710 Mr. E. Buckingham : Notes on 



simpler, and it gives just as useful results as the second, so 

 long- as we are interested only in a particular universe. The 

 second method is more general and, perhaps, more in- 

 structive; but for practical purposes it is quite immaterial 

 which course we pursue, and our preferring one course 

 or the other is a mere matter of convenience or custom. 

 When discussing a gravitational problem, it seems more 

 natural to regard the gravitation constant as a physical 

 quantity than to eliminate one unit and pass to the 

 unfamiliar system of dimensions in terms of only two 

 mechanical units. In thermal problems, on the contrary, 

 we are so familiar with the equivalence of heat and work 

 that it seems natural to dispense with an arbitrary unit 

 of heat and treat the mechanical equivalent as a pure 

 number characteristic of the system of units adopted. But 

 either sort of problem may be treated in either waj r , and 

 the same will be true of problems which involve other 

 universal constants such as the speed of light or the charge 

 of the electron. 



On the other hand, the mere existence of universal 

 constants which have nothing to do with the case in hand, 

 need not disturb us. For ' example, we cannot see that 

 the constancy of the speed of light has any connexion 

 whatever with the period of the pitching oscillations of 

 an aeroplane in flight; and we are entirely justified and 

 quite safe in regarding an equation for this time of 

 oscillation as complete without including in it the speed 

 of light. The fact that the speed of light is constant, 

 while interesting in itself, is quite detached from the 

 problem under investigation : our knowledge of this fact 

 adds nothing to our understanding of the behaviour of 

 the aeroplane, and we shall not learn anything more 

 about the aeroplane by dragging the speed of light into 

 the discussion. Accordingly, there is no occasion for us 

 to feel obliged to use any of the general relations in which 

 such universal constants appear for reducing the number 

 of fundamental units, unless the subsistence of the general 

 relation is a fact pertinent to our understanding of the 

 phenomenon in question. 



What it all boils down to is that, so far as the purely 

 alo-ebraic reasoning of the dimensional method is concerned, 

 these rather portentous universal constants about which we 

 hear so much nowadays are quite harmless ; they are to be 

 treated like any other dimensional quantities whether 

 constant or variable. 



If, as a mathematical recreation, we choose to write into 



