PHYSICS AND MATHEMATICS TO GEOLOGY. 129 
direction in which the axis of the bar is taken. Thus, in ordinary 
woods there is a marked difference between the value of Young’s mod- 
ulus in the direction of the pith of the tree and in any perpendicular 
direction. Materials in which Young’s modulus is independent of the 
direction in which the axis of the experimental bar is taken are termed 
isotropic; all others are termed veolotropiec. 
In an isotropic elastic solid it is supposed, on the ordinary British or 
biconstant theory, that the value of Young’s modulus, E, alone is insuf- 
ficient to define the elastic structure, and that some other elastic con- 
stant must be known. For many purposes the most convenient addi- 
tional constant is the ratio of the lateral contraction to the longitudinal 
extension—each measured per unit of length—in a bar exposed to sim- 
ple longitudinal traction. For instance, if the diameter of a bar under 
uniform longitudinal stress change from 10 to 9-9997 inches the lateral 
contraction is 0:00003, and if the longitudinal strain be 0-0001, the ratio 
of lateral contraction to longitudinal extension is 0:3. This ratio is 
termed Poisson’s ratio, and is represented here by 7. 
On the uniconstant theory of isotropy 7 must have the value 0-25, 
which certainly accords well with experiments on glass and some of 
the more common metals, especially iron and steel under certain con- 
ditions. 
On the biconstant theory 7 may have any value within certain limits. 
The existence of these limits, it must be admitted, is seldom recog- 
nized, and experimental results are not infrequently referred to which 
are inconsistent with the view taken here, viz, that 7) must lie between 
0 and 0.5. If, however, 7 were negative in any material a circular bar 
of this material, when subjected to uniform longitudinal tension, would 
increase in diameter; while if 7 were greater than 0.5, the bar, when 
fixed at one end and subjected to a torsional couple at the other, would 
twist in the opposite direction to the applied force. Until these phe- 
nomena are Shown to present themselves in isotropic materials—and the 
experimental verification ought to be easy—it seems legitimate to sup- 
pose that when experimentalists deduce values for 7 which lie outside 
of these limits, their experiments refer to bodies whose constitution is 
different from what is assumed in their mathematical calculations. 
The properties attributed to an isotropic elastic solid by the ordinary 
mathematical theory are as follows: 
(A) The strain must be elastic, 7. ¢., it must disappear on the removal 
of the stress. 
(B) The ratio of stress to strain must be independent of the magni- 
tude of the stress, or, in Prof. Pearson’s words, the stress-strain rela- 
tion must be linear. 
(C) The strains must be small. 
(D) The values of Young’s modulus and Poisson’s ratio in a bar of 
the material must be independent of the direction in which the axis of 
the bar is taken. 
H. Mis. 334, pt. 1——9 
