26 



Mr. J. Morrow. On the Distribution of [Oct. 27 , 



amount of flow when nearing the point of rupture, the curve of 

 distribution of stress over the cross-section of the beam becomes 

 parallel to the plane of the section when rupture commences. 



This suggests that the higher lateral strains may be due to the 

 amount of plasticity of the material just before fracture. 



In a tensile test no such plasticity can be observed. This, however, 

 does not invalidate the assumption, as it would be necessary to check 

 the plastic elongation, in order to measure it before complete rupture 

 occurred. 



One effect of the permanent set in the direct strains may be to 

 produce a more or less profound change in the distribution of stress 

 over the section. This might give rise to the existence of lateral 

 strains, which, though perhaps elastic in their nature, would not be 

 included in the observed values of the experiments. 



It has been pointed out* that, when the load on an overstrained 

 beam is reduced, initial stresses may result. The strain in the outer 

 layer might then be reduced by an amount greater than the real 

 elastic strain due to the load removed. 



It appears, however, to be far more probable that the departures 

 from theory which have been noticed are due to the inapplicability 

 of the theory employed; that is, mainly to the facts that (1) the Saint 

 Venant solution implies different conditions of loading and end-fixing, t 

 and (2) it is based on an assumption of the absolute proportionality of 

 stress to strain. 



In this connection it should be remarked that a different distribu- 

 tion of stress and strain over the section would not necessarily alter 

 the deflection or curvature of the centre line of a beam due to a given 

 bending couple. % 



The author hopes to deal more fully with these and other questions 

 in a future paper. 



Note on the Determination of Poisson's Eatio from Bending Experiments. 



The instrument described in this paper provides a method not 

 hitherto available for the determination of the values of the " stretch- 

 squeeze " ratio for different materials. 



The method appears at present only suitable for those materials and 

 stresses to which the ordinary theory of bending may be applied. 



It depends on the relation between the lateral strain at any section, 

 and the deflection of the centre line produced by the applied bending 

 couple. 



Consider a beam, of uniform rectangular section, supported at the 



* See "Encycl. Brit.,' vol. 22, article " Strength of Materials." 

 f See paper by L. TS. Gr. Filon, ' Phil. Trans.,' A, vol. 201, p. 83. 

 X See Wiedemann's ' Annalen der Physik mid Chemie,' vol. 52, 1894, paper by 

 W. Voigt, p. 536. 



