﻿in a Rectangular Bar by means of Polarized- Light. 21 



critical point observed, they do not show very good agree- 

 ment. The results are given in Table IV., the values in the 

 column headed c/b'^ (ciii.) being obtained from formula (21). 



Table IV. 



i. 



M /W (obs.). 

 in cm. 



qh' (obs.). 



qh'* (cal.). 



15° 



75° 



-201 

 -240 



-4-55 

 -4-99 



-3-60 

 -3-60 



The poor agreement may be due to two causes : (a) error 

 in the determination of M . This, although numerically 

 small, had to be obtained as the difference of two numerically 

 large couples, the determination of each of which was liable 

 to error ; (b) the node was further from the point of con- 

 centrated load than in the case of Table III., and this, as 

 pointed out above, may vitiate the approximations. 



§ 8. Observations of the Points where the Isocliuic Lines 

 cross the Vertical through the Load. 



To further test the mathematical theory referred to, the 

 points where the isoclinic lines crossed the vertical through 

 the load were measured by means of the network of squares 

 described in § 2, and compared with their positions as 

 indicated by theory. 



In the paper already referred to (Phil. Trans. A. vol. cci. 

 pp. 63-155) the formulas {86) given on p. 98 lead to the 

 following expressions for P — Q, 2S, when a couple M is 

 superadded. 



2 W « (r y cos vS ■ 2Wys/rY 



Fh-i 



2W < 



7T0 o 





+i 



2W,i 



7r£ 2 



7W v\ 



J 



The G's and F's are constants, having values given on 

 p. 99 of the memoir referred to ; .v and y are now measured 

 horizontal and vertically upwards from the centre of the 

 block of glass, r = s/x 2 -\-y® and <f)= tan"" 1 #/</. 



Along the vertical through the load,,?- and therefore (£=0 

 and r=y. Thus 8 = and the black band passes through 

 those points for which P — Q = 0, whatever the value of /. 



(22) 



WT4 



