152 PROF. E. G. COKER AND MR. K. C. CHAKKO: THE STRESS-STRAIN PROPERTIES 
Somewhat similar results are obtained on plates x 3 6 inch thick, but in both 
experiments, fig. 9, the curves of ffe have a rather higher linear limit than the 
corresponding ffe curve, but here again the ratio f/f is still linear to about the 
same range as in previous cases. 
The case of plates \ inch thick, fig. 10, is more especially interesting from the fact 
that the stress-strain curve there shown is, at a later stage, obtained entirely from 
the optical effects observed from an analysis of the spectrum of a beam under 
uniform bending moment. It is sufficient to remark here that the f/f curve shows 
a somewhat lower limit of linearity, although both the other curves have 
corresponding limits of 2000 lbs. per sq. inch. 
When these curves are corrected for the change of cross-section which occurs 
as the test proceeds it is found, as fig. 10 shows, that the stress-strain curve f/e is 
perceptibly raised beyond the elastic limit and therefore tends more towards linearity, 
and the equivalent stress/strain curve is lowered and diverges still, more from the 
linear relation. The stress/equivalent-stress curve has therefore a somewhat higher 
linear limit when this correction is made. Owing to the defective optical properties 
of still thicker material it was not found possible to examine these relations in 
a f-inch plate in a satisfactory manner. 
Fracture. —The behaviour of nitro-cellulose at fracture is somewhat unusual for 
so ductile a material. As the load increases the section diminishes very'uniformly 
at all parts removed from the enlarged ends, but there is little or no local contraction at 
any stage, and even at the fractured section, the cross-section differs but little from 
that at any other part of the bar, but after fracture there is a remarkable contraction 
in the total length accompanied by uniform expansion of the cross-section. This is 
shown in Table II., which gives a summary of the observations made and, except 
for one of the thin specimens and for the reasons given earlier, there is a recovery 
in length of from 6 to 9 per cent, after fracture. Various other measurements 
already described above are recorded here for convenient reference and also some 
ratios of the optical constants. 
Spectrum Analysis of the Stress in a Beam. —The results of the optical 
examination appear to show the truth of the optical stress law for simple stress well 
beyond the elastic limit of the material, but the importance of this fundamental law 
makes it desirable to examine the matter in an independent way and possibly 
by a more rigid test than a comparison beam affords. An investigation of the 
optical phenomena presented by a beam under pure bending moment was made 
therefore on a rectangular strip 22?r inches long, 1'005 inch deep and 0'2542 inch 
thick. Its specific gravity was approximately 1*361, this latter being deter¬ 
mined at a temperature of 64° Fahr. by measurement of its volume and weighing 
in air. 
The beam is supported as before on knife edges 2 inches apart, and the loading is 
applied at each end by dead weights having an overhang of 9f inches. 
