94 M. A. F. Sundell on Absolute 



sions of the new unit. Of course the rule holds good if the 



number of fundamental units is greater or smaller than three. 



Example 2. — The unit of force derived from the metre, 



j -i i m i metre x kilogr. Tl . , , 



second, and kilogramme = 1 $ — 2— . It now we take 



sec." 



the centimetre, the gramme, and the minute as new funda- 

 mental units, we put 



metre = 100 centimetres, kilogramme = 1000 grammes, 

 second = ^ minute, 

 and so obtain 



1 metre x kilogr. _ 100 centimetres x 1000 grammes 

 sec. 2 (^o minute) 2 



= 100x1000x80= ( = 360xlO'') ce " t ( i ;»: i ^-r ne ; 



that is, the first unit of force is 360 million times larger than 



the second. 



If here we wish to exchange the former unit of mass, the 



i ., r n. j • j -j. (sec.) 2 x gramme (Paris) 



kilogramme, tor the derived unit - — ; i -, 



° ' metre 



then by equation (32) we obtain 



metre x 1 (sec.) 2 x grm. (Paris) 



metre x kilogr. _ Q-Q09808 metre 



sec/ (sec.) - 



= 0-00Q808 8 Tamme (Paris). Compare equation (27). 



It is clear that the same rule holds for the reduction of any 

 magnitudes to new fundamental units. 

 Example 3. 



1 Daniell = 112 x 10 9 — 2 gr ' (Gauss- Weber system) 



_ n9 (Q-Q01 metre)* x (0*000001 kilogr.)* 



11^ X -LU n 



sec/ 

 _ 112 x 10 D metre* x kilogr.* 

 10* x 10 f sec. 2 



1in 1A 2 metre a x kilogr. 2 

 = 112 x 10 2 „ 6 . 



sec. 



metre 1 x ( - sec. 2 xgrm.(Paris)y 



11fl tAS X V0-009808 metre ) 



— 112 x 10 2 ^ 



sec.- 



112x10* metre x gramme (Paris)* , .. .. 



= ^0-009808 ^ST-^ (g'-antafon 



system, Equation 32). 



