Raimey'
One cold Rainy day, fit for neither man nor beast, as they say, rather than watching the idiot tube I sat down & Ciphered with a programable calculator. I put in a formula which after having entered a value for the dia of a 1 ga ball would determine the dia of any ga number entered. I worked in conjuction with a chart from the Birmingham proof listing gauge dia's to 3 decimal places. I first used 1.669" from the chart as dia of 1ga. & assumed all dimensions should be capable of being "Rounded" to the three places. I went through the formula for all 50 gauges listed & a few rounded .001" too small. I then went to 1.670" & tried again & a greater number rounded .001" too large. I noted in both cases those sizes which fell "Out of Tolerence". Working then only with those sizes I began closing in. It very soon became evident that to entirely "Fit" the chart required working with a 6 decimal place figure for a 1ga or a lb ball of lead. 1.669285" proved to be the approximate middle of the range. 1.66928 is too small & 1.66929 is too large. This 1.669285 also proved to be accurate on even the gauges which gave dias of less than the 50ga. For example 3√(1.669285^3 ÷ 172.28) = .299998 or rounded to 3 places .300". It is noted though, that working the other way, given that a sphere of lead of 1.669285" weighs 1 lb, then a cubic foot of this same substance would weigh 709.5 lbs. My Machinery's Handbook however states a cu/ft of lead weighs 707.7 lbs (0.3% variation). These same identical dias are listed in British proof charts from at least as early as 1855, for gauges from 1 through 50. It would thus seem someone was doing some highly accurate measuring & calculating pretty early on.
It must not of course be imagined the Gunmakers themselves worked to any such kinds of tolerences & guns all supposedly of 12 ga for instance can be found with widely varying bore dimensions.
It would seem that from 1855 to 2008 the size of a "True" 12ga has been listed @ .729" However using lead @ 707.7 lbs per FT^3 a 12ga would calculate to .730". Considering tools & technology in 1855 it appears to me someone was working "EXTREMELY ACCURATE".All this I suppose has little if any practical value, but is very interesting to me at least. It would of course be quite easy to say they simply were not working with pure lead, but we would have to assume it had a constituent which was denser,/heavier, while the majority of imputities found in lead will be less dense/lighter.
