90 M. A. F. Sundell on Absolute 



This equation becomes 



h^ — ^ma. 



We have between the old unit of force and the new one the 

 relation 



where n denotes the numerical, value of <? 2 . The new dimen- 

 sions of the units are determined by equation (22). 

 Example 1. — Let us take as the old unit of force 



r , n ., metre x kilogramme 



[*] = 1 7 ^2 > 



L (second)^ 



and as new unit of force the weight of a gramme at the Obser- 

 vatory in Paris ; then, by equation (2), since m— 0*001 kilo- 

 gramme, and « = </ = 9*808 7 — ^j 



° ; " (second)- 



[*,] -0-009808 met ''( s X ec k ( || 1 g a " lme =0-009808[i], 



i r fik ~\ 



Hence n= ■ and as the dimensions of c 2 are '• , 



the complete value of the new constant becomes 



1 (second)'- x gramme (Paris) 



° 2 ~" 0-009808 metre x kilogramme ' 



if we call the new unit of force a gramme (Paris). We have 

 further, 



1 gramme (Paris) = 0-009808 ""?"* X *? ° gr ' , 1 

 ° ' (second) 2 ' y 



. metre x kilog. 1 ,_ . . \ ' 



1 —7 rry = rTT^noTTo gramme (Pans). J 



(second) 2 0*009808 & } * 



II. One of the fundamental units of the old system is a 

 derived unit in the new system ; the remaining units are com- 

 mon to both systems. Since the new system contains one 

 fundamental unit less, it must also contain one constant less. 

 The new system is therefore obtained bv eliminating a constant. 



Let 



*L=M*N* (28) 



be the equation containing the constant a to be eliminated. 

 In the new system this equation assumes the form 



L^M'-N*, (29) 



and defines the conception 1^ ; the dimensions of its unit are 



