706 Mr. E. Buckingham : Notes on 



And if we apply the IT theorem to equation (21), which 

 contains 5 quantities requiring 3 fundamental units, one 

 solution is 



/&*&-<* <•» 



whence 



°=^*{^f) (25) 



If the circumstances are such that viscosity has no 

 sensible influence on the frequency, the equation reduces 

 to 



o-=NV/><y, (26) 



in which the value of the dimensionless numerical co- 

 efficient N depends on the values of certain length ratios 

 which fix the shape of the spheroid at some specified epoch 

 of the oscillation. Equation (26), which is equivalent to 

 the result given by Lord Rayleigh in the article referred to, 

 may also be obtained by omitting fi from equation (21), 

 i.e. by stipulating from the start that the frequency of the 

 vibration shall not be sensibly dependent on viscosity. 



The " universal constant " <y has here been treated like 

 any ordinary dimensional quantity, whether constant or 

 variable ; and the treatment is so obviously correct that 

 I hardly think anyone will be disposed to question its 

 validity. Lord Rayleigh remarked * of his own more 

 concise deduction : u there seems to be here no mistake 

 of procedure, and I take it the logic is right." 



But there is a second method of handling this problem 

 which is equally valid. Let us suppose that y is regarded 

 as something absolute and fixed in the nature of things, — 

 in short, as a pure number and not a physical quantity. 

 Then it need evidently not be included in our initial 

 equation as one of the essential quantities, and instead 

 of (21) we have 



F( ff , D, P ,p.) = 0. . . . . . (27) 



Since 7 is now a pure number, equation (23) must be 

 replaced by 



J [m- l Pr 2 ] = [1], (28) 



and one of the three fundamental units hitherto regarded as 

 independent must be derived from the remaining two. In 

 other words, we must now use the law of gravitation to 



* In calling my attention to an obvious misstatement in my Physical 

 Review paper, referred to above. 



