ON STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 203 
faces AB, CD (Fig. 1) constrained to remain plane and parallel and un- 
disturbed are given a translatory displacement relative to each other, 
parallel to their plane. 
Dr. Andrade found that along the middle plane EF of the block (half- 
way, that is, between the two faces whose displacement was prescribed) 
the distribution of slide gave two maxima at points H, K distant about 
one-sixth of the length from the unstressed faces perpendicular to the 
plane of strain, the slide falling gradually to a minimum at O. 
For a section E’ F’ near the middle plane an effect of the same type 
occurred, but was less marked. For a section EK” EF” near the face CD 
where the constraint was applied the slide remained fairly uniform over 
the greater part of the length of the section, going down rapidly at the 
ends to the value zero at CD. 
The problem attacked experimentally by Dr. Andrade is one of which 
no exact theoretical solution is known. Dr. Andrade himself attempted 
to fit his conditions by an approximate solution, but either through the 
failure of the approximation, or from some other cause, the results of 
observation and calculation agreed only qualitatively. 
The second method used for the investigation of the distribution of 
stresses inside a plate subjected to stress in its own plane depends on the 
property, discovered by Sir David Brewster in 1816, and independently 
by Fresnel, that glass and other isotropic transparent substances become 
doubly refracting under stress. 
Since then this effect has been studied by a number of observers (4). 
It may be taken as fairly well established that when a ray of polarised 
light traverses a plate stressed in its own plane, it is broken up into two 
components, polarised along the two lines of principal stress at the point 
where the ray crosses the plate, and the relative retardation of these two 
rays on emergence in air is 
C7(P—Q), 
where rt = thickness of the plate, P and Q are the two principal mean 
stresses in the plane of the plate, and C is a co-efficient depending upon 
the material and the wave-length of the light (5). 
Clerk Maxwell (6) was the first to go fairly fully into the theory of the 
appearances presented when a plate under varying stress in its own plane 
is placed between crossed Nicols. He showed that the light is restored 
at all points except those for which : 
(a) The lines of principal stress are parallel to the axes of the Nicols. 
Since the condition for extinction of the light is here independent of 
the wave-length, these lines will be quite black. These may be called the 
lines of equal inclination or isoclinic lines. 
(6) The principal stress-difference has such a value that Cr(P—Q) is an 
exact multiple of the wave-length. 
These will be lines of equal principal stress-difference, and will give 
a different set of lines for different wave-lengths. They are thus, in 
general, brilliantly coloured, the same stress-difference corresponding 
tothesame tint. The only exception is the line corresponding to P—Q=0. 
These may be called (following Maxwell) the zsochromatic lines, the 
black line corresponding to P—Q=0 being called the neutral line. 
Observations of the isoclinic lines have the advantage that these lines 
are exhibited under comparatively small stress and are independent of 
the co-efficient C. Their use does not, therefore, require straining the 
