140 Mr Shaw, On dimensional equations [March 10, 



\ 



q[Q] = q'[Q'l 



x[X]=x' [X] ! 

 z[Z] = z'[Z']\ 



And : since the equation between the numerical measures is 

 by agreement the same as before, since both systems of units 

 are absolute,. 



q, == oo a y'P z'y... ;. 



and hence 



i = f^X (iLY ( z lY 



q \xj \y) \z ) 



m = (WN (H3Y /IZlV 

 [Q] \[XV \[YV [[Z]j~ 



Thus if the fundamental units X, Y, Z be changed in the 

 ratios 



I ': r, V :1, i : 1, 



and the derived unit in the ratio p : 1, then 



p = t V f • 



This statement may be evidently expressed by the relation 



m=m*m?[zy (3), 



where, now, [Q], [JT], [T], [Z~\ no longer represent concrete units 

 but the ratios in which the derived unit [Q] and the fundamental 

 units X, Y, Z respectively are to be changed, it being understood 

 that the same method of defining the absolute system is to be 

 adopted throughout. 



The equation (3) giving the ratio in which a derived unit 

 is changed when the fundamental units are changed in any given 

 ratios is called a dimensional equation, and is very convenient 

 for determining the factor of conversion for any unit, from one 

 absolute system to another governed by the same principles. 



The following rule for calculating the factor of conversion 

 when the dimensional equation is given is easily remembered. 

 If in the dimensional equation we substitute for the symbols of 

 the fundamental units the value of each old unit in terms of the 

 corresponding new one, the result gives the factor for converting the 

 numerical measure of a quantity from the old system to the new. 



