1884.] and change of units. 141 



And if, on the other hand, for the symbols of the fundamental 

 units there be substituted the new units in terms of the old, the 

 result gives the factor by which the old derived unit must be 

 multiplied to give the new derived unit. 



We may under certain circumstances work backwards from 

 the dimensional equation to the physical law, in case we know 

 the dimensional equations from other sources. The problem in 

 this case is practically knowing the dimensional equation for q 

 to determine a, /3, <y. 



This may be applied for instance to prove the equation for the 

 velocity of sound, viz. v oc a /A . But, as others have already re- 

 marked, we make the assumption that the velocity depends upon 

 no other quantities but p and d, and thus get no indication of 

 the dependence of the velocity upon either temperature or the 

 ratio of the specific heats because neither of these quantities is 

 measured in units which vary when the fundamental units of 

 length, mass, and time vary. 



The method of proving a physical law by means of a di- 

 mensional equation may thus be sometimes misleading. Any 

 dimensional equation may be expressed as the product of two 

 others, one of which may be a dimensional equation of recognizable 

 form, but it does not necessarily follow that there is any physical 

 interpretation corresponding to it. 



The dimensional equations for electrical quantities on the 

 electromagnetic system may be deduced from those on the elec- 

 trostatic system by multiplying or dividing by a dimensional 

 equation representing some power of a velocity. 



It happens in this case that a physical meaning can be 

 assigned to this velocity, namely, that of propagation of an 

 electrical disturbance. But this need not always be the case ; 

 the form of the dimensional equation may be due to some hitherto 

 unrecognized physical fact, but it may sometimes represent a 

 relation between the ratios in which units are changed and 

 nothing more. 



