In the absence of a size reference for British Shrapnel balls, the quantity per pound is sufficient to define precisely the diameter. For:
3 and 18 pdr shell, 41 balls per pound, ball diameter = 1.267 cm ( .499 inch)
60 pdr shell, 35 balls per pound, ball diameter = 1.33 cm (.524 inch)
6-inch shell, 14 balls per pound, ball diameter = 1.81 cm ( .713 inch)
Doing the sums first for 13 and 18 pdr shell:
The balls are Mixed Metal, 7 parts lead to 1 part antimony. Density of lead is 11.34 g/cc and of antimony is 6.7 g/cc, so density of Mixed Metal is 10.44 g/cc.
41 balls per lb is 90.2/kg, so mass of 1 ball is 1/90.2 = 0.0111 kg = 11.1 g.
Therefore volume of 1 ball is mass/density = 11.1/10.44 = 1.06 cc
For a sphere of radius r, volume = 4/3 x Pi x r^3
Implies r = cube root {1.06x3 / 4xPi} = cube root 0.254 = 0.633 cm
Therefore ball diameter = 1.267 cm.
Repeating for 60 pdr shell, 35 balls per pound or 77 per kg,
Mass =13g, vol = 1.24 cc
r = cube root 0.297 = 0.667 cm; d = 1.33 cm.
And for 6-in shell, 14 balls per pound or 30.8 per kg,
Mass = 32.5g, vol = 3.113 cc
R = cube root 0.743 = 0.906; d = 1.81 cm.
Tom.