418 Mr. J. Morrow on an Instrument for 



^ for all materials : but it appears doubtful whether the 

 specimens dealt with were sufficiently isotropic to justify any 

 definite conclusion either for or against the uniconstant form. 



Practical methods for the determination of Poisson's ratio 

 may be divided into three classes. First, those by which two 

 coefficients of elasticity are obtained, and the required ratio 

 inferred by calculation. Second, those which depend on the 

 deformation of the section of a beam when bent. And, lastly, 

 methods by which the tensile and lateral strains are actually 

 measured in specimens of the material under direct tensile 

 or compressive stress. 



Kirchhoff experimented in 1859 upon cylinders, which by 

 means of a weight attached to a lever were put simultaneously 

 under the action of bending and twisting forces and the 

 strains produced were measured accurately. The values of 

 Poisson's ratio were calcalated from the ratio of the observed 

 displacements, and were 



Mean for three steel rods .... '294. 

 ., hard drawn brass rod . . 'St!?". 



Many others have worked on similar lines. 



Cornu (and later Straubel) explored the anticlastic surface 

 of a rectangular beam by means of the interference-fringes 

 produced between it and a plate of glass laid on it, thus 

 obtaining data for the calculation of cr. 



MaUock (1879) also examined the anticlastic curvature. 

 By means of a microscope he measured the movement of 

 four fine steel wires fastened to opposite diameters of a circle 

 on the surface, obtaining data for the radii. 



Another method of investigation would be to find the dis- 

 placements in the sides of a beam, either by measuring the 

 lateral strains at any section, or by attaching a mirror to the 

 side and fin din o- the ano;le throu<yh which it turns when the 

 beam is loaded. 



If f = the maximum tensile stress, the lateral contraction 



is 0-^6 (& being the breadth of the beam and E Young's 



modulus) and the angle turned through bv the side of the 



, . _, r h 



beam is tan " <t 'fs — 7. 



In all the above methods the practical accuracy of the 

 theory of elastic materials is assumed. 



Coming now to actual measurements of the lateral con- 

 traction of a tie-bar, it appears that Bauschinger {^Der 

 C'lvilingenieur, vol. xxv. 1879, pp. 81-124) was the first to 

 construct an instrument which would measure the alteration 



