262 Professors W. E. Ayrton and J. Perry on 



or 



a 2__ a 2 > 



2 1 ^ 



20 



Ki log 10 e 

 It will be found that 



u\— a^ = 20 approximately in all cases ; 



so that the above consideration reduces itself to 



or 



t 2 <10Knog 10 e, 

 O 2 



K 



< 4-343* (12) 



For small values of a, such as we have not to consider in cal- 

 culations of K, we use a different number from 2 in the ratio 

 of inequality and we get different results. Notably we see 

 that when a. is very small, as in Mr. McFarlane's experiments 

 (described in Proc. Roy. Roc. 1873), and in those on radiation 

 in different gases at different pressures which we are at pre- 

 sent carrying on, the second term in the series almost at once 

 becomes insignificant. 



Second. Our next consideration, in connexion with the de- 

 termination of the size of the ball, is to arrange that the fall 

 of temperature shall not be too rapid ; otherwise it cannot be 

 accurately measured, nor can the external temperature be kept 

 constant. We may take it for granted that when v is, say, 50° C, 

 the fall of temperature should not exceed 1° C. in 15 seconds, 

 or 



dv _ 1 . 



dt 



or mv, 



l K 



<15 



so that m, or -^-j, must be equal to or less than 



15 x 50' 



or 0-00133. 



This condition, for different values of a, becomes as follows :- 



o o 2 



If a = 10, then -^- must be equal to, or greater than, 22*904 ^ 



366-54 

 1465-9 

 2771-3 

 3298-1 

 3870-9 

 4489-2 J 



= 4U, 



>? 



?? 



V 



= 80, 



?? 



>? 



?? 



= 110, 



?? 



V 



V 



= 120, 



?? 



?? 



?? 



= 130, 



•? 



?J 



V 



= 140, 



V 



V 



>7 



