I have run figures for two different scenarios with all three above formula,s on steel having assumed Elastic Point of 50K psi (approx mill run 1035). First "chamber end" with dia of .800" & .100" wall (OD 1.000"). Next I ran bore dia of .730" with .030" wall (OD .790").
For allowable P in chamber I get;
Lamé's = 10,975psi
Alger's = 11,538psi
Alfer's = 19,852psi (as quoted by william)
For allowable bore P I get:
Lamé's = 3,941psi
Alger's = 4,000
Alger's = 9,562 (WEA)
Note; It appears, to me at least, the formula given by Mr Apperson looks to be much closer to the situation we expect to find in a gun bbl than the others. I thank you William for this formula. With wrought iron having an elastic limit of approx 25K psi these figures would be cut in half (rest of the formula would be identical for same dimensions, so P would be proprotionate to t for same dimensions) which can also explain why some fairly shoddy old guns have withstood firing with loads far stronger than were ever intended for. They are undoubtably running on the "Ragged Edge" but many have endured. With 4140 even in a fairly soft state running to 85K psi it is obvious the strength advantage to modern steels. All figures I have cited are also elastic limit (bulge point) not Ultimate Tensile which is much higher (Burst Point)
