156 PROF. E. G. COKER AND MR. K. C. CHAKKO: THE STRESS-STRAIN PROPERTIES 
length are noted with reference to the horizontal scale, and from these observations the 
c5 . 
constants in the equation 
a B , C 
X \ — -A- + T2+ w 
are found for calibrating the positions of the black bands. 
In the observations it is found that the depth of the beam does not appear quite 
constant throughout the field, an error due to the combined imperfections of the 
lenses and prisms employed. The maximum change of depth is about 2 per cent., and 
a correction is therefore necessary to reduce all vertical distances to a constant depth 
of beam. 
mam 
1 6 
o 
i 
o 
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JlLLL 
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li i i 
J-LL1 
Micrometer 
Read 
F bE 1) C 
Fig. 12. View of spectrum. 
The observations made are too numerous to give in detail but typical examples of 
some measurements are shown in the accompanying fig. 13, in which the black bands, 
due to extinction of light, are drawn for a bending moment of 178'3 in pound and inch 
units. This, however, is not the exact appearance of the bands in the field of view 
owing to variation in the wave-length which alters the horizontal scale, but is here 
made uniform for plotting. 
For some calculations, however, it is more convenient to show the form of the bands 
corresponding to a definite wave-length with a varying bending moment. Owing to 
the presence of a small amount of initial retardation in plates of nitro-cellulose, due 
to the method of manufacture, which leaves traces of initial stress, there is generally 
some slight difference between the bands on each side of the neutral axis, and a more 
accurate value is probable if the mean value for the two sides is taken. 
If relative retardation is a linear function of the stress difference, these new 
abscissas will represent the mean stress, but if the strain varies linearly they will also 
represent strains to another scale. 
