Measuvina the Lateral Contraction of Tie-hars. 419 



of cross dimensions of a niotal test-piece. His ap[)aratiis is 

 coni{)lioated. It is essentially a pair of levers, the small arms 

 of which are the diameter of small caoutchouc cylinders, and 

 the greater the double distance of the scale from a mirror- 

 To read the lateral contraction requires two separate obser- 

 vations by means of two telescopes and mirrors on opposite 

 sides of the specimen. 



Stromeyer (Proc. Roy. Soc. vol. Iv. no. 334, p. 373) 

 measured directly the lateral contraction of a bar under 

 tension by interference methods; a dark glass attached to 

 the specimen advanced or receded from the surface of a 

 prism as the diameter of the specimen altered, thus producing 

 change in the positions of the interference- bands. 



Elastic Constants, 



If a is the longitudinal strain produced by unit stress, and 

 /3 the linear lateral strain in the material^ then 



0-=-, Ji(=-, n— — — -7^, and k—-^, ^7-^; 



a' a' ^(« + /3) ' 3(a — 2^)' 



where E, n^ and k are Young's modulus and the moduli of 

 rigidity and of bulk respectively. 



If any two of the elastic coefficients be known Poisson^s 

 ratio can be calculated. 

 Also we have that : — 

 if cr=-|- the material is incompressible, and the extension and 



lateral contraction are such that the volume remains 



constant, 

 if <7 > -J A" would be opposite in sign to E and n, the material 



not being homogeneous and isotropic, 

 if (7=0 to ^ we have an ordinary elastic body, 

 if (r=0 either there is no lateral strain or the material is 



perfectly plastic. 

 cr = i is the value of the nniconstant theory which requires 



The New Form of Apparatus. 



With the object of measuring, in the most direct way 

 possible, the lateral contraction of a tensile specimen or the 

 dilatation of a compressive piece when loaded in an ordinary 

 testing-machine, the author devised the instrument shown in 

 the figure. 



Two hardened set-screws A and B, on opposite sides of the 

 specimen S, are pressed inwards by stiff springs C, 0. The 

 relative motion of the points of these set- screws is transmitted 



2E2 



