Fi ff . 1. 



[ 886 ] 



XCV. A Determination of Poisson's Ratio. By I. Williams, 



M.Sc, Lecturer and Demonstrator in Physics in the Uni- 

 versity of Bristol*. 



THE object of the experiments about to be described was 

 to determine Poisson's Ratio for a steel bar from obser- 

 vations on the distortion of the cross-section. 



Let ABCD represent either the normal cross-section of a 

 rectangular bar or a normal rectangular element of a bar of 

 any section. 



When AB and CD are perpendicular 

 to the plane of bending and AG and BD 

 are parallel to this plane, it can be shown f 

 that when the bar is uniformly bent AB 

 and CD become concentric circular arcs 

 each having a radius R x where 



R 



lateral contraction 

 ~ linear elongation ' 



R = Radius of curvature of the mean line of the 

 beam when strained. 



For convenience we may term R the longitudinal radius 

 and R x the transverse radius. 



Thomson and Tait refer to rubber as a substance for which 

 the curvatures may be easily observed. The earliest experi- 

 mental demonstration for metal bars of the distortion of 

 cross-section referred to above appears to be due to Franz 

 Neumann. He attached mirrors to the vertical sides AC 

 and BD of the rectangular section (fig. 1) and showed that 

 the rectangle became a trapezium under the influence of a 

 bending couple. He does not appear to have made a measure- 

 ment of the ratio by this method ; and I shall show later that 

 although it is quite possible to demonstrate the distortion in 

 this manner, it is not possible to obtain consistent values of 



the ratio ^- • 

 Ri 



* Communicated by the Author. 



t Thomson and Tait's Nat. Philosophy, vol. ii. p. 260. 



