Measures for Electric and Magnetic Quantities. 393 



With respect to the rest of the statements, I think I must 

 make one remark upon their form. I cannot admit it to be 

 mathematically correct to say that the number of the electro- 

 static units in an electromagnetic (or electrodynamic) unit is 

 equal to a velocity or to any power of a velocity. It is true 

 that Maxwell himself has, in another passage, somewhat 

 modified his manner of expression by adding the word " nume- 

 rically " to the word "equal ;" but other authors, who have 

 followed him in treating of the units, have paid no particular 

 regard to this addition, but have simply retained the above 

 form, to which they have thereby given wide diffusion. 



A manner of expression of this sort permits it to be inferred 

 that formulas of different dimensions in respect of their quan- 

 tity are compared with one another, which is inadmissible. 

 If one wishes to compare a static unit with the corresponding 

 dynamic unit with respect to quantity, one must, as we have 

 above done, express both in one and the same system of mea- 

 sures, and consequently either reduce the dynamic unit to 

 static measure or the static unit to dynamic measure. Thereby 

 are obtained formulas of equal dimensions; and when these are 

 compared with one another, it is found, not that the number 

 of static units is equal to a velocity or to a power of a velocity, 

 but that it is equal to the ratio of two velocities, or equal to a 

 power of that ratio. 



I believe that in investigations like that with which we are 

 here occupied, in which it is precisely the determination of 

 the dimensions of the different kinds of quantities that is 

 chiefly the question, it is essentially important that even the 

 manner of expression in regard to the dimensions be abso- 

 lutely correct. 



§ 7. The Practical System of Measures. 



In all that has been said hitherto the question has been only, 

 how can the units relating to electricity and magnetism be 

 represented by the fundamental units, namely the units of 

 mass, length, and time ? The quantity which has been given 

 to the fundamental units must now be discussed. 



Gauss and Weber, who introduced the electrodynamic 

 system of measures, selected as the units of mass, length, 

 and time the milligram, millimetre, and second ; while the 

 British Association (who in the rest have adopted the system 

 of Gauss and Weber) have, at the suggestion of Sir William 

 Thomson, chosen the gram, centimetre, and second as units of 

 mass, length, and time. 



Both systems of fundamental units, however, furnish elec- 

 trical units the magnitude of which is very different from the 



