September io, 19 14] 



NATURE 



51 



circular symmetry, and as the optical effects of these 

 latter disappeared at a small distance from the edge, 

 a field of view was obtained in which the optical 

 effects of load applied perpendicularly to the plate 

 were quite small, even when the internal stresses 

 were very great. 



Two circular plates clamped together to enclose 

 a space between them may therefore be used as 

 windows for observing the effect of a uniform pres- 

 sure upon a transparent specimen, which latter may 

 be a plate with its faces parallel to the end plates 

 closing the chamber. If cubical compression is ap- 

 plied by a fluid, the principal stresses in the plane of 

 the plate produce opposing optical effects, and any 

 remaining effect is due to perpendicular pressures on 

 the faces. The arrangement of experimental appara- 

 tus, therefore, took the form of a pair of transparent 

 windows separated by an annular disc, and firmly 

 clamped together by collars. The central chamber so 

 formed was subjected to pressure of air, or other 

 fluid, up to about one thousand pounds per square 

 inch, and afterwards the specimen was introduced and 

 the same pressure applied ; but no visible change of 

 effect could be observed. Finally, the specimen was 

 set in the field of view outside the chamber, and 

 pressure again applied by the fluid, but still no change 

 was apparent. In all three cases the optical effects 

 produced were small, and practically alike, so that 

 the experimental evidence appears to warrant the 

 conclusion that a principal stress in the direction of 

 an incident beam of 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 proportional to the stress dif- 

 ference j>erpendicular 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 re- 

 tardation 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 dis- 

 pensed with, and Filon has shown. In cases where a 

 theor\' 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 ad- 

 vantages, 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 com- 

 parison 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 prin- 

 cipal stress, and loaded until the total effect produced 

 Is a dark field denoting a zero value. The difference 



NO. 2341, VOL. 94] 



of the principal stresses is then measured in terms ot 

 a simple tension. This alone is insufficient to deter- 

 mine the distribution, unless one of the principal 

 stresses is zero, and, in general, another independent 

 measure must be obtained. This is very conveniently 

 supplied 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 com- 

 paratively 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 thick- 

 ness obtainable for optical work, a simple calculation 

 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 instru- 

 ment can only be pressed lightly against the surfaces, 

 and the weight must, therefore, be supported inde- 

 pendently of the model. In instruments so far con- 

 structed, 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 minor to give an angular deflection, 

 which latter is calibiated 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 posi- 

 tions 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 

 arrangement, a bracket carries the measuring in- 

 strument on a three-point support, 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. 



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 experi- 

 mental 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 experiniental 

 evidence Is available on a variety of practical engineer- 

 ing problems covering a very wide field of practice, 

 not merely qualitative, but quantitative, and ap- 

 proximating to the needs of the physicist and mathe- 

 matician, 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 



