Magnetic Pole in the Electrostatic System of Units. 433 



strength of either pole by the distance between the poles, we 

 must have, in every system, 



Pole x Length = k 3 x Current x Area; . . (3) 

 that is, 



Pole = k 3 x Current x L, 



where k 3 depends on the system employed. Clausius defines 

 his unit pole by making k 3 ~l, and thus obtains 



Pole = Current x L 



= M*L*T- 2 x L 



= MiIiT~ 2 . 



This result disagrees with that of the two preceding investi- 

 gations; and hence the two equivalent assumptions k x — l, 

 k 2 =. 1 are inconsistent with the assumption k 3 =l. Maxwell 

 has chosen the former alternative, Clausius the latter. On 

 Maxwell's system we have 



^=1, k 2 = l, £ 3 =T 2 IT 2 . 



On Clausius's system we have 



I'l — T ll ", k% = T" L , A.'g = 1 . 



In fact it can be shown that, if v be the ratio of the electro- 

 magnetic to the electrostatic unit of quantity of electricity, k 3 



would be — 2 on Maxwell's system, and fa x and k 2 would each be 

 ~2 on Clausius's system. When we bear in mind how fre- 

 quently laws I. and II. are applied in practical calculation, 

 and how extremely rare is any practical application of law III., 

 it seems clear that, if we were driven to employ an electrostatic 

 system in calculations relating to magnetism, the best choice 

 we could make would be Maxwell's. 



It is further clear that electrostatic systems are essentially 

 inconvenient for calculations relating to electromagnetism. 

 The electromagnetic system makes &i, k 2 , and k 3 each unity, 

 and also gives the value unity to the factor # 4 which occurs in 

 the general expressions for the attractions and repulsions 

 between currents. For example, the force with which two 

 parallel currents, one of very great length and the other of 

 length I, attract or repel each other, is given in any system by 

 the formula 



Force =& 4 x Product of currents x 21-— Distance, . (4) 



