42 Mr. J. H. C. Searle on the Epctwf 



For the same tone Rayleigh gives 



p:p = 1 + 2-3241 p. 



His value, however, would become identical with the above 

 had he taken the correct value of a, viz., a = \7° 26' 8", 

 instead of a=17° 26' as used by him. 



IV. 1. Clamped- clamped Bar. 



f= d cos 7l J + d' sin 7l f + d" cosh 72 £ + d'" sinh 72?- 



Origin at either end. 



Here, / =0,1 



df S> when f=0. 



.-. d+d" = 0, and 7l rf / + 72 ^ // ' = 0; 

 .-. f=d(cosy 1 tj— coshry 2 £)+d f (smy t t;— -^sinh y 3 f ). (23) 

 Also 



# A I when f =-==/'. 



:0 I JC 



.-. = d(cos 7/ — cosh y/) +^7 sin 7/— -sinh y/J 



an( l = d( — 71 sin y x V — y 2 sinh y/) + d' (y x cos y v V — y 1 cosh y 2 Z') 

 .*. Eliminating d and d', 



1 — cos 7/ cosh y 2 / ; p — sin y^' sinh y 2 r=0; 



— / 1 / 2 



Or, using relations (0) 



l_ cos y/ cosh y/- ^sin y,Z 7 sinh y/=0. . (C) 



Neglecting X 2 and writing y 1 = y 2 = X, we have 



1- cos W cosh XZ'=0, 



the ordinary equation when rotatory inertia is neglected. 

 (23) in virtue of (24) now becomes 



f— D[(cos 7l £ — cosh y 2 £) (y 2 sin 71Z' — 7l sinh y 2 l') 



— (y a sin 7l f — 7 i sinh y 2 f) (cos 7l ^ — cosh 72 0]- • (D) 



