226 On the Dimensions of a Magnetic Pole. 



an electric current, since this statement is only intelligible on 

 electrodynamic considerations. The theory in this form seems 

 rather hypothetical for the foundation of a system of units. 

 Prof. Clausius does not think it objectionable that his formula 

 for the magnetic force between two poles is not in the electro- 

 static system of units of the dimensions of a force. But since the 

 attraction between two poles is as much a force as the attraction 

 of the sun on the earth, if the expression mm' / r l is not of the 

 dimensions of force on the electrostatic system, it is clear that 

 this formula no longer represents the force between two poles, 

 and that another factor must be introduced to make the ex- 

 pression of the right dimensions. Now it is one of the great 

 advantages of Maxwell's system that all his formula? are true 

 as they stand, and do not require the arbitrary introduction of 

 a factor on passing from one system of units to another; these 

 factors introduce themselves naturally through symbols repre- 

 senting some physical property of the body or medium. As 

 Maxwell does not dwell on this point in his book, I may be 

 pardoned if I quote a few illustrations of it. 



Using the notation of Maxwell's treatise, the force between 



ee' 

 two electrified particles = — :,, where k is the specific induc- 

 tive capacity of the substance. Now in the electrostatic 

 system the dimensions of e are (M^L^T -1 ), and k is of no 

 dimensions in mass, space,.and time. In the electromagnetic 

 system the dimensions of e are M^IA and k is of dimensions 

 L -2 T 2 . Thus in both these systems the expression ee' / nr* 

 is of the dimensions of force; and the factor changing from 

 the one system to the other makes it appearance in the k. 



The same thing is true for the force between two magnetic 

 poles. The expression for the force is mm' / fir 2 , where fi is 

 the magnetic permeability of the substance. In the electro- 

 static system m is of dimension [M*L^], and fi of dimensions 

 [L -2 T 2 ]; in the electromagnetic system m is of dimension 

 [MjL'T -1 ], and fi of no dimensions; thus in both systems 

 the expression mm! / fir 1 is of the dimensions of force. Other 

 illustrations might be given; but the reader can easily verify 

 the statement that in Maxwell's system every equation is true 

 as it stands; and consequently, whenever we have a purely 

 dynamic effect, the expression for it will be of the same di- 

 mensions in both systems of units. 



I am, Gentlemen, 



Your obedient servant, 



J. J. Thomson. 



