Mr. G. F. C. Searle on the Elasticity of Wires. 195 



where E is Young's modulus, and I the " moment of inertia " 

 of the area of cross-section of the wire about an axis through 

 its centre of gravity perpendicular to the plane of the arc. 

 Also, if <j> be the angle turned through by either bar from its 

 equilibrium position, we have p = l/'2<f> } where I is the length 

 of the wire. 



If K be the moment of inertia of either bar about a vertical 

 axis through its centre of gravity, we have for the motion of 

 either bar 



dt 2 p I Y v J 



Hence, if t l be the time of vibration. 



'i = 2-\A 



2El' 



(2) 



When the wire is of circular section with radius a, I = ^7ra 4 . 

 In this case we find on substitution in (2) 



If now we unhook the bars from the strings and clamp one 

 to a shelf or other suitable support so that the wire G G' is 

 vertical, and then cause the other bar to vibrate about a 

 vertical axis, we can determine the simple rigidity. For i£ n 

 be the rigidity, the couple required to give to one end of a 

 wire of length I and radius a one radian of twist relative to the 

 other end is 7r/?a 4 /2Z*. Hence the couple experienced by the 

 bar when turned through an angle 6 is 7rna 4 d/2l, and the time 

 of vibration of the bar is 



h = ^\/~l • .'■'. • . (4) 



V Tinas 



so that 



n= lJoT- ' ( 5 ) 



The value of K in (5) is the same as that in (3) , since the 

 bars are square in section, provided either that the hooks are 

 light or that they are removed for this experiment. 



We are thus able to compare E and n by the simple com* 

 parison of the squares of the periods of vibration, for we have 



n~t? ( b) 



* Stewart and Gee, < Practical Physics,' vol. ii. p. 169. 

 02 



