90 
BIRNIE. 
measurements made, the highest being p = 78,280 at the 
bore of the breech middle section. It will be understood 
that the stated measured stresses correspond to the measured 
strains per inch for a modulus of elasticity, E = 30,000,000 
pounds. For example, the value of p just stated is derived 
as follows: 
0.00835 (strain) 
' 3.2 (diameter) 
30,000,000 = 78,280 (stress). 
(i) 
The sections taken for examination are the breech, breech 
middle, muzzle middle, and muzzle before annealing, and 
the breech and muzzle after annealing. In the dimensions 
of these sections we have -nearly the counterpart of four 
principal cross sections of the 3.2-inch field gun. 
The principal objects of discussion will be— 
1. To compare the measured stresses in the forging after 
treatment with those anticipated by theory and required to 
make the resistance to interior pressure a maximum. This 
will show the degree of uniformity in the actual stresses and 
how nearly they conform to the requirements of the law for 
maximum resistance. 
‘ 2. Taking the actual stresses as measured in each section, 
to determine the elastic resistance of the section to interior 
pressure. This, while admitting every irregularity of the 
stresses or strains induced by the treatment, will give a final 
measure of its efficacy. 
The formulas* to be applied, which are fundamentally 
the same as those for the built-up construction, relate to a 
gun or cylinder made of a single piece, with initial tension 
produced by interior cooling. 
( 2 ) 
P = 
3 (Pi 
R<?)P 
(4 R? -f 2 JRJ) — 3 {R? 
« 
(3) 
*For these formulas see Gun Making, Appendix B, Military Service 
Institution Monograph, 1888. 
