On the Dimensions of a Magnetic Pole. 531 



Clausius gives "C x L 2 =P x L in any consistent system ;" so 



P C 

 The equation C X L 2 = P x L leads to ^ = f > which would 



in the electromagnetic system be consistent, since each 

 member =1. Again, TL = /x; that is, PL must represent a 

 magnet ; consequently C x L 2 is put equal to a magnet. But 

 the passage of the current ordinarily produces effects, such as 

 the movement of a galvanometer-needle, which we explain 

 more naturally by saying that the circular current produces a 

 magnetic field at its centre, than by saying that the current is, 

 or makes, or even is equivalent to, a magnet. Herwig's deri- 

 vation, therefore, in which a magnet placed in a field experi- 

 ences a couple, conforms to the ordinary way of thinking 

 better than the way of Clausius, and is the way used in the 

 derivation of the electromagnetic system. Again, if 



P e =M*L*T- 2 , 

 then 



I e P e L = M^L^T- 2 .M*L^T- 2 .L = ML 4 T- 4 = acouplexL 2 T- 2 . 



How can this result be explained, consistently with the known 

 effect of a circular current on a magnet ? It may be noted 

 that, in all discussions except that of Clausius, the magnet 

 pole P is introduced into a field. Clausius produces a field by 

 the pole P. Also that the ratio of the two values of P is the 

 square of a velocity. 



Herwig says, with regard to the step from I to /u, in the elec- 

 trostatic system : — " It may be remarked that for this purpose 

 we cannot use the formula of § 64, fM — 7rr 2 C, which expresses 

 the relation between the magnetic moment jju and the current- 

 strength C ; for the validity of this formula is dependent 

 (gehiiqjft) on the use of the magnetic system " (p. 78). 



A comparison of the derivation of the same units in the two 

 systems will strengthen our belief in the view, that Clausius 

 has proposed a new way, for which, rather than for the older 

 one, a justification is needed. Taking the least number of 

 steps that will lead from P to Q, or vice versa, we have these 

 equations in each system: — 



Magnetic, 



-jy =F( = a force). PL=yu.; I/u-= a couple ; -jy =1; 



Q=CT. . . (1) 



