or 



704 Mr. E. Buckingham : Xotes on 



If equation (15) is completed by the inclusion of /-t, 

 the application o£ the II theorem gives 



n^'^r) = (18) 



«=§ + (^} <*« 



a familiar equation which is known to represent the 

 observed facts. If the circumstances are such that a 

 change of viscosity has no sensible influence on the flow, 

 the undetermined function 0(DSp//a) must be simply a 

 constant, and equation (19) reduces to (17) which is 

 correct for this case. Equation (15) is complete on the 

 supposition that viscosity is of no importance, but not 

 merely because of: a stipulation that the viscosity shall 

 be constant. - 



On the other hand, in steady stream-line flow, i. e. at 

 low speeds, the fluid is not accelerated, its inertia does 

 not come into play, and the density cannot appear in 

 equation (19). Hence the form of the unknown function 

 must be 



0(DS/o//a) = const, x (/a/DS/o), 



so that (19) reduces to 



G = const, x^j, (20) 



a form of Poiseuille's law. If the problem had been 

 limited, from the start, by saying that inertia effects should 

 be insignificant, the equation 



F(G,S,^D) = 



would have been the appropriate complete equation for 

 the phenomenon subject to this condition. The II theorem 

 would then have led directly to equation (20), which is 

 the correct solution under this condition but is not generally 

 correct for liquids of the same density, merely because they 

 are of the same density. 



7. The usual method of treating Dimensional Constants. 



The question how ordinary dimensional constants are to 

 be treated is pretty clearly answered by the foregoing 

 example. The fact that a particular quantity remains 

 constant during the phenomenon which is to be described, 

 does not, of itself, authorize us to ignore this quantity and 



