532 Mr. 0. K. "Wead on the Dimensions of a 



Electrostatic, 



5Q=F. 5 = C; <j^=I; I^= a couple; /*=PL. (2) 

 Electrostatic (Clausius), 



<j^=F. ^ = C; CL 2 =/*=PL (3) 



^ It is obvious at a glance that, after the fundamental opera- 

 tion has been performed of finding P M or Q e , the remaining 

 operations take exactly the opposite order in the two systems; 

 the corresponding equations in the two are the same; while 

 this is not true of series (1) and (3). In (1) we may find the 

 dimensions of Q in terms of P, and from (2) and (3) of P in 

 terms of Q. The results are: — 



Q m =MI^"T- I -HP roJ (1') 



P e = ML 2 T~ 1 -Q e , (20 



P^LT-^Q, (30 



Since in the two systems P and Q play similar parts, are 

 we not justified in expecting such a symmetry as is shown by 

 (1/) and (2'), rather than the want of it shown in (1/) and (3')? 

 If the values of P m and Q e , M*L*T _1 are substituted in the 

 above, we may group the results thus : — 



P m =M^L*T" 1 , Q^MJLfT- 1 ; 

 Q m = M*L*, P e =M*L* (20, or M'UT" 2 (30- 



Of course these are not presented as three independent lines 

 of argument in favour of Maxwell's view, as they are all in- 

 volved in the series of operations (1), (2), and (3). 



It will now be shown that to write "CxL 2 = PL in any 

 consistent system" is simply begging the whole question. 



No physical formulas are better established than those used 

 in finding with the magnetometer M and H, the moment of a 

 magnet and the horizontal component of the earth's mag- 

 netism : — 



MPT- 7rK • M -i y 5 tan ft—*/ 5 tan ft' 

 * 2 (l + 0)' H~~ 2 7 2 —/ 2 



in which K = a moment of inertia = ML 2 , t — a time = T, 

 y and ■/ are lengths = L, and the other quantities in the second 

 members are numerical. In the usual notation, therefore, 

 ^I = ML 2 T~ 2 , /*-i-I = L 3 ; whence we find the dimensions 

 of /^M'L^T -1 , and of I=M*L~*T -1 , the same as in the 

 magnetic system. But one has the same right to declare that 

 " in any consistent system " both the above formulas must be 



