100 



Mr. P. F. Ward on the Transverse 



Fig. 7. 



8. To obtain the case of the conical rod we put ra=l. 

 The equation to determine .t' 1? and therefore X, is 



= 



or 



+ 



/£ 



OS" 



+ ...,. (36) 



4!5! 1!5!7! 2!6!9! 3 ! 7 ! 11 ! 

 the lower roots of which are 



17-416, 35*027, 57*380. 



Also we find n j /dijrA , , . /^>A . , ,1 , Q ->. 



It is found that the positions of the nodes and points of 

 maximum excursion are as follows : — 



First Mode 1 = 17*416). 

 u = C{4-61034i/r 1 (» + •OO382O170 1 (»}. 





x. 



zjl. 



Nodes 



6-72715 

 1468195 



•386263 

 •843012 





Loop 



9-82786 



•564301 





Second Mode (^ = 35*027). 

 u=C{52-6544^ 1 (*)--OOlO35150 1 (*)}. 





X. 



zjl. 



Nodes 



6-59080 



17-86855 

 30-60030 



•188163 

 •510138 

 •873620 





Loops 



10-18619 

 2334072 



•290810 

 •666363 





