434 On the Electrostatic Dimension* of a Magnetic Pole. 



where k t has the value unity in the electromagnetic system, 



and the value -s in the electrostatic system, there being here 



v 

 no difference between Maxwell and Clausius. 

 The mutual force of two magnetic pole- is 



h x Product of poles -f- (Distance)-, . . (5^1 



where k s is r 2 in the electrostatic system of Maxwell, and -^ in 



that of Clausius, but is denned as unity in the electromagnetic 

 system. 



On the other hand, the mutual force of two charges of elec- 

 tricity is 



Z- 6 x Product of charges -h- (Distance) 2 , . . (6) 



where k 6 is defined as unity in the electrostatic system, but 

 has the value v 2 in the electromagnetic system. 



A comparison of the foregoing six equations shows how 

 cautious we ought to be in asserting that a particular dimen- 

 sional relation " must hold in every system of units." The 

 laws of nature which connect dissimilar quantities are laws of 

 'propwtion, and it is only by convention that they can be stated 

 as laws of equality. Clausius was in error in the assertion, 

 which I adopted from him in my last communication, that in 

 every system the product of the current by the area enclosed 

 must be equal to the moment of the equivalent magnet. Pro- 

 portional would be the correct word; and the factor £ 3 , which 

 remains constant as the current and area vary, does not neces- 

 sarily retain the same value when we pass from one set of 

 units of length and time to another. Maxwell says (§ 482) : — 



" It has been shown by numerous experiments that the 



magnetic action of a small plane circuit is the same as 



that of a magnet .... whose magnetic moment is equal to the 

 area of the circuit multiplied by the strength of the current ;"' 

 but the passage occurs in a discussion in which the " Electro- 

 magnetic system of measurement " is employed and defined 

 (see § 479). I do not think that the charge of mistake brought 

 against Maxwell has been substantiated. The controversy, 

 however, has done good in exposing the difficulties : and 

 dangers which lurk in applications of electrostatical units to 

 magnetism. 



