Triangular pile.
Rule.—Multiply the base by the base plus 1, this product by the base plus 2, and divide by 6.
Square pile.
Rule.—Multiply the bottom row by the bottom row plus 1, and this product by twice the bottom row plus 1, and divide by 6.
Rectangular, or oblong pile.
Rule.—Multiply the breadth of the base by itself plus 1; and this product by three times the length of the base plus 1, minus the breadth of the base, and divide by 6.
In the following formulæ let the letter (L) denote the number in the bottom row, or the length; and (B) the breadth of the lowest course.
| Triangular pile | L × (L + 1) × (L + 2) |
| 6 | |
| Square pile | L × (L + 1) × (2L + 1) |
| 6 | |
| Oblong pile | B × (B + 1) × (3L + 1 - B) |
| 6 |
The number of shot in any pile,
(whose base does not exceed 21) may readily be ascertained by referring to the following Table, [page 284].