﻿in a Rectangular Bar by means of Polarized Light. 19 



loop passes over into a fork. As q increases further nega- 

 tively, qb' 2 reaches its maximum and returns to the value 

 -co . Thus after a time we have a second change, the fork 

 passing over again into the loop. The two critical points 

 correspond to the same value of qb' 2 , namely, that given by 



^/2 = _4sin 3 |*/sin2z*, . . . . (21) 



but to different values of q, there being two values of q for 

 any given value of qb' 2 . 



The reader should note that figs. 5—9 are merely diagram- 

 matic, and are intended to give a rough sketch of the curves. 

 They are not intended as accurate graphs. 



§ 7. Observation of the Tsoclinie Lines near a point of 

 concentrated load. 



The polarizer and analyser being crossed, their inclination 

 to the horizontal and vertical was read. This gave the 

 angle i. The ratio of M /W was then steadily varied by 

 altering the forces acting on the projecting arms. Starting 

 from a fairly large positive value M / W was diminished down 

 to a fairly large negative value, i remaining constant all the 

 time. This gave a range covering the various critical cases 

 dealt with in the theoretical discussion of § 6. 



The beam was examined for the values 0°, 15°, 30°, 45°, 

 60°, 75°, 90° of i ; critical changes in the appearance of the 

 black band were noted in each case. 



The values i~0 and 2 = 90° gave, as was to be expected, 

 a vertical black band throughout, whatever the value 

 of M /W. 



For other values of i, starting from M /W = 7 cm. (the 

 height 2b of the bar being 3'60 cm.) the appearance of the 

 black band first of all coincided with that shown in fig. 6. 

 As M /W (and therefore qb'*) decreases, we find that, as 

 predicted from theory, the loop eventually passes into the 

 fork. The values of M /W for which this occurred were 

 noted for the various values of i. From these values of qb" 2 

 were obtained, and these were compared with the values of 

 qb' 2 calculated from equation (17). The results of the com- 

 parison are shown in Table III. below. 



C 2 



