Systems of Physical Units. 105 



from which the new unit of force 



1 kilogr. 2 _ 615 metre x kilogr. 

 metre 2 — 10 13 sec. 2 



= 9-808 1 xl0^ kilogr - (Faris) - 

 The dimensions of the other principal units become 



w=[p], ra=[f*], w-w-w 



(according to the fundamental equations of the Gauss-Weber 

 system), 



ra=[f], "-[*]• 



and so forth. A quantity of electricity is given in ordinary 

 units : we find the electrostatic unit 



1 millim.' x milligr. 2 _ 1Q 5 m jrj^ ffr 



second \/615 



or 



1 n1 . V615 millim." x milligr i 



1 milligramme = 5 . ^— Weber units; 



10 5 



or about 4000 milligr. ordinary matter has equal 



\/615 

 action at a distance as 1 Weber unit of electricity. 



Instead of eliminating the constant of attraction, we may 

 obtain a system with two fundamental units by eliminating 

 the constant 



eo=3 i x i i»Ei!!™-. 



sec. 



If, in doing this, we wish to make the unit of time a derived 

 unit, we must put 



1 second =31 x 10 10 millimetres. 



Time must therefore be expressed as a length, the new unit of 



time 1 millimetre = gi — ttuo sec - 



The units of the four electric systems have the same dimen- 

 sions and the same magnitude, with the exception of the units 

 of the electrodynamic system. The dimensions of the most 

 important units are as follows: — 



