Systems of Physical Units. 107 



it is not e , but e ^2 which is eliminated by putting 1 sec. = 31 

 X 10 10 VH millim. = 44 x 10 10 milliin. The new unit of time is 



-T-. — ^7-Tn sec. The constant of attraction, too, is eliminated 

 44 x 10 10 ' ' 



b v Weber by introducing a unit of mass 



2x3PxlO" ( = 314xlo;2)k . logr 



(nearly half the earth's mass*). These last two formulae ap- 

 pear to us equally simple ; but the first of them, as we saw 

 above, has the advantage of combining the three electrical 

 systems into one. In returning to the ordinary systems, 

 attention must be paid to equations (44) and (45). 



Example 9. — The quantity of electricity 1000 millimetres 



is to be expressed in electrostatic units '- s_l_ _ yy e 



r sec. 



have 1000 millim. electricity 



= 1000 n 4^=31 ! x 10 20 x 1000 HH^ (equation 45) 

 millim.' sec. - v 1 7 



=31 , xl(p /mi]Wy miffimJ = W 



\ sec.- J sec. v^625 



1A o, millim." x kilogr. 2 , 

 x 10- 3 ^— (equation 44) 



= 10 2 x31 2 xl0 23 xl0 3 / = 10 28 x31 2 \ millim. I x mgr.* 

 ^615 \ v/615 ) sec. 



It is to be observed that a system with two or with onlv one 

 fundamental unit is not completely determinate, unless its 

 connexion to the ordinary systems with three fundamental 

 units is given by relations such as equations (44) and (45). 

 The systems with three fundamental units are therefore to be 

 regarded as the fundamental systems of mechanics. f 



11. The ordinary units of mechanics are not convenient nor 



* Weber and Kohlrausch (Zollner, /. c. p. 130). 



t The above systems with less than three fundamental units may be 

 regarded as the result of taking the unit of length, the unit of velocity 

 and the unit-of-attraction constant as fundamental units. If, for example 

 we take the millimetre, the velocity e , and the attraction-constant c[ as 

 fundamental units, we obtain, from c 1 = 61o x 10 _4 mm. 3 x sec- ~ 2 x kilo°T\ - 1 , 

 1 kilogr. = 615xl0- 4 mm. 3 X sec r-Xc' 1 ; and from e =31xl0'° mm.x 

 sec.~M sec. =31xl0 10 X mm. Xe" 1 ; which expressions become iden- 

 tical with (44) and (45), if we omit c x and e from the dimensions. The 

 constants c x and e should be left in the fundamental equations, so as not 

 to disturb their homogeneity. 



