426 PROCEEDINGS OP THE AMERICAN ACADEMY 



By combiuing equations (e) and (d) we obtain 



and d7n may be written 



dm =. — d 



S 



(in 



de\' 



These equations were obtained by Lippmann. They show the close 

 relation existing between contact electricity and superticial tension. 

 The equations contain all the results of Lippmann's experiments ; and 

 though these experiments were made only upon special substances, yet 

 it seems probable that the conclusions can be extended to all sub- 

 stances. 



If the electrical charge for any transformation is kept constant, 



From Section IV., page 422, it is seen that — is plus below a cer- 



a e 



tain value of e for mercury. As the curve representing the change of 



d^k . de 



k with e is concave toward e, -^—r^ is minus. Hence y-^ is plus, or be- 



low a certain limit the difference of potential increases as the area of 

 the surface increases. 



Substances which do not act chemically on each other follow Volta's 

 tension law. In any closed circuit at uniform temperature the sum of 

 the differences of potential between the elements of the circuit is null. 

 From II. of Lippmann's experiments is obtained a simple method 

 of finding the superficial tension between two liquids, which do not 

 act chemically upon each other, when we know the superficial tension 

 between each of these liquids and a third liquid. 



Let the contact electromotive forces between A JB, B C, CA, be 

 Cy e.„ fg, respectively. Let ^-j, k.^, k^ be the superficial tensions corre- 

 sponding to these differences of potential. 



^j = <^ (e,) .*. ^1 = 4>~^ K' 

 Also, 



e., ■=. <ji~^ k^ and e.^ = <jr^ k^. 



