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



When the material is isotropic, Poisson's ratio, viz. lateral 

 contraction / longitudinal extension, is easily found by the 

 formula 



'-I- 1 (7) * 



Two points remain to be noticed in connexion with the 

 determination of E. The wire will not generally be absolutely 

 straight. But it is easily shown that small initial curvature 

 (not necessarily uniform) in the horizontal plane is without 

 influence upon the time of vibration. Curvature in a vertical 

 plane calls the rigidity of the material into play; but the effect 

 upon the time of vibration will be small when the wire is 

 nearly straight. 



The second point refers to the correction due to the finite 

 mass of the wire. The processes of the theory of the trans- 

 verse vibrations of rods enable the period to be calculated to 

 any desired accuracy; but a close approximation can be 

 obtained by a very simple method. The process turns upon 

 calculating the kinetic energy of the system on the assumption 

 that for a given angle between the bars the form of the wire, 

 when in motion, is the same as its form when at rest f . 



In fig. 3 let F be the middle of the wire, H the centre of 

 gravity of the whole system. Then, provided that the sus- 

 pending strings are very long, H is fixed in space, and we 



Fisr. 3. 





may use it as a fixed point to which to refer the velocities of 

 the parts of the system. Let S be the centre of gravity of 

 the two bars. Let M be the mass of each bar, and m the 

 mass of the wire. Let P be any point on the wire, and let 

 PN=y, NH = .r, SH = ^. Since H is the centre of gravity 



* Stewart and Gee, ' Practical Physics,' vol. ii. p. 175. 

 t Lord Rayleigh, ' Theory of Sound,' ed. 2, vol. i. § 88. 



