Loaded Shaft supported in Three Bearings. 649 



Table I. 



Value Coefficient Coefficient Coefficient Coefficient Coefficient 

 of of of of of of 



C t . Y. Y'. XaU = |. X'aU' = §. 



Ox 



1 



o 2 



* 



E 2 



1 

 2 



K 3 



i 



Ox' 



2 



c 2 ' 



1 



K 2 ' 



1 



G, 







a 2 







H 2 







H 3 







O/ 







a 2 ' 







H,' 







Ox 







Y 







Y' 







EIm x 



EIv x 





 n 







21 

 " 32 

 21 

 32 

 111 







9 

 32 



_ Hi 



32 







5_ 

 64 

 _5 



59 

 128 



















9 

 32 







15 



32 







15 



64 











21 

 " 32 







21 

 ~ 32 



















1 



32 







3 



32 







3 

 64 











5 

 64 







5 

 64 











4095 

 11776 







139 

 363 







45 

 134 







5396 



188416 







1290 



1^ 



32 

 3^ 

 32 



_ 3999 



23552 



43 



736 



141 



368 



1290 



188416 



1285 



188416 



When there are more section change points there will be 

 more constants C, G, K, H ? C, G', K', E 7 . When there are 

 more loads there will be more columns for X and X', and 



JTT TTT 



for M and M' : and also more rows for -^- u and -^ v, as 



„ ,, . mdu , Eidv l ° l 



well as those tor -„- -y- and -^- -j- . 



I 2 az b d: 



On substituting for X and M their values ma>' 2 i( and 

 mPco 2 -^, the determinantal equation for the whirling speeds 

 may be written down. 



§12. The case of a turbo-blower will next be considered 

 as a further example of a three hearing machine, in which 

 the number of section changes of the shaft and the number 

 of loads are great. 



Phil. Mag. S. 6. Vol. 42. No. 251. Sor. 1921. 2 X 



