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



each load acting separately. At any point z s in /, and at 

 zj in V, we have 



-miu s =Z Z s \Yz s \3l-z s ) + 6Kz s + 6R\ 



+ %i s \ -X: s \2>z-z s )+mz s 2 + Yz s *(3l-z s ) 



+ 6Cz s + 6G\. 



- 6EVr a =2Z'{Y'z,'*(M-z M ') + 6K'z s ' + 6H'j 



+ % i :,{- XV 2 (3^' - zj) + 3M V 2 + Y V 2 (3^' - c/) 



The first summation to z s is taken for all the loads 

 X and M that lie between and z s: and the corresponding- 

 values of K, H, and Y. The second summation includes all 

 the loads from z s to /, taking the corresponding values of the 

 constants C, G, and Y. Similarly for the second span. 



To find C 1? C/, Y, Y' 3 work through the constants to the 

 end (K w , ~H W , KJ, HJ), so that we have them expressed in 

 terms of Ci and Y (or of C/ and Y'). Then use the equations 



^Y/ 3 + KJ + H w =0. 



JY7 ,3 + K,r + H,' =0. 



Xextput^- = j\; and Yl + Y'l' = X 1 :, + X l 'z 1 '- Mi-M/, 



and we can solve for C : and Y (and C/ and Y'). 



Thus we find all the C's and K's, and therefore we have 

 the equation of the curve at each part in terms of X and M. 

 Similarly for the other loads. The summation of all the 

 deflexions at any point due to the separate loads (X and M) 

 gives the deflexion at that point due to all the loads 

 simultaneously. 



§ 7. From the preceding equations for the deflexion the 



values of — and - 1 - / may be obtained. Tims 



dz dz J * 



+ 2is{-X i .(2«-.*,)+2Ms.+Y2,(2J-3.) + 2C}. 



-2EI'(g,) =2f {YV(2Z< -zj) + 2K' } 



+%!,.{ -X , z s '(2z'-z s ')+2Wz s ' 



+Y , zJ(2l'~z s ') + 2C , \> 



