COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 355 
were taken in inches. The results, however, are not affected by the scale of the 
diagram. 
Unit stress was taken to be that which produced the retardation corresponding 
to the ‘ tint of passage.’ 
A preliminary curve was drawn giving P — Q to x, as obtained from the inter- 
sections of the isochromatics with Ox. Krom this curve the values of P — Q corre- 
_ sponding to z/r = 0-1, 0-2, 0-3, etc., were read off, and 4y was the vertical intercept 
aa a , 
for those values of x between the isoclinics ¢ = + 5° and @ = — 5°, so that Ap 
= are 10°. The results are shown in Table I. 
TABLE I. 
CALCULATION OF P atone OX. 
| 
| 2 | 
| ay z P P > Q Q 
| ar | P—Q He 
(inches) + Graphical) Theory |Graphical| Theory 
oy 
0 4-08 co 0 0-84 1-06 —3:24 | —3-18 
0-1 3°94 3°05 0-226 0-81 1-02 —3-13 | —3-10 
0-2 3-53 2-03 0-304 0-72 0-90 —2-81 | —2-86 
0:3 3°04 1-45 0-366 0-61 0-74 —2:-43 | —2-51 
0-4 2-53 1-08 0-409 0-48 0-56 —2-05 | —2-09 
0-5 2-03 0-88 0-403 0-35 0-38 —1-68 | —1-66 
0-6 1-50 0-74 0-354 0-23 0-24 —1:27 | —1-23 
0-7 1-00 0-65 0-269 0-13 0-12 —0:87 | —0-85 
0-8 0-60 0-59 0-178 0-06 0-05 —0-54 | —0-52 
0-9 0-28 0-59 0-083 0-01 0-01 —0-27 | —0-23 
1-0 0 0-60 0 0 0 0 0 
The integration for P (graphical) was carried out by simple addition of mid- 
ordinates. The columns marked P (Theory) and Q (Theory) were computed as follows: 
The values of Q obtained graphically were taken from the seventh column and 
+r 
| Que computed. This was found to be 10-84, and this value was taken as the 
—?r 
total applied force F ; and the theoretical stresses for a disc under forces F diametri- 
cally applied were computed. The Q values are seen to agree quite well. The P 
values shown by the graphical analysis are somewhat lower (but not really by large 
absolute amounts) than the theoretical values ; but the spread of the applied pressure 
already mentioned would act in this sense. 
7. The next step was to compute P along the lines of stress marked A, B, C, D in 
fig. 4 (E was omitted as the observed lines were too crowded for the drawing to have 
been sufficiently accurate). 
Formula (7) was now used, bearing in mind that at the boundary Py is zero; and 
the observed values are tabulated for the intersections of the stress line with the 
_ successive isoclinics. 
