644 Prof. H. H. Jeffcott on the Whirling Speeds of a 



Eliminating the deflexions and slopes u, r, -j- and -j- 

 £rom these equations, we obtain 



= 0. 



d\ — (/> a 2 « 3 ... a r ... a/ ... a r ' 



6 X /> 2 -(/> 6 3 ... 6 r ... /V ... b r ' ... 



j, z, / 3 ... / r .../ 1 '-0... v ... 



| 



^1 P-2 PZ ... Pr'-... Pi' ...pr -$... 



The solution of this determinautal equation in <£ gives the 

 various values of the whirling speed. 



§9. The evaluation of the constants a 1? a 2 ...hi... is tedious 

 but straightforward. For each force and moment X! and 

 Mj we determine the values of the constants C, G, K, H, 



z z 1 



and of Y and Y'. It is convenient to write <=y, and t'=~, 



z z' . 



5= y, and s'=Tf for section change points s=a m , etc. 



Then from § 5 we have, from to P, 



6EI wi m v,2/q, a . ^ Ml /2j.V/2/a /U 6C,1! /4. 6Gm 



from P to L, 



CEI„m _ 



/ 3 ~ 



Also : from to P, 

 du 

 dz 



t 2 



2EI M 





2C, 



= -X 1 *(2t 1 -*) + 2^+Y*(2-*) + 



from P to L, 

 2EI - 



I 2 



Yt(2~i) + *%*-, 



and similar expressions for the span OL ; . 



