PRESIDENTIAL ADDRESS. 495 
polarised light has no optical effect in a thin plate, or at any rate is so small 
that it may be neglected. 
That the retardation between the ordinary and extraordinary rays is pro- 
portional to the stress difference perpendicular to the incident beam within the 
elastic limit of the material may, therefore, be taken as reasonably accurate, 
although future research may show that it is only an approximation, or even 
that it is more accurate to commence from a fundamental strain equation; but 
according to present knowledge there appears to be no warrant for such a 
procedure. 
A more pressing difficulty arises with regard to the optical constant connecting 
the wave-length retardation with the stress difference. The recent researches of 
Filon on glass show that the value of this constant is curiously dependent on the 
previous history of the material, especially as regards its heat treatment. Until 
further knowledge is gained on this matter it appears to be necessary to guard 
against errors in stress measurement from this cause by a careful selection and 
treatment of the material used, since for other artificial bodies we may find that 
the variation in the constant is not less in magnitude, and is at least as complex 
as in glass. In some instances the stress optical coefficient may be dispensed 
with, and Filon has shown, in cases where a theory of stress distribution has 
been worked out and it is desired to compare it with the results of optical 
measurements, that the isoclinic lines offer many advantages, since they are 
independent of photo-elastic constants, and the material need only be subjected 
to small stresses. 
The experimental analysis of stress distribution in a body depends on the 
‘possibility of finding the magnitudes and directions of the principal stresses at 
every point, and in practice it is found the simplest plan to determine the 
directions of stress from the lines of equal inclination obtained in plane 
polarised light, and to measure the stress difference by comparison with a wave- 
length standard, such as a Babinet compensator, or by comparison with a simple 
tension member set along one of the lines of principal stress, and loaded until 
the total effect produced is a dark field denoting a zero value. The difference 
of the principal stresses is then measured in terms of a simple tension. This 
alone is insufficient to determine the distribution, unless one of the principal 
stresses is zero, and, in general, another independent measure must be obtained. 
This is very conveniently supplied, as Mesnager suggested, by the change in the 
lateral dimensions of the plate under stress, since this change may be taken, in 
the absence of a third principal stress, as proportional to the generalised sum of 
the principal stresses throughout the thickness. 
The determination of the lateral strains in a comparatively thin plate, forming 
part of a model of a machine or structure, necessitates measurements of 
extremely minute linear quantities. If, for example, a plate of xylonite is 
taken, of the maximum thickness obtainable for optical work, a simple calcu- 
lation shows that these strains must be measured to an accuracy of one or two 
millionths of an inch. Several instruments have been designed and constructed 
for this purpose, to fulfil conditions which appear to be essential for successful 
use. It is necessary to avoid all chance of injury to the surface of a transparent 
material, so that the measuring points of an instrument can only be pressed 
lightly against the surfaces, and the weight must, therefore, be supported inde- 
pendently of the model. In instruments so far constructed, the measuring 
mechanism is carried on a U-shaped frame, for convenience of movement from 
point to point of the specimen. One measuring needle is secured and operated 
by a calibrating screw, and the other is free to move a multiplying lever system, 
and thereby tilt a mirror to give an angular deflection, which latter is calibrated 
by reference to the standard screw when the instrument has been finally secured 
in place. In recent work the labour of accurately setting the instrument in a 
number of different positions has proved so great, that my assistant, Mr. F. H. 
Withycombe, has designed a useful adjunct in the form of a mechanical slide- 
rest, to effect the required changes easily and expeditiously. In one arrange- 
ment, a bracket carries the measuring instrument on a three-point sup- 
port, and movement is effected by slides arranged to give displacements along 
three axes at right angles, and their amounts are measured by micrometer screws 
to an accuracy of rather less than one-thousandth of an inch. 
