Hugh;
No problem with your math, but I would point out, the 3√ of 4.6578 is 1.670". All the British proof charts I have ever seen give a 1 gauge as 1.669". True only one little ol thousandths of an inch, "But", it don't fit the charts perfect, 4.65148337 does. This does not exactly fit however any listing I have ever seen for the density of lead, but the math is otherwise perfect. My Machinery's handbook incidently give the SG of lead @ 11.342 rather than 11.352. For the formula to perfectly fit the charts requires lead to weigh in @ .41059 lbs per CuIn or 11.365 gms/cm3. The 11.352 wt is closer than 11.342, but neither is quite heavy enough to fit perfect.
.276" (222) is nominal bore dia for most bolt action military 7mmm Mauser rifles or .008" under groove dia of .284". This of course does not guarantee that some German maker of a Drilling did not make a 7mm with a tighter bore than this. Undersize bores with deep grooves seem to me to be rather common on German rifles.
