94 
BIRNIE. 
underlining the critical measured stress; for example, 42920 
on the diameter 9.54 inches in the breech section, and so on. 
In each case it is seen from the table that the corresponding 
stress in action is 60,000 pounds, while the stresses on other 
diameters are less than this; hence the condition is fulfilled. 
Taking again the breech section (second stage) before an¬ 
nealing as an example of the method of computation, the 
elastic resistance of the section and the stresses on given 
diameters for the state of action are derived as follows: 
The measured stress which in this section will first reach 
the limit, 60,000, is 0 = 42,920 on the diameter, 9.54 inches. 
The increase of stress allowable on this diameter in passing 
from the state of rest to action is therefore: 
0 = 60000 — 42920 = 17080 pounds. 
The corresponding value of P 0 is then found from (4), 
with r = 4.77. 
0 = 17080 H 0.32602 P 0 . * . P 0 = 52390 pounds. 
The interior pressure being thus determined, equation (4) 
is further applied to determine the increase of stress at other 
given radii. For this purpose it is convenient to reduce it 
to the form by substituting known values: 
0 = 5553 + 
262300 
in which, by substituting the several values of r, we obtain 
the increase of stress for that radius, and, taking the alge¬ 
braic sum of this result and the measured stress at the same 
point (at rest), we have finally the stress pertaining to the 
applied interior pressure, P 0 = 52,390 pounds. Thus: 
Increase. Measured, f) {action). 
d =- 3.81, r = 1.905: 6 = 5553 -f 72280 = 77833 — 71260 = + 6573 pounds. 
d — 4.41, r = 2.205: 6 = 5553 + 53949 = 59502 — 56800 = + 2702 “ 
******* 
d = 9.54, r — 4.77: 0 = 5553 + 11528 = 17080 + 42920 = -f 60000 ‘‘ 
(Proof.) 
as given in table A and shown on the accompanying 
plate 6. 
