I'JIG] on Polarized Light and its Applications to Engineering 577 



Laws of Optical Effect, 



We must now inquire what are the simplest means of measuring 

 the stresses produced in a plate of transparent material caused by 

 any given system of loading in its own plane, and it will be apparent 

 that if the stress is merely simple tension or compression, its intensity 

 can be read off at once by reference to the colour scale already 

 estabHshed. Many cases of this kind occur in practice. If, for 

 example, a simple ring is cut through one side and loaded after the 

 fashion of a hook it is very severely stressed, especially at its principal 

 horizontal section, and the distribution across this section consists of 

 tension and compression stress only. 



We may therefore read off the stress at any point of the section 

 and obtain curves of distribution, such as those now shown, in which 

 the stress intensities for several loads have been determined and plotted. 



In this case the experiments agree fairly well with the calculations 

 of Andrews and Pearson on the stress distribution of a hook of this 

 cross-section, and they also show the interesting result that as the 

 load increases the neutral line moves away from the tension side. 



In most cases, however, the stress distribution is more com- 

 plicated to deal with, but it is known that any case of stress in the 

 plane of a plate, can always be represented by two principal stresses 

 at right angles, and if the magnitude and direction of these are 

 determined for all points the stress distribution is solved. 



In order to obtain an experimental solution of this problem, it is 

 necessary to inquire into the relation of the optical effect to the 

 principal stress intensities at a point, and it is easy to show this 

 by simple experiments. If, for example, we take two tension 

 members and subject them to the same uniform stress intensity, 

 the colour effects produced by interference will be precisely the 

 same for each, while if they are superposed, or if we interpose a 

 double thickness, the colour effect is that produced on a single 

 member under twice the stress. Experiments on three or more 

 members readily verify for simple tension and compression that the 

 optical effect is simply proportional to the stress intensity, and also 

 to the thickness of the plate. If, however, two equally stressed 

 tension members of the same thickness are crossed, the common area 

 gives a dark field, showing that the stress effect of one neutralizes 

 that of the other. The same dark field is produced if an equally 

 stressed compression member is placed with the direction of stress 

 parallel to that of the tension member, and we may readily verify 

 in all cases that tension and compression stresses in the same 

 direction add their effects, while stresses in directions at right angles 

 subtract them. 



The latter result is of chief importance, since the stress at any 

 point of a plate can always be represented by the stresses p and q 

 Vol. XXI. (No. 110) 2' q 



