98 
BIRNIE. 
7th. When one point of the initial tension curve is given 
(either an assigned or measured value of p) the curve will 
be fixed, as has been illustrated in the examples worked out. 
It is important to observe that this curve as defined and 
laid down is, barring the presence of local strains in the 
metal, that which should be naturally formed under the 
conditions of equilibrium between the positive and negative 
strains in the wall of the cylinder at rest. This equilibrium 
must exist, and the curve as defined fulfills this condition, 
since it is dependent upon it. The straight line, represent¬ 
ing the state of uniform strain in action, used in every case 
as the datum line for the initial tension curve, is dependent 
upon the condition of equilibrium between the pressure and 
the elastic strains in the metal. That line, however, is the 
initial tension curve itself in a particular position. On the 
withdrawal (supposed) of the force P the right line falls to 
the position of the initial tension curve, having lost nothing 
of its property to express the equilibrium of the forces which 
cause it to exist. This being, then, the only curve which 
can be formed under the circumstances, and since the value 
of p cannot exceed the given elastic limit, it may be seen 
why in cylinders thicker than 0.65 caliber the conditions of 
maximum pressure and uniform strain to the elastic limit 
of the metal in action cannot exist together. An initial ten¬ 
sion curve, starting with the limit p at the bore and having 
higher strains than the natural curve toward the exterior, 
might be laid down which would become a straight line with 
P increased sufficiently to stretch the bore to the elastic 
limit, but such an initial tension curve is not attainable in 
practice. 
To compute the possible maximum resistance of the pres¬ 
ent sections of cylinders we will take, as before, the con¬ 
servative limits, & = 60,000 = p. The breech (after anneal¬ 
ing) and the breech middle sections are respectively 0.75 and 
0.81 caliber in thickness. Their maximum resistance will 
therefore depend upon the assumption that the bore is ini¬ 
tially compressed to the limit p at rest and extended to the 
