S6 M. A. F. Simclell on Absolute 



nition are much simplified ; since the constants of the equa- 

 tions are partly eliminated, partly regarded as new concep- 

 tions, it may be said that the equations from which an absolute 

 system is derived contain no constants — that is, no numerical 

 factors; each side of the equation has only one term. We 

 will call these equations the fundamental equations. Together 

 with these equations there occur in physics a large number of 

 equations or formulas; but these are not distinct from the fun- 

 damental equations, but are formed from them by various 

 combinations and methods of calculation, integration, and so 

 forth : they are therefore not so simple as the fundamental 

 equations; the two sides may contain several terms, into which 

 various numerical factors enter. It is necessary in our choice 

 of units not to lose sight of these equations derived from the 

 fundamental equations ; only, in using them, we must express 

 the quantities in the units obtained from the corresponding 

 fundamental equations. If, for example, we employ the for- 

 mula for centrifugal force, 



, _ m7i 2 

 r 



we must express k } m, h, and the radius of curvature r in the 

 units which correspond to the fundamental equations (8), (9), 

 and (12). 



In the same way, the general equation for uniformly acce- 

 lerated motion, 



s = Ji t + ±at*, 



requires the units for s, t, h, h , and a, which are obtained 

 from the fundamental equations (8) and (9). 



3. According to what has been explained, in an absolute 

 system certain units may be chosen at pleasure ; these are 

 termed fundamental units. The magnitudes of all the other 

 units are determined by the condition that the constants in 

 certain equations of definition are to be equal to unity : such 

 units are therefore termed derived units*. We see that, in con- 

 sequence of the mode in which the absolute units are deter- 

 mined, the fundamental equations will be satisfied if in them 

 we replace the quantities by their units. If, for example, we 

 take equation (8) for velocity, it will also hold good if we 

 replace the quantities by their respective units. But if we do 

 this in the ordinary way, by putting h = l, s = l, and t=l, wo 

 arrive at the identity 1 = 1, which is of no further use to us. 

 But if we put s= unit length, t= unit time, h= unit velocity, 



* Kolilrauscb, Leitfaden, 3rd ed. p. 200 : Maxwell, ' Treatise on Elec- 

 tricity and Magnetism/ i. pp. 2 k 5, 



