Magnetic Pole in the Electrostatic System of Units. 533 



true as that CxL 2 = PxL. In the magnetic system both are 

 true ; in the electrostatic system with Maxwell's value the 

 first is true, the second is not ; with Clausius's values the 

 second, and not the first. Maxwell (or at least Herwig) 

 openly uses the first; Clausius impliedly uses the second ; for 

 if CL 2 = PL=^ and C-=-L = I, 



In deducing the dimensions of physical quantities, there is 

 much that is as arbitrary as the order in which several num- 

 bers shall be multiplied together*. Thus, the familiar equation 



I=k 3 is true in any conceivable system of units, 



(l 2 + d 2 y 

 where r is the radius of the current-circle, and cl the distance 

 from the centre on a normal to the plane. In the electrostatic 

 and electromagnetic systems, the dimensions of either C or I 

 being given to find the other, r, I, and d being lengths, k is 

 arbitrarily made equal to 1, and then I or C is found : if I and 

 C had both been given, ordinarily its value would not be 1, 

 nor its dimensions = L°M°T . To pass from I to P or to 

 PL=/£, either of two equations may be used : — 



I=£P-^ 2 ; (1) 



fil—h'x a couple (2) 



Clausius arbitrarily makes k = l in (1), letting k' assume 

 whatever concrete value will satisfy (2). Herwig, to obtain 

 Maxwell's result, as arbitrarily makes k' = l, paying no atten- 

 tion to k. If arbitrarily we make k=k , = l, /ju and I must 

 come out as in the magnetic system. 



In making k' — l rather than k, there is the advantage of 

 introducing a mechanical unit ; and we use the equation (2) 

 that is both more familiar in experimental work, and the one 

 used in the derivation of the magnetic system. Further, if P 

 be changed, three other quantities of the twelve that Maxwell 

 discusses must have their dimensions changed, and confusion 

 would be introduced into his system, that is based on fifteen 

 equations, in each of which the second member is some simple 

 mechanical quantity, as work, time, &c. Until it has been 

 clearly shown how this system will be affected by the proposed 

 change, and why the new expression is to be preferred to the 

 older one, that has been " unimpeached " for some twenty 

 years, is it not clearly better to write P e = M^ L* ? It is not a 

 question merely of correctness, but of consistency, simplicity, 

 and usefulness; and on all these grounds Maxwell's expression 

 seems to the writer to deserve the preference. 



University of Michigan, 

 Ann Aroor, May 29, 1882. 



* On this point, compare Everett's ' Deschanel,' p. 783. 



Phil. Mag. S. 5. No. 84. Suppl. Vol. 13. 2R 



