1016] on Polarized Light and its Applications to Engineering 579 



outer surface of the pipe is approached. In this case there is known 

 to be a radial compression stress accompanied by a circumferential 

 tension stress, and the optical effects produced at any point are pro- 

 portional to the algebraic difference of their intensities— in this case 

 their numerical sum. 



In a thick cylinder of these proportions the radial stress is not 

 large, and its intensity can be determined independently, but the 

 combined effects of both stresses have been measured here, and are 

 plotted in Fig. 2, in which the firm line gives the experimental values 

 obtained, while the dotted curve represents the results of calculation. 



If p is the circumferential stress and g the radial stress at any 

 radius r of a cylinder with free ends, calculations show that their 

 values are given by — 



P 



4^r'^+ 1) 



so that 



V 





where p^ is the applied pressure, and r^ and r^ the inner and outer 

 radii of the cylinder. 



In an experiment carried out on a ring in which the inner radius 

 rj = 0*71 inches, and the outer radius r^ = 1 '43 inches, a pressure of 

 900 pounds per square inch was applied to the interior of the ring, 

 and the experimental values compared with those obtained by calcula- 

 tion. The followino- results were obtained : — 



2 Q 2 



