212 A. Tanakadate on the Thermal Effect due 



not. In the present case q > q', hence we infer that h > h' from 

 the existence of a maximum. The point of inflexion in the 

 temperature-curve is given by 



***($) <*-*>■■ 



which shows that when there is a maximum the point of in- 

 flexion takes place at a later period than the maximum. 



The ultimate temperature when the current is kept run- 

 ning for a very long time is given by 

 v = q/h — q'/h' ; 

 and, therefore, we see that the curve does or does not 

 cross the zero-line of temperature according as the ratio 

 q/h is < or > q'/h!. See fig. 20, where the temperature of 

 iron ring above that of wooden ring is taken positively. 



So much for continuous current, that is, when the supply 

 of heat is derived solely from the magnetizing solenoid, which 

 forms a kind of anchor-ring shell. Now, when an alternating 

 current is passed, the whole mass of the iron ring becomes a 

 source of heat, which is the subject of the study. The dissi- 

 pativity h! will no longer be the same as before; for the whole 

 mass of iron, instead of conducting away heat from the surface 

 shell, becomes a source of heat, and therefore, when its rate 

 of generating heat is greater than that due to the current it 

 gives heat to the outer shell. 



Put Q for the heat produced per unit time by reversals of 

 magnetization, and H the dissipativity at the point where the 

 thermoelectric junction is placed, then 



v 2 = — tj (1— e~ m ) for the iron ring, 



v 1 = q/h {l~e~ M ) „ wooden ring. 



Expanding v 1 and v 2 and subtracting, 



V2-v 1 =v = (Q + q'-q)t-{(Q + q')H.-qh\ t ^ + .. . 



But q and q r will have a constant ratio, as they are both pro- 

 portional to the square of current, so that we may put 



q — q' = uc 2 , 



and this is what is approximately true, as found by experi- 

 ment (see fig. 22). 



Also as h and H are constants, and H < h and q' < q, from 

 the foregoing investigation we may put 



Thus the rise of temperature of the iron ring above the 

 wooden one, when the same alternating current is passed 



