Determining the Radiation Constant. 211 



given above, 



lt =pAe~^ 



and since we only want the initial rate of rise of temperature 

 d!l 



^ - [pAe-P t ] t=0 =pA 3 



but d# _ XpAn 2 



dt t=0 ~ p 2 — kp-\-n 2 ' 



Hence ^t _ \_ y-k P +n 2 del 



dt t= - pK ~ ~tf~~ 'Ttf" 



By plotting galvanometer deflexions against the times, 



we can eliminate the oscillations and obtain the initial rate 



30 I 

 of change of 6, i. <?. — /X, from the curve. (And since we are 



I dO I 



only concerned with the ratio of -j- / A, we can use galvano- 

 meter scale-divisions instead of radians.) 



Consequently, then, in order to obtain the initial rate of 



dO ! 

 rise of temperature, the observed -=- M, must be multiplied by 



(p 2 — kp-\- n 2 )/n 2 . 



Should p 2 — kp be small in comparison with n 2 , this fraction 

 may evidently be neglected. But to test this we must first 

 find n, p, and k for the particular galvanometer in use. 



(i) To find n : 



If the circuit is open, k is negligible and 2ir/n is the time 

 of swing. Or, if the observed period of free swing be P 



then n = 27r/P. 



(ii) To find &: 



For the deflexion on closed circuit we have 



and if successive deflexions or elongations 0j, 2 , 3 , and 4 

 be observed it is easily seen that 



aAK 



