Square pile.
Multiply the bottom row by the bottom row + 1, and this product by twice the bottom row + 2, and divide by 6.
Rectangular piles.
Multiply the breadth of the base by itself + 1, and this product by 3 times the difference between the length and breadth of the base, added to twice the breadth + 1, and divide by 6.
Incomplete piles.
Incomplete piles being only frustrums, wanting a similar small pile on the top, compute first the whole pile as if complete, and also the small pile wanting at top; and then subtract the one number from the other.
Rules for finding the dimensions and weight of shot.
The weight and dimensions of shot or shells might be found by means of their specific gravities; (see the word [Gravity],) but they may be found still easier, by means of the experimented weight of a ball of a given size, from the known proportion of similar figures, namely, as the cubes of their diameters.
1st. To find the weight of an iron ball from its diameter.—An iron ball of 4 inches diameter weighs 9 lb. and the weights being as the cubes of their diameters, it will be as 64, (the cube of 4,) is to 9, so is the cube of the diameter of any other ball to its weight.
2d. To find the weight of a leaden ball. A leaden ball of 4¹⁄₄ inches diameter weighs 17 lb. therefore, as the cube of 4¹⁄₄ is to 17, (as 9 to 2 nearly,) so is the cube of the diameter of any leaden ball to its weight.