The Pyrotechnist's Treasury; Or, Complete Art of Making Fireworks

by Thomas Kentish

5³ : 1440oz. :: 1³ : 11·52oz.

so that a 12-ounce, or 3-quarter-pound rocket, ought to be a trifle above an inch.

Required the weight of a ⁶⁄₈ rocket. 5 inches = ⁴⁰⁄₈.

40³ : 1440oz. :: 6³ : 4·86oz.

So that a ⁶⁄₈ is a trifle too large for a quarter-pound.

If, conversely, we require to know the size of a half-pound, or 8-ounce rocket,

1440oz. : 40³ :: 8oz. : 3200/9

and ∛(3200/9) = ∛(9600/27) = (∛9600)/3 = 7·08

So, properly, a half-pounder is a trifle over ⁷⁄₈. The names in use enable the makers to understand each other, but they are not mathematically correct, and are of no utility to an amateur.