588 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



color effects appear. A first order fringe will have red (absence of violet) 

 nearest the zero order fringe and violet (absence of red) furthest from 

 the zero order fringe. High order fringes will not appear at all in white 

 light since they are the resultant of a number of colors which add up 

 to white light. 



Having located the zero order fringe, a simple count will give the 

 number of times the factor (S8/h) has to be multiplied by to obtain the 

 number of pounds per square inch. This stress will, however, only be a 

 stress difference and in order to resolve this into stresses along X and Y 

 axes and a shearing stress in the XY plane, other information 

 is necessary. 



One part of the information is obtained when the isoclinic directions 

 are obtained. These directions are the directions of the principal stress 

 axes and these are obtained by taking out the quarter wave plates and 

 rotating the axes of the polaroids (keeping them crossed) until the 

 polarization axes coincide with the principal stress axes at any point. 

 When this occurs, the picture will be black because if no model were 

 there, the polarized light passed by the polarizer would be cancelled by 

 the analyzer. If the principal axis of the stress eUipsoid coincides with 

 the direction of polarized light from the polarizer, only one ray will be 

 generated whose plane of polarization coincides with that of the polarized 

 Ught and hence this will be cancelled in the analyzer. The isoclinic lines 

 show up much better if a white light source is used. Hence, the isoclinic 

 Hnes locate the direction of the principal axes of the stress ellipsoid. 

 From equations (20) and (23) we have 



r-^)" 



sin 2(9, Ti - T2= {T[ - T2) cos 26. (30) 



Hence, if we know 6 (the direction of the principal stress axes with re- 

 spect to the axes for which the stresses are to be analyzed) the shearing 

 stress T« and the difference between Ti and T2 can be obtained from 

 equation (30). 



The other necessary relation can be obtained from the equilibrium 

 stress relations that have to be satisfied by any stationary body, namely 



'^ + fi =0; ^^ + '^ = 0. (31) 



dx dy dy dx 



Integrating these equations 



