304 MEASUREMENT OF CURRENTS. 



Integrating this expression for the time 0, and determining the 

 constant by the condition of having T = T , for /=0 we get 



/. 



I-y i+( a -y)T JM ;o 

 The coefficients a and < being very small, we may write 



If the current is constant, the first member of this equation is 

 equal to I 2 . With a variable current the experiment gives the mean 

 square of the intensity. As the phenomenon only depends on the 

 square of the intensity, the method may be used for alternate 

 currents. 



We may vary the experimental arrangements in many different 

 ways. One of the simplest is that in which the calorimeter itself, 

 having the shape of a thermometer, gives the temperature directly. 

 If the current passes continuously, the heating of the calorimeter 

 is constantly compensated by the loss of heat. As this latter 

 is sensibly proportional to the excess of temperature of the ther- 

 mometer over that of the surrounding air, the mean square of the 

 intensity of the current is proportional to this same excess of tem- 

 perature. 



One source of error, which is inherent in the method, is that 

 during the passage of the current the interior of the wire is neces- 

 sarily at a higher temperature than the external. It follows from this 

 that the real resistance is greater than that calculated' for the tem- 

 perature of the calorimeter. The method would give in general too 

 high a value for the intensity of the current. 



In order to determine this intensity in absolute value, we must 

 know the absolute values of R and J. The number J is usually 

 expressed in kilogrammetres, and the quantity of heat in kilogramme 

 degrees. Seeing that the kilogrammetre (612) is equal to io 5 C.G.S. 

 units, and that Joule's number 425 is generally assumed for the 

 equivalent of heat, it follows that the value of J in C.G.S. units, 

 the heat, being expressed in gramme degrees, is about 4.17 x io 7 . 



* JAMIN and AMAURY. Comptes rendus, Vol. LXX., p. 661. 1870. 



