>(z) must be of 

 the form 



which, it will be seen, is a special case of <f>(z, a,/3). 



