Loaded Shaft supported in Three Bearings. 663 



whirling speed only, we may impose coincidence between 

 the curves at the middle point of the first span. Then we 

 assume 



u = az + hz 2 + cz 3 + dz* + ez b ; 



and the resulting determinantal equation becomes 



= 0. 



p 



Q 



R 



S 



T 



1 



i 



P 



I 3 



¥ 



1 





.I' 2 



-I' 3 



v± 







i 



3l 2 . 



6l 3 



10/ 4 







V 



3/' 2 



-6P 



ior 4 



§ 19. When each span of the shaft is of uniform section, 

 we use the results of § 15. Adopting similar coincidences 

 between the assumed and actual displacement curves as in 

 §18, we find the same determinant of the sixth order as 

 there given. 



The values of PQRSTU are, however, simpler in this 

 case, and may be evaluated directly. Thus, when the 

 moments of the loads are negligible, and with z r =^l ) we 

 have 



P = X^2^ 2 (3P-^ 2 ) + Si z 2m^-e){3Z 2 -4CZ~^) 2 } 

 -48™!. 



CD 2 



Q = tl l 2mz%3l 2 -4,z 2 )+t ¥ 2mz\l-z){SP--4,(l^zyi 

 -24^ 2 . 



H = 1^2mz i {3I 2 -Az 2 ) + ll l 2mz 3 (l-z){3P--i(l-^yi 



3/x/ 



3/- 



fjul 



^ 2 H('-^ 2Z -^7v^-o'» V '(^'---')(2/'-y) 



-12^. 



