Systems of Physical Units. 97 



6. The systems of units most frequently employed in physics 

 are that due to Gauss and Wilhelin Weber, whose fundamental 

 units are those of length, time, and mass, and that employed 

 in many text-books (e. g. in Wiillner's Experimental-Physik), 

 as well as by engineers, which has for fundamental units the 

 units of length, time, and force. In this last system the gra- 

 vitating force of a unit of weight is taken as the unit of force. 

 This system may therefore be termed the gravitation system. 

 The Newtonian equation (7) holds good for this system with 

 the introduction of a constant (constant of attraction). The 

 examples given above (examples 2 and 3) show how a quantity 

 given in the Gauss-Weber system may be transformed into 

 the gravitation system: the unit of mass of the first system 

 must in general be replaced by the derived unit of mass of the 

 second system. Conversely, if we wish to pass from the 

 second system to the first, we must replace the unit of force 

 by the derived unit of force of the first system. For this pur- 

 pose we employ relationships of the same kind as equations 

 (32) and (27). 



The reduction is made most simply by employing the gravi- 

 tating force of the unit of mass (in) of the first system as the 

 unit of force (k t ) of the second system. We have then 



and hence >..... (35) 



where g expresses the numerical value of the acceleration of 



gravity at the place. Since the name of unit of weight is 



employed both for the unit of mass and for the unit of force, 



these units may be easily distinguished from each other by 



attaching to the name of the unit of force the name of the 



place where the gravitating force of the unit of weight is equal 



to the unit of force, as we have done in previous examples. 



Example 7. 



r* , „- metre x kilogramme ( Paris) 



(Jne horse-power = ( o - = - - 



second 



(gravitation system) 



n OAO metre x kilogr. 



metre x 9-808 -j^- 



_„_ second- 



secon „„ c „x metre 2 x kilogr. 



= 75 x 9'808(= /3o-b) 19 ° 



v second 2 



(Gauss- Weber system). 



The chief constant of the two systems is the constant of 



Phil Mag. S. 5. Vol. 14. No, S6. Aug. 1882. H 



