106 M. A. F. Sundell on Absolute 



[A] = [7%i°] (abstract number), 



M«[j]i W = [f]' W=K» [ A ]=H; 



constant of attraction [cj = — , [e] = [/a] = [wl^], 



K=[f]=[ E ]. 



We see that, by eliminating the constant (e ), the distinction 

 of the units by their dimensions is lost for the most part — a 

 result which was to be expected, since e Q has no independent 

 dimensions, but is to be regarded as a velocity. 



10. The systems with two fundamental units have yet an- 

 other constant ; if this be also eliminated, we have a system 

 with only one fundamental unit. If we start with the system 

 given above, with the fundamental units of length and time, 

 we may eliminate the remaining constant c by the relationship 



1 sec. = 31 xlO 10 millimetres (45) 



We thus obtain a system in which the unit length is the only 

 fundamental unit. The three electrical systems now combine 

 into one. The dimensions of the units are as follows : — 



\K] = [l°] (abstract number), [*] = [I], [a] = [*] , 



M = [f|, [k] = m, [A] = [/], [e] = [>] = [/], 



W = [E] = [Z°]. 

 The distinction of units by their dimensions is now completely 

 lost; velocity, force, current-strength, and electromotive force 

 are abstract numbers; time, mass, work, quantity of electricity, 

 and magnetic pole are to be regarded as lengths. 



m, .. ., millim. 3 , 10 4 , ., N , 



Ihe unit-mass 1 ^ 2 (= ^ kilogr.) becomes equal to 



oj2 — r?p millim. Consequently the unit of mass 



1 nL, = W x 10*2^= ^T(-«7 x l^kilog., 



or nearly one fourth of the earth's mass (650 x 10 22 kilogr.). 

 Weber's formula may now be written 



Weber himself simplifies the formula thus: — 



If we compare this formula with formula (43), we find that 



