210 A. Tanakadate on the Thermal Effect due 



It was found, however, in the course of experiment that 

 when a continuous current was passed through both the rings, 

 the tendency of the temperature of the thermo-j unction at the 

 wooden ring was to rise above that at the iron ring, principally 

 due to the difference of thermal diffusivity. But when the 

 current was made to alternate, this was entirely overmasked 

 by the heat arising from reversals of magnetization. 



Thus, in order to find how much heat is due to the reversals 

 of magnetization, a proper amount of allowance must be made 

 for the heat diffused and radiated. A satisfactory way of 

 arriving at the rate at which heat is generated in the substance 

 of iron would be to solve the general equation of the conduction 

 of heat when part of the conducting medium is generating 

 heat. Such an equation will be 



dv o / 



— =,cy 2 v + q/c, 



with proper boundary conditions as to time and space : v being 

 the temperature, t time, k diffusivity, q the rate of genera- 

 tion of heat per unit volume per unit time, c thermal capacity 

 per unit volume. 



Now when q is constant and the sole source of heat, 



t=0, V = 0, 



and therefore fdv\ , 



that is, the time-rate with which the temperature begins to 

 rise is the true measure of the rate of generation of heat in 

 the substance. As soon, however, as the elevation of tempe- 

 rature becomes sensible, heat will be diffused inside the body 

 and radiated into the outside space. But whatever be the way 

 in which heat is conducted in the body, when we consider the 

 time-variation of temperature at a definite point in the body, 

 the law of diffusion of heat will be expressed by 



dv 1 



where h is a mixed coefficient depending upon conduction and 

 emission, as the generating body is in contact with other 

 conducting body as well as being exposed to the air. This 

 mixed coefficient h might be called dissipativity, as it measures 

 the rate at which heat is taken away from the generating 

 body irrespective of how it is done. 



Putting the single letter q for q/c for convenience, the above 

 equation with the initial condition t = 0, v = 0, gives 



v=Ul-e- M ). 



This will be strictly applicable to the rise of temperature in 



