664 Prof. H. H. Jeffcott on tlie Whirling Speeds of a 



or 



T = 2f2m- 6 (3P-4- 2 )+2j,2m- 6 (?--)^3Z 2 -4(Z--) 2 } 



-3^. 



O) 2 



U = X^ 7 (3/ 2 -4^ 2 )-{-^2m.: 6 (Z-:){3/ 2 -4(/-.-c) 2 } 



2 co 2 ^ 



Similar values may be written for P' Q' P' S' T' IP, taking 

 Z J = U'. They may be got from the values of P Q K S T U 



by putting m! for m, ~' for z, V for I, - for /x, P for I. 



Similar expressions may be obtained by imposing co- 

 incidence between the assumed and actual displacement 

 curves, at other points in the spans. 



It is to be noted that this method gives best results when 

 the loads predominate at those points at which coincidence 

 between the curves is imposed. If this condition is not 

 fulfilled the resulting speeds will be less exact, unless 

 suitable correcting factors be applied to the masses to give 

 a result equivalent to securing more perfect coincidence of 

 the assumed and actual displacement curves at the load 

 points. 



§ 20. We may apply the method of the last paragraph to 

 the example of § 17 as an illustration. 



We have m' — m, f*>=i, V = %1. _ 3072EI 



By the formulas of § 19 we find, if 0= ma} ^ > 



P=gi(101-2</>], P' = ^f (59-2*). 



Q =g(83-2*), Q-!g!(-l3-2*)- 



