50 



NATURE 



[September io, 1914 



tive properties of trar.sparent bodies under stress, a 

 discovery made by Sir David Brewster almost exactly 

 one hundred years ago, and but rarely made use of 

 since by engineers, although Brewster himself imme- 

 diately saw its value for experimental purposes, and 

 suggested that mode's of arches might be made of 

 glass, and the effects of stresses due to loading ren- 

 dered visible in polarised light. 



Brewster carried his investigations further, by the 

 invention of a "chromatic teinometer " for investi- 

 gating the nature of strains, and consisting of plates 

 or bars of glass subjected to flexure in definite ways 

 for comparison with the body under stress. 



At a much later date (1S41) Neumann developed 

 an elaborate theory for the analysis of strain in trans- 

 parent bodies due to load, unequal temperature, and 

 set, while, still later, the }'outhful genius of Clerk- 

 Maxwell supplied an algebraical solution for the stress 

 distribution in any plate subjected to stresses in its 

 own plane. 



The early history of the development of this branch 

 of science is, in fact, remarkable for notable con- 

 tributions at long intervals of time, and the almost 

 complete disregard by engineers of its practical im- 

 portance. 



The application of optical investigation to the deter- 

 mination of stress distribution in engineering struc- 

 tures and machines has, however, been hindered by 

 causes which, although apparently insignificant, have 

 been very real obstacles, and among these was the 

 absence of a transparent material which could be 

 fashioned into shapes suitable for investigating 

 technical problems. It is not an easy matter, for 

 example, to construct a glass model of a bridge free 

 from internal stress, in the manner suggested bv 

 Brewster; and, moreover, glass is extremely fragile 

 under load, especially in cases where the stress dis- 

 tribution in it varies very much, while the cost of con- 

 struction is very great. Happily there is now no 

 necessity to employ glass for experimental investiga- 

 tion on engineering problems, since modern chemistry 

 has supplied artificial bodies, such as the nitro-cellulose 

 compounds used for many trade purposes, which have 

 optical properties very little inferior to glass, are able 

 to bear great stresses without injury, and also are 

 capable of being fashioned with the ease and certainty 

 of a wooden model. Photographic processes are also 

 able to reproduce the brilliant colour effects caused by 

 stress in transparent materials, so that permanent 

 records can now be made for future reference. 



The construction of polariscopes for examining 

 models on a large scale is very essential for technical 

 research, and the great scarcity of Iceland spar of 

 sufficient purity and size for use as Nicol's prisms has 

 caused much attention to be paid to the construction 

 of apparatus for producing plane polarised light by the 

 aid oiF sheets of glass. Fortunately this presents little 

 difficultA', and although the light is not nearly so well 

 polarised as that obtained from a Nicol's prism it is 

 sufficiently so for the purpose. Large quarter-wave 

 plates of mica have also been constructed by my col- 

 league. Prof. Silvanus Thompson, for obtaining cir- 

 cularly polarised light, and these have proved suffi- 

 ciently exact and exceedinsrly useful for larg-e models. 



It is of Importance to show that the stress distribu- 

 tion revealed bv a polarised beam of light passing 

 through an elastic transparent material in no wav 

 differs from that obtained by other means, and evi- 

 dence is available in modern researches, especially bv 

 Filon, that the experimental results obtained with 

 glass agree with those of the theory of elasticity, while 

 a satisfactory agreement of a sirnilar kind has also 

 been obtained with nitro-cellulose compounds, although 

 not in so complete and direct a manner. Such an 



NO. 2341, VOL. 94.1 



agreement may be expected on theoretical grounds, 

 since the values of elastic constants do not affect 

 the fundamental equations for stresses in a plane, and 

 although for three-dimensional stress the effect of the 

 stretch-squeeze ratio causes some difference, yet this is 

 usually negligible. 



Most of the physical constants of glass have been 

 determined with very considerable accuracy, but other 

 transparent substances have so far received little atten- 

 tion, and their optical constants are not well known. 

 Ihe stress-strain relations of glass and nitro-cellulose 

 have been determined with considerable accuracy, and 

 a useful idea of their relation to metals may be gained 

 from the value of the stretch-modulus, E, and the 

 stretch-squeeze ratio, <r . 



The accompanying table shows some average values 

 for a few important materials, and it is of interest 

 to note that the stretch-squeeze ratios of cast-iron and 

 plate-glass are very similar, while the values of the 

 stretch modulus are nearly a^ three to two. These 

 two materials also possess other like characteristics : 

 they are both very brittle, and possess well-developed 

 crystalline structure, so that we may expect the pro- 

 perties of cast-iron under stress to be very faithfully 

 followed by plate-glass. 



Material E a 



Steel 30,000,000 ... 025 



Wrought iron ... 28,000,000 ... 0*28 



Cast iron ... ... 15,000,000 ... 025 



Plate-glass ... 10,500,000 ... 023 



Nitro-cellulose ... 260,00010300,000 ... 0*40 



The high values of the stretch modulus for steel and 

 wrought iron are not, apparently, approached by any 

 transparent material having similar ductile proper- 

 ties, but although nitro-cellulose has a stretch modulus 

 of rather less than one-hundredth that of steel, its 

 stress-strain properties are not unlike. In some recent 

 experiments with a miniature testing machine fitted 

 with an arrangement for recording the stress-strain 

 relations of xylonite throughout the whole range of 

 stress up to fracture, the main characteristics of steel 

 appear on a very reduced scale, and give additional 

 confidence that the results of optical experiments on 

 this material are applicable to metal structures. 



The complete analysis of stress , distribution in a 

 plate is not, however, a simple matter, and the 

 analysis of Clerk-Maxwell was intended to provide a 

 solution based on the properties of the isochromatic 

 and isoclinic lines, coupled with the law that the 

 optical effect is proportional to the difference of the 

 principal stresses at a point, and to the thickness of 

 the plate. 



A principal stress perpendicular to the bounding 

 planes is assumed to have no optical effect ; but since 

 many cases have arisen where there are three prin- 

 cipal stress components, it seemed desirable to 

 examine such a case experimentally. 



It is a matter of some difficulty to arrange ap- 

 paratus to stress a specimen in the direction of the 

 incident beam, and at the same time observe the 

 optical effect free from disturbing causes, since a 

 transparent medium must be interposed for applying 

 the required load, and this will be subject to stresses 

 which may interfere with the optical effect on the 

 specimen. 



Some observations on circular plates clamped at 

 the edges and uniformly loaded over one face, showed 

 that the bending stresses produced in the plate caused 

 very little optical effect, since the tension and com- 

 pression stresses neutralised one another, while the 

 shear effects also appeared to be practically negligible. 

 The only remaining stresses of importance, were those 

 caused by the clamping plates at the boundary, which 

 produced radial and circumferential stresses having 



