1891.] 



On the Plasticity of an Ice Crystal. 

 FIG. 9. 



341 



i 



The bar is represented in fig. 9, with a weight W hanging from 

 the middle. The length between the supports is I, the breadth b, 

 the depth d. U is the force per unit area which acts on a small 

 vertical interface in a vertical direction, and when U is positive the 

 matter to the left of the interface is urged upwards. The force per 

 unit area on a horizontal interface in a direction parallel to the length 

 of the bar is necessarily the same, and is also denoted by U. Consider 

 the equilibrium of the part of the bar to the right of any cross 

 section PP'. It is urged upwards at the support by a force equal to 

 ^W ; therefore, if we neglect its weight, the total vertical force on the 

 section PP' is also W. 



KU be the average of U over the section 

 bdU = iW (2). 

 annot be constant over the section, for it necessarily vanishes at 

 the upper and lower surfaces of the bar. 



The average shear over any cross section being the same, except that 

 the sign suddenly changes at the middle of the bar, it is reasonable to 

 suppose that the same amount of plastic shearing strain would take 

 place between the layers perpendicular to the optic axis at every cross 

 section. This condition makes the bar bend sharply when the weight is 

 applied, and keeps the two halves straight. In tke earlier experiments, 

 where the bending was considerable, this form was observed before its 

 cause had been perceived. For this form to be assumed without 

 elastic strain, the plastic strain must be the same, not merely in corre- 

 sponding points of different cross sections, but also throughout each 

 cross section itself, and, in fact, throughout the entire half of the bar. 

 But as we have seen, the shearing stress must vanish at both the 

 upper and lower surfaces. Doubtless the truth is that the state of 

 shearing strain is nearly uniform throughout the bar, except close to 

 the surface, where it rapidly diminishes to zero. Probably in these 

 regions the elastic strains are very great, and quite different from 

 what they are elsewhere. 



