444 MEASUREMENT OF ELECTROMOTIVE FORCES. 



that is to say, that this integral is given by the area of the curvi- 

 linear trapezium MQQjMj. 



Considering a circuit of any two metals A' and A, the electro- 

 motive forces of contact H and Hj are represented by the rectangles 

 MQ' and MjQj, the electromotive force by the curvilinear trapezium 

 MM'MjMj, and the total differences of potential corresponding to 

 the Thomson effect by the curvilinear trapeziums MQQjM^ and 



These different surfaces also represent the calorific energies 

 absorbed or liberated at the corresponding points of the circuit 

 during the passage of unit current. 



1037. RELATION OF THE ELECTROMOTIVE FORCE TO THE 

 CHEMICAL ENERGY IN CLOSED COUPLES. In any closed hydro- 

 electrical battery, the electrical work is evidently taken from the 

 chemical energy; and we cannot conceive any battery in which 

 the reactions, considered as a whole, are not exothermic. The 

 expression for the sum of the chemical works fcr a current of in- 

 tensity I is I2J0/ (259). On the other hand, if the current does 

 no external work, the electrical work is represented by El. If 

 these two orders of work are equivalent, we have 



E = 2J0/. 



In the Daniell couple with sulphates the chemical work reduces 

 to the replacement of copper by zinc, equivalent for equivalent. 

 This replacement corresponds to the disengagement of 25,300 for 

 the chemical equivalent, which, from the preceding relations, gives 

 for the electromotive force of DanielFs element 



2 -53 x 0-432 = i -09 volt. 



a number which agrees perfectly with direct determinations. 



It may be observed that if we assume that the difference of 

 potential is null at the contact of two solutions of copper sulphate 

 and zinc sulphate, the excess H' - H of the differences of potential 

 of the solution over the corresponding metal, leads (1033) to a value 

 very near i'o6 volt for the difference of potential of copper and of 

 zinc. 



The agreement is also satisfactory for the couple zinc-cadmium 

 and sulphates of Regnauld. So remarkable an agreement between 

 theory and experiment had led Sir W. Thomson to propound the 



