666 RICE ART. L 



equation [612], whereas, owing to [613], pis practically constant 

 throughout the interior of the film. The law of variation to 

 which the behavior of the potentials will actually approximate 

 may be worked out in the simple case dealt with in this para- 

 graph. Let *Si be the water and S2 the soap, which exists in 

 excess at the surface, so that r2 > Ti; we may take it that in 

 the interior 71 > 72. Since 



and 



da = — Ti dn\ — V2 d/jL2 

 da , . 



it follows that 



TiMi + r2ju2 + (Fi + V2)gz = constant. 



Moreover, since the pressure is practically uniform through- 

 out the interior 



dz ' 



and so by [98] 



or 



dm dn2 



TiMi + 72M2 = constant. 



From these two equations in /xi and H2 we can eliminate fii 

 and obtain 



(ri72 - r27i)Mi + 72(ri + T2)gz = constant. 



Since by our assumptions the coefficient of ni in this is 

 essentially negative while that of z is positive, it follows that 

 fii, the potential of the water in the film, increases as we rise. 

 On the other hand in the atmosphere the potential of the water 



