hersey: laws of lubrication 545 



in which r stands for all the length ratios /•', r" , r'", etc., and in 

 which (p2 and ^po are unknown functions. 



While the list in question does include all the determining 

 factors met with in ordinary cases, it certainly does not include 

 all that might be encountered in extreme cases. For example, 

 with exceptionally high speeds and wide clearances the effects 

 of centrifugal force and of turbulent motion would begin to be 

 felt, thus involving the density of the oil in addition to its viscos- 

 ity. The question of just where the dividing line comes between 

 "ordinary" and "extreme" cases is an important one but must be 

 passed over in the present abridged report. 



5. Derivation of general form of the laivs of lubrication by dimen- 

 sional reasoning. A straight forward application of the principle 

 of dimensional homogeneity^ to equations (7) and (8) throws 

 them at once into the form 



F = L-„(>^,l,^,S,r) (9) 



and 



, = c-^,[^,^,i,S,r) (10) 



Combining (9) and (10) with (1) and (2), then gives 



and 



or 



c \ V D D I 



^I^=e(^',l,S,r) (13). 



fxn \c D D I 



Now wjien ( — ) = ( — ),?? = Po by definition. Hence from (13), 



calling ^0 the value of the function Q when (~ ) = (— ) ' 



Po = do' fin (14) 



3 See for example, Buckingham, Windage Resistance of Steam Turbine Wheels, 

 Bull. Bureau of Standards, 10: 191-234, 1913; Physically Similar Systems, Phys. 

 Rev., 4: 345-376. 1914. 



