Optical Determination of Stress. 741 



plates, the effect of notches and holes of various forms in 

 tension and compression members, beams, pillars, and shafts, 

 the distribution of stress in built up structures such as plate 

 girders, rivetted frames, masonry dams, and the like. 



In most of these cases the distribution of stress has not 

 been completely solved. 



One of the most suggestive and instructive experimental 

 methods is suggested by the differential equations of plane 

 strain which, under certain conditions, have identically the 

 same forms as the equations of stream-line motion in a 

 perfect fluid. Thus in irrotational plane strain when u and 

 v are the displacements in the direction of the axes of x and 

 ?/, we obtain 



while if u and v are the displacements of a perfect fluid 

 moving irrotationally we obtain similar equations. The 

 stress problem has therefore an analogous problem in hydro- 

 dynamics, but the restrictions to which the analogy is subjected 

 seriously limit its applications. 



Many experimental researches on the behaviour of materials 

 have also been made using models shaped in rubber, and by 

 measurements of the comparatively large strains produced 

 in this material under various conditions of loading, the 

 stresses in the structure have been determined. 



A method invented by Brewster depends on the applica- 

 tion of polarized light for observing the condition of a 

 specimen made of glass, and he suggested that models of 

 arches might be made of this material and their optical 

 properties examined under stress. 



This matter has received a considerable degree of develop- 

 ment at the hands of Neumann* and Maxwell t; but the 

 difficulty and expense of making objects in glass has hindered 

 the progress of the experimental method. 



In an attempt to obtain an optical verification of the 

 mathematical theory of the stresses at the principal section 

 of a hook, one or two models were shaped from a square of 

 glass, aud their behaviour under stress examined by polarized 

 light. The experiments showed that to produce any measurable 

 effect the glass must be very thick and the stresses dangerously 

 near the breaking stress of the material. 



Several other materials were tried, and a suitable material 

 was ultimately found in " xylonite," which possesses most of 



* "Die Gesetze der Doppelbrechung- des Lichts," F. E. Neumann, 

 Abhandlunqen der K. Ahademie der Wissenschaften zu Berlin, 1841. 



f " On the Equilibrium of Elastic Solids," J. C. Maxwell, Collected 

 Papers. 



