33. How is the diameter of a cast-iron shot of a given weight found?
Divide the weight in pounds by 0.134, and extract the cube root of the quotient, which will be the diameter in inches.
96]
34. How is the quantity of powder which a shell will contain found?
Multiply the cube of the interior diameter of the shell in inches, by 0.01744 for the weight of powder in pounds.
Note.—The above multipliers are found as follows: Suppose W to represent the weight of a body, D its density, V its volume, and g the weight of the unit of mass, then W = DVg. Now, if a cubic inch be taken as the unit of volume, then g will be numerically
| 62.5 | pounds. |
| 1728 |
| Hence, W = DV | 62.5 | = 0.036201; |
| 1728 |
| DV = 0.03620 D = | π | d³ |
| 6 |
(supposing d to be the diameter, and the body to be spherical)