88 M. A. F. Sundell on Absolute 



[t~], and [&] for fundamental units, the dimensions become 



M=[j], M-gJ, W=[f], W-SJ. (") 



If, on the other hand, we leave the constant of equation (6) 

 standing, we obtain new fundamental equations (8), (9), (6), 

 and (13) for a system with three fundamental units, and the 

 equations of the units become 



W=[|] i W-f*]* M = [^H- W=[y], (18) 



where c 2 denotes the constant of equation (6). If, again, we 

 choose [7], [/], and [wj] as fundamental units, we obtain the 

 dimensions 



m-g], w=[?]> M = [|r], M=[^].(w) 



We see that the dimensions of units change not only with 

 change of the fundamental units, but also when the funda- 

 mental units remain the same and the fundamental equations 

 are taken differently. 



If we wish to regard only [l~\ and [f\ as fundamental units, 

 all four constants are eliminated; the equations (8), (9), (12), 

 and (13) become fundamental equations, and the dimensions 

 become 



M = [j] , W = [£] , M = g] , and [i] = g] . (20) 



On the other hand, if we assume four fundamental units, we 

 must leave two constants standing. If we take equations (8), 

 (9), (6), and (7) as fundamental equations, the equations of 

 units become 



M = [j\ , M = \j], W = [wl, M = [* ^] ■ (2i) 



If [/], [*], [m], and [/•] are the fundamental units, the dimen- 

 sions become 



W-gJ. M-S]. W-g], W-@|. ,(**) 



The choice of fundamental units is limited only by the consi- 

 deration that they must not all occur in the same formula. 

 Hence we see from equation (15) or (16) that [/] [/] and 

 [A], [A] [«] and [*], [/] [f] and [a], or [*] [m] and [a] 

 cannot be fundamental units atone and the same time: on the 



