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

 Further 



L a l + ibP + JcZ 3 + ^ + -l 2 eP + A/Z« = ^ 



Now w r = az r + &Z r a + CSV 3 + a 7 - / + 6>c/ + fz r 6 



substituted in the exact displacement curve relation gives an 

 equation of the form 



Pa + Qb + Re + Sd+ Te + U/= 0. 



Substituting thus for u± and i\, we get the two equations 

 Pa-t-Q& + Rc + Srf + Te + U/=0 ; 



and P'a + Q'- +R'c + S'd + T'^+ U7=0 ; 



A* 



in which P, Q,...U ; F, Q' V ..U' are known. 



Eliminating a, 6, c, d, e, /, we obtain the determinant 



p 



Q 



R 



S 



T 



u 



P' 



Q' 



A* 



R' 



S' 



T' 



TT' 



1 



/ 



Z 2 



Z 3 



Z 4 



Z 5 



1 



Z' 

 A* 



t' 2 



-r 3 



Z /4 



-z' 5 







/ 



3l 2 



6Z 3 



10Z* 



15Z 5 







Z' 



A* 



3Z' 2 



-6Z' 3 



10/' 4 



-15/' 



= 0. 



Tnis is a quadratic for go 2 , leading to the first and second 

 whirling speeds. 



The values of u, and v> may be got from 



- 6EI^=Sf {|YZ 3 + 3KZ+ 6H} 



+ SiJ-iXZ 2 (3^-iZ) + |MZ 2 + |yZ 3 + 3CZ+6G} ; 

 and 

 - 6EI^=Xf {|Y'Z' 3 + 3K'Z' + 6H'} 



when the values of Y, Y' and the C's, G's, K's, and H's are 



first determined. 



If we wish to find an approximate value of the first 



