BIRNIE. 
92 ‘ 
Additional formulas deduced from those given in Ap¬ 
pendix B, “ Gun Making,” can be given to determine, first, 
the changes in the stresses at given radii due to reaming 
out or enlarging the bore of a cylinder under initial ten¬ 
sion ; second, the changes due to turning off or reducing the 
exterior of the cylinder. Such formulas would be useful in 
the practical working of this method, but it will be sufficient 
to state here that any reduction of the thickness of wall 
should cause a lowering of the initial strains or stresses. 
This result has not been uniformly shown in the present 
experiments. Exceptions may be noted in the earlier stages 
of dismantling the breech and the breech middle sections. 
In these cases it would appear that the metal near the sur¬ 
face of the bore was overcompressed by the treatment, and 
local strains were produced which became manifest when a 
part of the metal was removed. 
To explain the application of the formulas we may take, 
for example, the breech section before annealing. 
Stress Curves for the State of Rest .—Taking the measured 
compression, 71,260 pounds, on the diameter, 3.81 inches, as 
a basis for constructing the “deduced” curve of stresses, we 
first find the corresponding compression at the surface of 
the bore from equation (6), in which 
= R 0 = 1.8, r, #= 1.905, R 1 = 4.86, Pl = 71260. 
r 
Then: 
_ 1.0647 — 0.15898 — 2.0695 _ 1.41228 
Po 1.0647 — 0.15898 — 1.5446 Pl 1.16378 
X 71260=86477 lbs. 
Next, applying equations (3) and (2) with /> 0 given, we 
find: 
3 X 20.38 
X 86477 —91870 pounds. 
07.00 
0 u = a P u = 0.70997 X 91870 = 65225 pounds. 
These latter values express the theoretical condition, 
assumed only for auxiliary purposes, that, having a com- 
