of Beams and the Whirling of Shafts. 



87 



For the next higher frequency, it appears from the graph 

 that K/ 2 is a little more than 200°. From the tables- 

 <p(206°) = — 1'0488, and from a table of circular fuuctions 

 <i> (274° 400 = 1- cot 274° 40', =- 1-0816. Interpolation 

 gives 205|°, 274^°. 



Vis. 1. 



-2 









i 





























/ 



!\ 











/ 











V 





**\ X 















A 





4-5° 



90° 



135° 



ISO* / 



7 



\225° 















270 



The third frequency is given approximated by K/ 1 = 287.\°, 

 KZ 2 =383£°. 



The actual frequencies are in the ratio of the squares of 

 the corresponding angles, or 1 : 1*96 : 3'82, 



Dunkerley gives, on page 297 of his paper already 

 quoted, solutions of the problem of two bays Tor various 



integral values of the ratio y 1 -. The author's results in these 



