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 XLVIII. Intelligence and Miscellaneous Articles. 



ON THE DIMENSIONS OF A MAGNETIC POLE IN THE ELECTRO- 

 STATIC SYSTEM OF UNITS. BY PROF. J. D. EVERETT. 



A PAPER* by Clausius, dealing with Electrical and Magnetic 

 -*-*- Units has just reached me ; and I think I shall be doing good 

 service in laying before the readers of the Philosophical Magazine 

 the principal novelty which it contains. 



Electricians are familiar with the fact that a circuit with a cur- 

 rent flowing in it is a species of magnet, and that the moment of 

 the magnet thus constituted is the product of the current by a cer- 

 tain area. 



Hence the moment of a magnet must have the same dimensions 

 as a current multiplied by an area. That is, we must have 



Pole x Length = Current x (Length) 2 ; 

 or, more simply, 



Pole = Current x Length. 

 This equation must be true in any consistent system of units. 



In the electrostatic system, the dimensions of Current (or 

 quantity of electricity divided by time) are M* Ls T~ 2 (M deno- 

 ting Mass, L Length, and T Time). Hence, by the above equation, 

 the dimensions of a Pole are M^ L* T -2 . 



This is substantially Clausius's reasoning, though I have for bre- 

 vity somewhat altered its form ; and it appears to me unimpeach- 

 able. Nevertheless the result differs (as the author points out) 

 from Maxwell's formula for the dimensions of a pole in the electro- 

 static system, namely M^L^. This formula will be found in Max- 

 well's ' Electricity and Magnetism,' § 626, where the name " quan- 

 tity of magnetism " is used instead of " strength of pole," or the 

 briefer name " pole." It will also be found in the Reprint of 

 Reports of the B. A. Committee on Electrical Standards, page 90 ; 

 but in neither work have I been able to find an explicit statement 

 of the reasoning by which the result is obtained. Perhaps some 

 reader of the Philosophical Magazine can give the necessary expla- 

 nation. 



In my own treatise on Unitsf the question at issue is not raised, 

 as practically the dimensions of a magnetic pole do not enter into 

 electrostatic discussions. 



The dimensions of a pole, calculated in the ordinary way from 

 the mutual repulsion of two poles, are M^L^T -1 ; and from this, 

 by considering the force exerted by a current upon a pole, the 

 dimensions of Current in the electromagnetic system are found to 

 be M J L* T -1 . The relation between these two, it will be observed, 



* "Ueber die verschiedenen Maasssysteme zur Messung electriseher 

 und magnetischer Grossen," von R. Clausius. Vorgetragen 6. Marz 1882. 

 Separat-Abdruck aus den Verhandhingen des naturhid. Vereins der prems. 

 Hheinlande, Bd. xxxix. [A full translation of this paper will appear in 

 an early Number of this Magazine. — Ed.] 



t ' Units and Physical Constants ' (Macniillan : 1879). 



