92 M. A. F. Sundell on Absolute 



"Retaining the former units, we have 



1 seconcWO.009808 ™^™ogr* 



gramme (Paris)* 



1 metre* x kilogr.- 1 i 



1 ■ — -s — = — 7 — — = second. 



gramme (Paris)* \/O009808 



(33) 



In the same way we find, if [I] is to be made a derived unit, 



, , 1 gramme (Paris) x sec. 2 -j 



metre _ . 009808 - kilogr. " ' I , 



1 gnunme(Pai-is)xsec. 2 ss0 . mm metre< J ' 

 kilogr. 



It is to be remarked that the relations (27), (32), (33), and 

 (34) may be regarded as determinations of the four units from 

 any one of them. 



III. By successive employment of the two preceding me- 

 thods we are able to exchange one fundamental unit for 

 another, while retaining the same fundamental equations. 

 In one of the examples given, we have in fact exchanged the 

 unit of mass (kilogramme) for the unit of force (gramme, 

 Paris) while retaining the two remaining units (metre and 

 second). 



IV. By successively employing methods I. and II., we may 

 change the system of fundamental equations by transferring a 

 constant from one equation to another without altering the 

 number of the fundamental units. If, for example, we wish 

 to pass from the system (15) to the system (18), we first of 

 all eliminate the constant of equation (7) by method (II.), 

 and then introduce a constant into equation (12) by method I. 

 We may of course adopt the reverse method. The calculation is 

 most simple if it is possible to retain the same fundamental units. 

 If, for example, in the system of equations (8), (9), (12), and 

 (7) the constant is to be transferred from equation (7) to equa- 

 tion (8), we must make the following substitutions, [/], [m], 



and [t] being the fundamental units : — in equation (7), - asjfe, ; 



in equation (12), k = k 1 c, and hence - =a x ; in equation (9), 



h c 



a = a x c, and hence - =h x ; and in equation (8), li^l^c. We 



obtain thus the fundamental equations 



, Is 7*1 , j m 2 



