430 On the Electrostatic Dimensions of a Magnetic Pole. 



such a relation as to the magnetic action of a current, we must 

 assume tacitly these previous relations (which in fact supply 

 our only mode of comparison and verification), viz.: — 



(1) (Pole) 2 x IT 2 = Force, 



(2) Current x L x Pole x L~ 2 = Force. 



The first of these is the purely magnetic starting-point of 

 the electromagnetic system ; and the second is the relation 

 which must be used to connect current with pole on any system. 

 But the electrostatic system naturally starts with the dimen- 

 sions of electric quantity as deduced from the law of inverse 

 squares, whence those of current are deduced at once. Now, 

 the only simple fact of nature which connects pole with cur- 

 rent is Oersted's phenomenon (as developed by Ampere) of 

 the existence of a mutual force between them : this is expressed 

 by (2); and hence by this relation must we deduce the dimen- 

 sions of pole from those of current already found. The some- 

 what recondite fact that the magnetic action of a small circuit 

 carrying a current may be represented as due to two fictitious 

 magnetic poles, does not seem to possess any claims to supplant 

 the natural statement of the only fundamental relation which 

 makes natural poles play a part in electric theory at all. That 

 relation is, of course, itself in its very nature electromagnetic. 



It might be said that the system objected to built up the 

 theory from electric foundations, inasmuch as its fundamental 

 magnet is a small electric current. But, in reply, it is the 

 existence of actual magnets which introduces the idea of pole 

 at all, other than as in Ampere's purely mathematical directrix 

 of electrodynamic action ; and the above considerations seem 

 to show that this result is only obtained at the cost of prefer- 

 ring the fulfilment of the practically composite relation (A) to 

 that of the fundamental electromagnetic relation (2), in the 

 specification of an electrostatic system. This, though allow- 

 able if consistently adhered to, does nor seem to be natural — 

 if indeed the specification of a magnetic pole on an electro- 

 static system is a matter of importance at all. 



The method indicated gives Maxwell's dimensions, L*3lA 



In practice, one would most probably investigate the dy- 

 namic relations of statical charges with a galvanometer, and 

 not with an electrodynamometer. 



Queen's College, Gahvav. 

 May 10, 1862. 



