"The Modern Shotgun" by Burrard, Appendix III, page 277.
"" A most interesting outcome of pressure measurements on shotgun cartridges using the piezoelectric gauge has been the comparsion of the maximum pressure readings with those of the lead crusher gauge. By mounting the "TWO GAUGES" on opposite sides of the same gun at one inch from the breech face ""Simultaneous"" readings on the same cartridge were possible. As had been known for some time, the crusher readings were les than those given by the piezoelectric gauge due to the time lag in the plastic deformation of the lead-the piezoelectric gauge piston only moves about 1/100,000 inch when subjected to 2.5 tons per sq in and is thus free from this error. Over the ranges of pressures usually encountered at the one inch position in shotguns the readings given by the two gauges are related by the equation;
P = 1.5L - 0.5 tons per sq in
Where;
P = the maximum pressure indicated by the piezoelectric gauge
L = the maximum pressure indicated by the lead crusher gauge ""
Take it for whatever it appears to be worth to you, but do note the formula was "Derived from actual Simultaneous readings by both gauges recording the exact same pressures". Also note it is a conversion of Lead crusher pressures to tranducer pressures.
From the formula;
2 tons (4480) = 5600psi (386BAR)
2.5 tons (5600) = 7280psi (502BAR)
3 tons (6720) = 8960psi (618BAR)
3.5 tons (7840) = 10640psi (734BAR)
4 tons (8960) = 12320psi (850BAR)
As can be seen this formula is not totally linear but would be a part of a curve, nor does adding 1,000lbs get very close. I have nothing to indicate it would be accurate much beyond this limited range from which it was derived,but then this is the range in which we are primarily concerned. It would not of course be aplicable to CUPs as used for Rifles, & not sure it would apply to US LUPs as actual measurement & calibration may not be identical. This IMO should be quite adequate for any British gun with proof marks given in Tons which denote the service pressure.
With all due respect to the figures Larry has posted from the Birmingham proof house I think they are not stating the same situation as this formula. The 14.5 conversion is of course a mathematical conversion for measurements taken by the same method, thus recording the same pressure, not for conversion from one system to another. I may be wrong but I believe "Continental" BARs are tranducer figures.
Note if the gun was originally proofed @ 3tons & subquently given a re-proof of 850Bar for 650BAR service loads, both given in crusher measurements, & I have no reason to doubt that what Larry stated is totally true, it has in fact been re-proofed to a higher pressure level than the original 3ton proof. The formula I have given is in fact more conservative & I believe would be a safer course on older guns not bearing a re-proof. Also I believe the still older British "Nitro" 1 1/8oz proof is essentially the same as the 3ton proof.