1921] on Elasticity 3 3 



and the rigidity coefficient are known (and both are easily deter- 

 mined), the volume compressibility can be deduced from the relation 

 (derived from the expression for E in terms of k and n) — 



All, or nearly all, the values of the coefficient of volume com- 

 pression given in books of reference or in table of constants are 

 reached in this way. 



But Jc may also be found if the values of Poisson's and the 

 rigidity are known, for from the expression for jx it will be seen that 



n (1 + /x) 



If 



3 (1 - 2 fJL) 



Poisson's Ratio is not perhaps as easily determined by direct 

 experiment as Young's Modulus or the rigidity coefficient. In 

 1877, however, I employed a method which was applicable to most 

 materials and was susceptible of considerable accuracy. This I will 

 shortly describe and illustrate the procedure by a model. 



When a flat bar is bent the material on the convex side of the 

 neutral plane is stretched in the direction of the length and com- 

 pressed on the concave side, with the result that diameter of the bar 

 is reduced on convex face and increased on the concave. In 

 consequence the cross-section of the bent bar is no longer rect- 

 angular, but has its faces curved in the opposite sense to the 

 curvature of the longitudinal section. It is easy to see that the ratio 

 of the two principal radii of curvature depends on the ratio of lateral 

 contraction to longitudinal extension, and that if this ratio of the 

 curvatures can be measured the value of /x for the material of the 

 bar can be deduced. 



In my own experiments the bar was bent by equal couples 

 applied at the end ; thus the bar originally straight became an arc of 

 a circle. On the middle part of the surface a circle was described 

 whose diameter was a little less than that of the bar itself, and at the 

 ends of the diameters of this circle, parallel and perpendicular to the 

 length of a bar, four fine steel wires were planted forming normals 

 to the unstrained surface. The wires remain normal to the surface 

 from which they spring when the bar is strained. Hence the free 

 ends of the pair on the longitudinal diameter move apart when the 

 bending couple is applied, while those on the transverse diameter 

 approach one another. (See Fig. 2.) 



The distances through which they moved were measured with a 

 microscope and micrometer, and a comparison of the displacements 

 of each pair gave the data for the calculation of /*. 



The elastic properties of matter vary with the temperature, and 

 during the last few years I have examined the changes which occur 



