112 Prof. A. W. Riicker on the Suppressed 



magnetic induction in 10 electromagnetic units of a system 

 in which the units of length, mass, and time are the metre, 

 centigram, and second respectively, and in which the specific 

 inductive capacity and the refractive index of the standard 

 medium with reference to air are 2 and 1'5 respectively. 

 Assume that K~2/A~i is proportional to the velocity of light 

 in the medium. 



We have already seen that 



[3?]= [M^L-iT-V'] = [Mi L-t K-i]. 



Hence if a subscript refers to air, 



X [(gram)2(cm.)~^ Ka~^] 



= 10 [ (centig.)^ (metre) "^ (sec.)~^ ^^J. 



We may now make the substitution 



K«-^=3 X 10>| (cm.) (sec.)-i -, 



or else calculating the velocity of light in the medium from 

 the refractive index, we may write 



1*5 



^^^ 3x10^ '^"'^"^^^^'^-' ~' ^^^^'^' 

 By the first substitution we get 

 A' X 3 X 10^° [(gram)^ (cm.)~^ (sec.)"^ fx^'] 



= 10 [ (centig.)i (metre)"* (sec.)~^ /i.^] ; 



-'^\M^H0 



= i X 10-" X 1-5 (!")*= 272^^'""- 



By the second substitution, 

 X [(gram) 2 (cm.)"^ Ka "i] 



1*5 

 ^^^^ 3x10^ ^ (centig.)i (metre) "tK"*] 



(10^ Uoy UooMk; 2s/2 



•'• ''~ 2x10^ 



which is the same result as before. 



In such a problem the amount of time and thought saved 

 by the method of dimensions extended to secondary funda- 

 mental units is considerable. 



I think that these examples are sufficient to justify the 

 change in the method of exhibiting the dimensions of electri- 

 cal quantities which I advocate, apart from the great theo- 

 retical advantage of being able to write electrostatic and 



