Systems of Physical Units. 95 



By the aid of this rule, the elimination of a constant is 

 more easily effected than as given above by II. If the con- 

 stant to be eliminated has the value 



u = n[P a Q b R c ] ; 



vhere [P], [Q], and [R] are the fundamental units, and if 



we wish to make the fundamental unit [P], for example, into 

 a derived unit and at the same time to eliminate the constant, 

 L e. to make it equal to unity, we must put 



[P]=»-£[Q-« Pr«], 



where a. becomes equal to unity. 



If, again, we wish to eliminate the constant 



1 sec. 2 x gramme (Paris) 



° 2 ~ '0-009808 metre x kilogramme 



introduced into example 1 by making the unit of mass a de- 

 rived unit, we do so by putting 



, , ., 1 sec. 2 x gramme ("Paris) 

 1 falognmme- -^^ *L__J > 



(compare equation 32) ; c 2 becomes equal to unity, and we 

 have a system in which the only fundamental units are the 

 units of length, time, and force. In order to make the unit 

 of time a derived unit, we put 



i - a aancAo metre x kiloo-r* 



1 sec.- = 0-009b0b /Tt ° 



grm. (Paris) 



or 



inetre* kiloor.i 



lsee.=v/0-009808 



grm.2 (rans) 



(compare equation 83), and so on. 



"We may follow a similar rule in using a physical formula 

 to find the value of an unknown magnitude. We introduce 

 the numerical values of the known magnitudes into the 

 formula, together with the appropriate dimensions or names of 

 the units, and solve the equation, thus finding at once the 

 value of the unknown magnitude and its dimensions. 



Example 4. — Let us determine the value of the constant e 2 

 from the equation k 1 = e 2 ma (compare example 1). If the 

 force k x = l gramme (Paris) act upon the mass m=0*001 kilo- 

 gramme, it produces the acceleration 



a=g (Paris) 9-808 ™^. 

 * v second- 



