176 
MR. A. A. GRIFFITH ON 
The average value of R y/c is 239, and the maximum 251. 
According to the theory, fracture should not depend on Q, and R \/c should have, 
at fracture, the constant value 
In the case of the glass used for these experiments, E = 9-01 X 10 c lbs. per sq. inch, 
T = 0-0031 lbs. per inch, and o- = 0-251, so that the above quantity is equal to 266. 
These conclusions are sufficiently well borne out by the experimental results, save 
that the maximum recorded value of R y/c is 6 percent., and the average 10 percent., 
below the theoretical value. It must be regarded as improbable that the error in the 
estimated surface tension is large enough to account for this difference, as this view 
would render necessary a somewhat unlikely deviation from the linear law. 
A more probable explanation is to be obtained from an estimate of the maximum 
stress in the cracks. An upper limit to the magnitude of the radius of curvature at 
the ends of the cracks was obtained by inspection of the interference colours shown 
there. Near the ends a faint brownish tint was observed, and this gradually died out, 
as the end was approached, until finally nothing at all was visible. It was inferred 
that the width of the cracks at the ends was not greater than one-quarter of the shortest 
wave length of visible light, or about 4 X 10 -6 inch. Hence p could not be greater 
than 2 X 10 -B inch. 
Taking as an example the last bulb in Table II. and substituting in formula (21), it 
is found that 
2R 
E 
= 8-13 X 10~'\ 
whence the maximum stress F > 344,000 lbs. per sq. inch. The value given by the 
first order expression 
F = 2R a / c 
V P 
is 350,000 lbs. per sq. inch. 
A possible explanation of the discrepancy between theory and experiment is now 
evident. In the tension tests, the verification of Hooke’s law could only be carried 
to the breaking stress, 24,900 lbs. per sq. inch. There is no evidence whatever that 
the law is still applicable at stresses more than ten times as great. It is much more 
probable that there is a marked reduction in modulus at such stresses. But a decrease 
in modulus at any point of a body deformed by given surface tractions involves an 
increase in strain energy, and therefore in the foregoing experiments a decrease in 
strength. This is in agreement with the observations. 
