108 Prof. A. W. Riicker on the Suppressed 



as J, which is based upon others which have themselves 

 involved the introduction of mass. 



The open admission in the symbols employed that the 

 dimensions of some of the quantities are unknown is more 

 important in the case of the electrical and magnetic than in 

 that of the thermal units. 



As Maxwell showed, the independent relations between 

 these quantities are one less than the number required to 

 determine them completely. The electrostatic and electro- 

 magnetic systems are therefore deduced from assumptions 

 which are equivalent to suppressing the dimensions of induc- 

 tive capacity and magnetic permeability respectively. It 

 would, I think, be better to retain in the tables of dimensions 

 symbols which represented these quantities as secondary fun- 

 damental units. The student would thus have brought more 

 clearly before him the cause of the difference of the dimensions 

 in the two systems, and the factors necessary to transform 

 from the one system to the other would be indicated. 



Thus if, instead of suppressing the dimensions of inductive 

 capacity, we treat it as a secondary fundamental unit of 

 unknown dimensions, we have the equations 



[^g] = [ML-iT-2], [2)] = [Kg]; 

 whence 



[2)] = [M^L-*T-'K^]; 



[g]=[M*L-^T-iK-^]. 



In a precisely similar fashion we get 



[23] = [M^L-*T-V^], 



[.a] = [M^L-^T-V~^]- 



By means of these relations all the units can be expressed 

 in terms of M, L, T, K and M, L, T, jju, and the dimensions 

 of M, L, T are those of the electrostatic and electromagnetic 

 systems, according as the first or second mode of expression 

 is adopted. 



For since 



[^1)] = [e L-2] , .-. [e] = [M^^ L' T'l K^j ; 



and since 



[^]=[mL-2], .-. [m] = [M^L'T-V^]; 



and from the dimensions of [e] and [?7i] those of all the other 

 units can be found. 



Maxwell has given a Table in which the dimensions of each 

 of the electrical and magnetic units are expressed in terms of 



