382 Di\ R. A. Lehfeldt on Electromotive 



where i is now a factor no longer identical with l-\-(n — l)y, 

 but such as to take into account the deviations from Boyle's 

 law as well, the deduction by means of the cyclic process will 

 still be true ; yielding equation (2) in the form 



which in turn gives the same graphic result as before — that 

 expressed by equation (3). 



Now with regard to' the deviations from Boyle's law, the 

 most natural assumption one can make is that the osmotic 

 pressure changes roughly in the manner indicated by 

 van der Waals's equation, i. e. as the pressure is increased 

 the volume (dilution) tends towards a limiting finite value 7 

 rather than towards zero. The effect of this difference is 

 important : if the electromotive force of a concentration-cell 

 be proportional to fPdV, its value as calculated from 

 van der Waals's equation might not differ sensibly from that 

 calculated according to Boyle : indeed, if we put 



p =vS W 



(neglecting the surface-tension term in the gaseous equation), 

 we obtain a rectangular hyperbola parallel to the original one 

 and the value of fP^Y is strictly unchanged. But if the 

 electromotive force depends on \YdF, the case is different: 

 as may easily be seen by reference to the diagram, the area 

 between the curve and its vertical asymptote is increased by a 

 rectangular portion whose area is simply proportional to the 

 difference of pressure between the limits of the integral. 



(iv.) TJte Electrolytic Solution Pressure. 



Now Nernst's representation of the electromotive force 

 between a metal and solution by means of the electrolytic 

 solution pressure of the metal consists essentially in finding 

 what value of P must be taken as the upper limit of the 

 integral in order that, with the osmotic pressure of the 

 solution for lower limit, its value may correspond to the ob- 

 served electromotive force. In order to accomplish this with 



E proportional to fPdV (and assuming Boyle's law to 

 p 



logYr) it is necessary to take for the value of P at the upper 



1 

 limit 



XI = 10 19 atmospheres 



