﻿20 Prof. L. N. G. Filon : Investigation of Stresses 



Table III. 



*. 



M /W (observed) 

 in cent! metres. 



qb" 2 (obs.). 



qb' 2 (cal.). 



15° 



043 



6-79 



6 64 



30° 



4-44 



421 



4-41 



45° 



4-26 



3-98 



4-00 



60° 



4-83 



4-71 



4-41 



7o° 



6 64 



7 06 



6-64 



]f we bear in mind that the exact moment when the fork 

 passes into the loop is very difficult to determine experi- 

 mentally, the field being very dark in the region where the 

 change takes place, we may say that the experiments are 

 in fair agreement with the theory within the limits of 

 observation. 



As M /W is still further diminished the fork of the band 

 broadens out, and we observe the appearances shown in fig. 5. 

 On continuing to decrease algebraically M / W, we eventually 

 make V <0 and obtain the appearance shown in fig. 7. 

 From this point, however, a difference occurs, according to 

 the value of i taken. For i = 30°, 45°, 60°, the two branches 

 of the curve shown in fig. 7 gradually bend round until we 

 get the double loop of fig. 8, after which no further critical 

 change occurs. As M increases negatively these loops 

 gradually shrink, and soon present the appearance of two 

 faint short brushes, which become practically invisible. 



But for i = 15° or 75° (which gives i>72° 30' or < 17° 30') 

 the band first shows a fork in one sector as in fig. 9 ; when 

 M /W passes a certain negative value, this fork passes into 

 the double loop of fig. 8. This corresponds to the second 

 critical point mentioned on p. 19. Tiie existence of the 

 first critical point, in which the loop passes into the fork, 

 I have not been able to detect experimentally. The reason 

 for this will be obvious if we look at the equations giving 

 q and qb'. We see there that if q be very small, V is very 

 large (since qV is not small with q). Now the node is always 

 at a depth bj2 below the point of loading. It follows that 

 a node corresponding to a numerically small value of q 

 will be outside the field of view, or, at all events, so far 

 from the point of loading as to render our approximations 

 invalid. 



Turning to the actual numerical values obtained for the 



