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XVII. The Determination of Values of Young's Modulus 

 and Poissons Ratio by the Method of Flexures. By 

 H. Harrington, B.Sc.,M.Sc., Teck.A.M.I.Mech.E* 



THE determination of Young's Modulus and Poisson's 

 Ratio by the method of flexures involves the accurate 

 measurement of the principal curvatures of the anticlastic 

 neutral surface of a beam or rod of suitable cross-section 

 when it is bent by couples applied to its ends. The couples 

 should be applied so that the curvature of the longitudinal 

 axis is a principal curvature of the surface. When this is 

 the case, the curvature of the neutral axis of any normal 

 cross-section is the other principal curvature. If the longi- 

 tudinal curvature and the values of the corresponding- 

 couples and dimensions of the cross-section are known, 

 Young's Modulus corresponding with the length of the beam 

 can be calculated. Also Poisson's Patio corresponding with 

 longitudinal strain in the direction of the length, and lateral 

 strain in the direction of the breadth, is numerically equal 



. Lateral Curvature 



to the ratio - f ^ — T . — j-^ ? • 



Longitudinal Curvature 



Values of Poisson's Ratio for glass were obtained by the 

 method of flexures by M. A. Cornu f (1869), who explored 

 the anticlastic surface of a beam of glass by means of inter- 

 ference fringes produced between the surface of the beam 

 and a glass plate laid upon it. 



The method was also used by A. Mallock % (1879;, who 

 obtained values for a considerable number of materials, 

 including three for white pine and two for box and beech. 

 Mallock placed four short wire pillars in the beams : one 

 pair in the plane of the longitudinal curvature and the other 

 pair in the plane of the lateral curvature. By measuring, 

 by means of a microscope, the distance between the ends of 

 each pair of pillars before and after a beam was bent, he was- 

 able to determine the principal curvatures of the surface, and 

 hence the values of Poisson's Ratio. The writer is not aware 

 of any record of the use of the method subsequent to 1879. 



The method described in this paper differs essentially from 

 the above in the manner in which the curvatures were 

 measured. The method will be explained by reference to 



* Communicated by the Author. 



t Comptes Rendus, p. 333 (1869). 



\ Proc. Royal Society, vol. xxix. (1879). 



