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

 We now have from to P, on section m, 



-EU^Yfi/^-i^-XiC^^-J^ + iM^ + C^ + G^; 



and from P to L on section n, 



-Er^ = Y(i^-^ 3 ) + K^ + H, ( . 



This is for the loads X ls X : '. If we take a number of loads 

 we can sum the deflexions to get the resulting deflexion at 

 any point. 



§4. To deal conveniently with the constants, we write, 

 from to Pj 



fAO + 0.. 



From P to L, 



Xow -=- and z* have equal values for consecutive values 

 as 



of the constants, when z is the value at the junction, and 

 equal to a m (or a n ). 



T1 e C) m + f(a m ) C m +i+.f(a m ) 

 lheretore t— = y-^ — -, 



J- Mi J-W + l 



-. G m + C m a m + $(«,„) _ G- m+ i 4- C m+ ia m + <£ (a,„) 

 a n ci y — T ■ — - • 



*i,; K n 4--^(aJ K n+ i4-^'(a») 



AIsO = = = , 



J-B J-n + 1 



and H a 4-K >l fl, l + yfa t ) _ H )i+1 4-K„ +1 q n + %(a ;i ) 



If the load be at the point z==a r , which is not a section 

 change point but a load point, 



C, +/(«,) = K, 4- yfr (a r ), 



G. r 4-C r a r 4 : ^(a r )=H r 4-K J ar + %M. 



