A0 B0 1 - A0 1
[alpha] = ------, [beta] = ------ = ------ = ------------. (15)
1 - A0 1 - B0 1 + A0 1 + 2[alpha]
The length of the shot being denoted by l and the calibre by d, and
the length in calibres by x
l/d = 2a/2b = x, (16)
x 1
A0 = ----------- ch^(-1)x - ------, (17)
(x²- 1)^3/2 x² - 1
-x x²
2B0 = ----------- ch^(-1)x + ------, (18)
x² - 1)^3/2 x² + 1
x sh^(-1) [root](x²-1) x
x²A0 + 2B0 = ---------------------- = ------------ log [x + [root](x² - 1)]. (19)
[root](x²-1) [root](x²-1)
If [sigma] denotes the density of the metal, and if the shell has a
cavity homothetic with the external ellipsoidal shape, a fraction f of
the linear scale; then the volume of a round shot being 1/6 [pi] d^3,
and 1/6 [pi] d^3 x of a shot x calibres long