the Method of Dimensions. Ill 



our initial equation some universal constant that really has 

 nothing to do with the problem, the undetermined operator 

 in the final result will have one more dimensionless operand, 

 which will contain this extra and superfluous quantity. But 

 if, after all, we decide that this quantity might as well be 

 suppressed, we may cross it out of the final equation and 

 what remains will be unaffected thereby. 



If, for example, in Lord Rayleigh's problem of the non- 

 viscous liquid spheroid we include the speed of light C in 

 the initial equation and write it 



F O, D, p, 7 , C) = 0, . . . . . (39) 

 the II theorem gives us the equation 



But if in reality C has no influence on the frequency, 

 cf) must reduce to a constant as was found before. If 

 gravitation were propagated with the speed of light, 

 JD/C would be the time of propagation from one side 

 to the other of the spheroid, and it is clear that this time 

 might be an important factor in determining the frequency. 

 As things really are, we have merely encumbered the algebra 

 with a superfluous symbol. 



11. Second Method of treating Dimensional Constants, 



It has just been shown that universal constants may be 

 treated like any other quantities, but that there is also 

 an alternative procedure which we do not usually think of 

 in connexion with ordinary dimensional constants. This 

 second method is, however, applicable to such ordinary 

 constants, as will now be illustrated. 



Instead of taking a new problem, we return to Reynolds's 

 problem of the flow of liquid through a pipe, already dis 

 cussed in section 6, and start with the equation 



F (G, D, S, ft M ) = 0, (41) 



which is known to be sensibly complete because equation (19), 

 obtained from it by the use of the II theorem, is a good 

 description of the observed facts. 



Let us now suppose that the liquids to be discussed are 

 always to have a particular density p which is never, on any 

 account, to change. In other words, let us ask what would 

 happen in a universe where all liquids, without exception. 

 had the same fixed density, so that p* was a '•universal" 

 constant. 



