On the Physical Umts of Nature. 59 



dimensional equations. Remembering, as is well known, that the 

 dimension of a unit of velocity is I ^ I, that of a unit of coefficients 



of attraction ^=-p~^ , and that of an electromagnetic unit of 



quantity [VLM], we find from equations (1), (2), and (3) respec- 

 tively, that Li _ j^ h u\ 



m;t? =^ .7m? ^''^' 



VL^,= C VJ^, (6). 



in which Lj, Mj, and T^ are used to designate the units of length, 

 mass, and time in the ' Natural ' series, while l^, m^ and t^ repre- 

 sent the corresponding units in the metric series, viz., the metre, 

 gramme, and second. A, B, and C also are used, for brevity, to 

 stand for the numerical coefficients of equations (1), (2), and (3), 



2 1 1 



viz. : — For the numbers 3 VIII, ^ yTu' '^^^^ XX ff' 



Solving equations (4), (5), and (6), we find 



Ca/B 

 L, = -—^ I, .........(7). 



T: = -^ ^. (8). 



^> = VB "*' ^^)- 



Substituting for A and B their numerical values, and writing 

 metre, second, and gramme, for l^, t^, m^ 



' "" 3^15 XTV' nietres. 



^1=^3 VTf XXn' seconds. 



Ml = C 3VT5 XIV grammes. 

 or, more simply, (inasmuch as 10 is sufficiently near to S\/15 to 

 be used instead of it in an approximation like the present) 



Li = C ^^ metres (10). 



T, = C o yyjjy seconds (11). 



M, = C XV grammes (12). 



In obtaining these equations we have only used the numerical 

 values of V^ and Gj, which are known to a satisfactory degree of 



