Apparatus for determining Young's Modulus. 259 



T Y 



^ -j where a is the cross section of the wire and e is 



ae 



the Young's modulus of its material, Hooke's law being 



supposed to hold up to the maximum value of T used. 



Therefore m m 



1+- -i2=secCBD 



ae 



Mg a T 



- cosec o — 1 



1+- -= sec 6. 



ae 



=?cosec0-T o = ae(sec<9-l) . . (1) 



From equation (1) it is evident that T should be taken 

 as small as possible to secure the maximum accuracy of 

 determination of e. 



If a second mass M\ suspended from C produce a deflexion 

 1 at B. 



-— cosec 6 l — T Q — ae(sec 6 X — 1). 



it 



Hence eliminating T , 



- (M x cosec 1 — M cosec 6) = «e(sec 0j — sec#) 

 <7 M t cosec #j — M cosec 6? 



Or 6 = §- . q 7) • 



'la sec #j — sec a 



Or, in terms of the half-length /of the wire and the depressions 

 y y, at the centre 



£= 2« 



, M V^(^ t - M V i +(^)' 



or 



M, / l + Cvi/Q 8 M 

 2a . / l+( y/1 //)« __ W 



V i+(y//j« 



In all the experiments which follow ^ is sufficiently small 



to allow the expression under the root to be written 1 in the 



numerator and 1+ \,n m tne denominator; and the 



equation then takes the simpler approximate form 



M,_M 



e=' ,p) - !, \ 'i (3) 



S2 



