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



easily shown that practically 



8m __ 8v 

 m v ' 



and we know from experience that there is no great error in 



the determination of m unless the determination is made from 



ov 

 very small values of v : consequently — is small. Again, 



since 



SN 8m 8v 



-—=77^ — + — ; 



JN m v 



and as m is about O'OOl in our experiments, mt will be prac- 

 tically between 1 and 3 for values of t between 1000 and 3000 

 seconds, so that 



-^7? is between 2 and 4 times — 



If we suppose the errors in the measurements of r and C (the 

 radius and specific heat per unit volume) to be negligible, we 

 have for the error SK in K, arising from an error 8v in v and 

 8v in v , 



SK _ 8m 8cc 



K m a 



= 2 — approximately. 



But it may be easily shown that the error 8a in a is such that 



8a _ /SN _ 8v \ N (a— sin a cos a) 2 



a \ N v J 2v a sin a (a 2 + a sin a cos a — 2 sin 2 a) 



_U to 4^__. H'\ (sin«-acosft)(a-sin«cos«) 

 \ v v / a sin «(a 2 + a sin a cos a — 2 sin 2 a) ' 



consequently it follows that the value of -~- will, as a rule, 



really depend on the value of the trigonometrical expression 

 in equation (10). 



Similarly we may prove that 



SE _8m 8a a 2 -{-a sin acos a — 2 sin 2 a 

 E m a sin a(sin a — a cos a) 



&> /^ j j $0 8u \a — sinacosa . . , ,.,.,,. 



= {-(2 to 4 ) ^ approximately: (11) 



v \ v Vq/ asm - a rr ■" v J 



