382 Mr. A. Mallock [May 27, 



The extension due to the two shearing stresses is therefore 



+ X *\ 



n 9 / 



and hence 



Young's Modulus (E) 



\3 n 



Jc + ri 



Although no force is exerted on the lateral face this does not imply 

 that there is no change of lateral dimensions, for the contraction due 



p 

 to the shearing stress is — in both lateral directions, while the 



6« p 



dilatation in the same direction is only — -. 



If the extension due to a direct pull is compared with the con- 

 sequent change of diameter, it will be found that 



Lateral contraction 3 k - 2 n 



Longitudinal extension ~ ^ 3Jc + n' 



This ratio, generally denoted as /x, plays an important part in many 

 physical and mechanical problems. It is known, rather ironically, 

 as " Poisson's Ratio " — Poisson having proved, as he thought, that 

 the ratio was the same for all solids, and equal to one-quarter. 



As a matter of fact it may have any value between \ and 0, 

 according to the relative magnitudes of the volume elasticity and 

 the rigidity. 



If a solid is easily distorted but offers great resistance to com- 

 pression, the sides move out or in by almost half the distance by 

 which the ends are moved in or out, and if the rigidity is great 

 compared to the volume compressibility, the reduction or increase of 

 length makes hardly any difference in the diameter. 



This may be shown by a simple experiment. I have here a 

 cylinder of indiarubber and a cylinder of cork, placed between two 

 washers on steel bolts. Indiarubber is a substance which can be 

 easily distorted, but offers great resistance to volume compression. 

 Cork, on the other hand, resists distortion much more than it does 

 volume compression. It will be seen, when both are reduced to 

 about half their original length by turning the nut on the bolt, that 

 the diameter of the indiarubber has increased by nearly one-quarter, 

 while that of the cork has hardly changed. 



The whole of the mathematical theory of Elasticity turns on the 

 four quantities Jc, n, E and /x, together with the assumption that 

 these are constants for the range of strains and stresses contemplated 

 in the problems. 



As before mentioned, there has been very little direct experi- 

 mental work en volume compressibility, but if Young's Modulus 



