44 Mr. J. H. C. Searle on the Effect of 



Thus 1% 1 k 2 i « ) n Q l 



n=n |jL- -^-J ;z cot^ G -2 j » cot^°J 



In this case, 



jo :p = n 2 : n 2 = (n + <ny : n 2 = l 

 1 k 2 



or 



1 k C n ~) n 



= 1 + ^ f | ^o tan |° +2 j n tan ^° 



(26) 



according as n lies in the first or fourth quadrant. 



When the order of the tone is moderate the ratio becomes 



p:^ = l-I^(„ -2K , . . . (27) 



For the first root of (25) Strehlke gives 

 , ?o = 4-7300408, 



^? =2-3650204, 



=-135° 30' 20"-47, 

 tan^° = -'9824679; 



... rc tan^° = -4-6471132; 



u 



.-. |7:^ = l + 6-1513111^ 



for the fundamental of a clamped-clamped bar. 



V. 1. Free- free Bar, 

 f=d cos Y]|f + d' sin y x f -\-d" cosh y 2 £ + d f '' sinh y 2 f- 



Origin at either end. 

 Hence, from (12), 



d ? l,whenf=0. 



and xi d£ + <Pf 



d^ dt, 



d^= iv. 



and <?(\Vi - 7i 3 ) + *'" (Xtyj + Y2 3 ) = 0. 



