496 TRANSACTIONS OF SECTION G. 
These methods of stress determination avoid the difficulties of the Clerk- 
Maxwell analysis, which necessitates the determination of the equations to both 
families of isochromatic and isoclinic bands, usually a mathematical problem of 
considerable complexity. In some simple cases Mr. Scoble and I have verified 
the accuracy of the method of lateral measurements for determining the sum of 
the principal stresses, by comparing the calculated stresses with the experimental 
values obtained in a plate of transparent material. We have lately carried these 
experiments a stage further, and have shown that the measured sums of the 
principal stresses in steel agree with the calculated values. This experimental 
solution, in fact, gives the stress at a point in a plate, if the conditions are those 
assumed by the mathematical case of a plate where generalised equations of 
stress apply. 
It is at once obvious, if the utility of experiments on models of this kind is 
admitted, that experimental evidence is available on a variety of practical 
engineering problems covering a very wide field of practice, not merely qualita- 
tive, but quantitative, and approximating to the needs of the physicist and 
mathematician, and well within the known variations of the materials with which 
the engineer has to deal in his daily practice. 
During the last few years much attention has been paid to the determination 
of the stresses in structural elements of primary importance, but only a small 
number of cases have been examined, since even the simplest problems have 
proved somewhat difficult, and much time and labour have been spent in per- 
fecting optical and mechanical appliances to suit the special conditions required 
for investigations on transparent models. A simple example of a case easily 
examined and of practical importance is that of a tension member subjected to 
an eccentric load. The optical effects here show a linear distribution of stress 
due to the combination of direct pull and bending, while the neutral axis moves 
towards the tension side as the stress increases. Not only can these effects be 
measured, but if the specimen begins to fail some indication is obtained of the 
way in which the stress distribution is changed to meet the new conditions, and 
there is found a tendency to an equalisation of the maximum stress at the 
boundary, although at present the form of the curve of distribution beyond the 
elastic limit is largely conjectural. 
A case like that of a very short member subjected to direct compression is 
also not without interest, partly because it reveals unexpected difficulties. In 
the first place it is not easy to apply a pure compression stress, and if the sur- 
faces in contact are not of the same materials it appears to be practically im- 
possible, since the lateral changes are unlike, and shear stress is therefore 
produced at the plane of the surfaces in contact. In a short member this shear 
has a very important influence, and by interposing a thin layer of a material, 
such as india-rubber, between the pressure plates and the short transparent block, 
the artificial shear effect produced by the india-rubber is easily shown to in- 
fluence the distribution throughout, and to increase the stress in a very marked 
way. Experiments on transparent materials show that the increase of stress may 
be twenty per cent. or even more. Such an elfect is known to take place when 
cubes of stone are crushed between lead plates, and optical investigations on 
models have enabled a quantitative measure of the effect to be ascertained in 
this and other cases, thereby confirming the theoretical investigations of Filon 
on the distribution of stress in such members under various practical systems of 
loading. 
The local effects produced near the points of application of a load are usually 
of considerable importance, and their influence on the stress distribution in 
beams has been examined by Carus-Wilson. 
The stress effects produced by discontinuities in materials is also of con- 
siderable interest, and the cases arising from the necessities of construction are 
infinite in their variety. 
The practical importance of an accurate knowledge of the change in stress 
distribution produced by changes of section in a member is so thoroughly appre- 
ciated that it needs no insistence, and it has received much attention from a 
mathematical point of view. Thus the local effect of a spherical cavity in a 
member subjected to uniform tension or compression load has been shown by 
Love to double the intensity very nearly, while Kirsch has shown that a small 
