Note 30 — Chapter I

Since 1792, musket-balls are seven-twelfths of an inch in diameter, and twenty go to the pound instead of eighteen. In the British service, eleven bullets to the pound are used for the proof of muskets, and fourteen in the pound, or twenty-nine in two pounds, for service; seventeen for the proof of carbines, and twenty for service; and twenty-eight in the pound, for the proof of pistols, and thirty four for service. The diameter of musket-bullets differs but one-fiftieth part from that of the musket bore; for if the shot but just rolls into the barrel, it is sufficient.

The diameter of any bullet is found, by dividing 1.6706 by the cube root of the number, which shows how many of them make a pound, or it may be done in a shorter way. From the logarithm .2228756 of 1.6706, subtract continually the third part of the logarithm of the number of bullets in the pound, and the difference will be the logarithm of the diameter required. Thus the diameter of a bullet, whereof twelve weigh a pound, is found by subtracting .3597270, a third part of the logarithm of 12, from the given logarithm .2228756; or, when the logarithm is less than the former, a unit must be added, so as to have 1.2228756, and the difference .8631486 will be the logarithm of the diameter sought, which is .7297 inches; observing that the number found will always be a decimal, when the logarithm, which is to be subtracted is greater than that of the pound; because the divisor is greater than the dividend in this case.

Hence, from the specific gravity of lead, the diameter of any bullet may be found from its given weight: for, since a cube foot weighs 11325 ounces, and 678 is to 355, as the cube 1728 of a foot, or 12 inches, is the content of the sphere; which therefore is, 5929.7 is to 16 ounces, or a pound, as the cube 1728 is to the cube of the diameter of a sphere which weighs a pound; which cube therefore is 4.66263, and its root 1.6706 inches, the diameter sought.