THE MECHANICAL INTERPRETATION OF JOINTS 15 
the transverse elongation (Fig. 15), that is, increase the area of the 
Figure under deformation.* 
This, however, leads to the conclusion that under simple non- 
rotational stress a brittle body suffers an increase of volume. 
Since the angle of shearing is the more acute the more brittle a 
substance is, we must expect the increase of volume under stress 
to be the greater the more brittle a material is. 
Fic. 14.—Diagram showing the position of the lines of no distortion in an ellipse 
of strain derived from a circle of equal volume. The angle of shearing is obtuse. 
This seems indeed to be the case. Chwolson? gives the following 
formula connecting the modulus of volume increase (under tension), 
n, with the modulus of longitudinal strain (Young’s modulus), a, 
lateral strain 
Aioe. JPOUSS CIS WYO) || a || a B 
longitudinal strain 
n=a(t—20). 
According to this formula, o=0.5, when 7=0, that is, when the 
volume remains unchanged during deformation. The change of 
t For the mathematical proof of this statement the writer is again under obligation 
to Dr. Brand. 
20. D. Chwolson, Lehrbuch der Physik, Vol. I, p. 713. 
