16 WALTER H. BUCHER 
volume, therefore, must be the greater the more a differs from o. 5, 
that is, the smaller it is. The following values of o for different 
substances completely confirm the inference drawn from the graphic 
representation of the 
strain ellipsoid. 
Paraffin ©.50 
Caoutchouc 0.50 
Copper °.348 
Mild Steel 0.304 
Tron 0.243 to 0.310 
Zinc 0.205 
Glass 0.197 to 0.319 
That brittle bodies 
suffer an increase of 
volume when deformed 
under tension, is well 
known. ‘That such an 
Fic. 15.—Diagram showing the position of the jncrease of volume also 
lines of no distortion in an ellipse derived from a : 
actually accompanies 
circle of smaller volume (increase of volume accom- : 
panies deformation). The angle of shearing is acute. deformation under one- 
sided compression, as 
demanded by the graphic construction of the strain ellipsoid, seems 
to be proved by the experiments made by Kahlbaum and Seidler? 
and more recently by Lea and Thomas. 
It is essential, therefore, before we use the strain ellipsoid for 
the interpretation of shearing planes in nature, that we decide 
which form of the ellipsoid corresponds to the conditions of the 
specific case. 
IV. PLANES OF SHEARING PRODUCED BY IRROTATIONAL 
AND ROTATIONAL STRAINS 
We may now return to the interpretation of planes of shearing 
observed in nature. We have learned that Hartmann’s law applies 
to brittle substances only, that is, that only in brittle materials the 
QO. D. Chwolson, Lehrbuch der Physik, Vol. I, p. 714. 
*R. Kahlbaum and Seidler, Zeitschr. Anorg. Chem. (1902), pp. 29-30, 254-94. 
3 F. C. Lea and W. N. Thomas, ‘‘Change in Density of Mild Steel Strained by 
Compression beyond the Yield-Point,” Engineering, Vol. C (1915), pp. 1-3. 
