110 Prof. A. W. Riicker on the Suppressed 



and if we employ the relation 



we see that the right-hand sides of these expressions are all 

 equal to each other and to [M L^ T~^]. 



In this case the secondary fundamental units disappear from 

 the final expression. This would not always be the case for 

 the product of any two units chosen haphazard, but it would 

 always be true that any product or quotient of units could, by 

 the relation 



[K-/.-] = [LT-], 



be reduced to the same dimensions in terms of M, L, T, and 

 either K or //., whether they were or were not originally ex- 

 pressed in terms of one of these two last quantities only. 



The method can be applied, not only to express more 

 clearly that the absolute dimensions of the electrostatic 

 and electromagnetic systems are the same, but to transform 

 the numerical expressions for given concrete electrical or 

 magnetic quantities from the one system of units to the other. 



In order to transform a length from one scale to another by 

 the relation ??, [Li] =n2[L2] we must know not only n^ or n^ but 

 also the numerical value of the ratio Lj/Lg. In like manner, to 

 transform electrical quantities from a system expressed in 

 terms of K to a system expressed in terms of fj,, we must know 

 the numerical value of the ratio 



K-i/ju-i/LT-K 



If, then, V be the numerical value of the velocity of light 

 expressed in terms of the units L and T, we can transform 

 both dimensionally and numerically by the relation 



Thus, to find the number of C.Gr.S. electrostatic units in 3/ 

 C.G.S. electromagnetic units of quantity, we have 



.-. a;=y[L-'TK-ifjL-i] 



To find the number of C. G.S, Electromagnetic Units of Resist' 

 ance in 20 C.G.S. Electrostatic units. 



Working this out from first principles we have, by Maxwell's 

 equations {loc, cit.) (2) and (4), 



[R]=pj =[ML2T-i.-2]; 



