Systems of Physical Units. 99 



and (7). If we choose for this purpose the constant of equa- 

 tion (6) (the force-constant) and that of equation (7) (the 

 attraction-constant), we obtain a system in which the dimen- 

 sions of the chief units are given by equation (22). We have 

 already found the value of the force-constant c 2 (example 1), 

 namely 



1 (second) 2 x gramme (Paris) 



C2_ 0-009808 metre x kilogramme 

 _ i (second) 2 x kilogramme (Paris) 



9'808 metre x kilogramme 



According to equation (22), the dimensions of the attraction- 

 constant are [ex] = 1 — g ; we may find its new value as fol- 

 lows: — Lm J 



_ 615 (metre) 3 _ 615 (metre) 2 metre x kilogr. 



Cl_ W 3 (sec. 2 ) x kilogr. " W 3 (kilogr.) 2 X (second) 2 



= W 3 w^y x ¥m kilogr> (Paris) (e<luation 35) 



615 _ (metre) 2 x kilogramme (Paris) 

 ~ 10 13 x 9-808 ~ (kilogramme) 2 ' 



or 



_ 627 (metre) 2 x kilogramme (Paris) 

 Cl ~ TO 14 (kilogramme) 2 



The other mechanical equations of definition would remain 

 unaltered. Thus we should have: — 



for the work A, the relation A = ks, with the dimensions 



[A] = [*f]j 

 for the vis viva, u = mh 2 , 



for the momentum, q = mh, 



M=[# 



and so on. 



Such a system has this advantage for a beginner — that he 

 is able to express either a force or a mass in units of weight, 

 and so would escape the reduction (difficult to understand and 

 often forgotten) of a force from units of weight into units of 

 force of the Gauss-Weber system, or of a mass from units of 

 weight into units of mass of the gravitation system. The 

 following circumstance may, however, perhaps be considered 

 inconvenient. The constant of force passes over into the equa- 

 tions which give the connexion between work and change of 

 H2 



