Part 455

To find the weight of an iron Shot whose diameter is given; and the contrary. Rule. Double the cube of the diameter in inches, and multiply it by 7; so will the product (rejecting the 2 last or right hand figures) be the weight in pounds.

Example. What is the weight of an iron shot of 7 inches diameter. The cube of 7 is 343, which doubled is 686, and this multiplied by 7 produces 4802, which with the right hand figures rejected, gives 48 pounds, the weight required.

N. B. This rule is sufficiently exact for practical uses.

To find the diameter of the Shot, when the weight is given. Rule. Multiply the cube root of the weight in pounds by 1.923, and the product is the diameter in inches.

Example. What is the diameter of an iron shot of 52 pounds? The cube root of 52 is 3.732, which multiplied by 1.923 gives 7.177 inches, the diameter required.

Rule by logarithms.

To ¹⁄₃d of the log. of 52 0.572001 Add the constant log. 0.283979 And the sum is the log. of the diameter 7.177 0.855980

To find the diameter of a SHOT, from the impression or cavity it makes by striking a brass gun, or other object. Rule. Divide the square of the radius of the cavity by the depth of it, and add the quotient to the depth; so will the sum be the diameter of the shot required.

Example. A shot having struck upon a brass gun, made a cavity of 1.49 inches deep, and 4.94 inches diameter; what was the size of the shot? The radius of the cavity is 2.47, and its square is 6.1009, which divided by the depth 1.49, the quotient is 4.1, to which adding 1.49, the sum 5.59 inches is the diameter required, answering to a 24 pounder.

SHOT.--Rules for finding the number in any pile.

Triangular pile.

Multiply the base by the base + 1, this product by the base + 2, and divide by 6.

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.

3d. To find the diameter of an iron ball. Multiply the weight by 7¹⁄₉ and the cube root of the product will be the diameter.

4th. To find the diameter of a leaden ball. Multiply the weight by 9, and divide the product by 2; and take the cube root of the quotient for the diameter.

Table of diameters of English iron round shot.

+------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ |Kind | 68 | 42 | 32 | 24 | 18 | 12 | 9 | 6 | 3 | 1 | +------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ |Inches|8· |6·684|6·105|5·547|5·040|4·403|4·000|3·498|2·775|1·92 | +------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | Diameter of French iron round shot in English inches. | +------+---------+---------+---------+---------+---------+---------+ |Kind | 36 | 24 | 16 | 12 | 8 | 4 | +------+---------+---------+---------+---------+---------+---------+ |Inches| 6·648 | 5·808 | 5·074 | 4·610 | 4·027 | 3·196 | +------+---------+---------+---------+---------+---------+---------+

Table of grape shot, for sea and land service.

-----------+-------------+------------ | |Total weight | Weight of |of the grape Kind. | each shot. | complete. -----------+-------------+------------ |lbs. oz. |lbs. oz. 42 pounders| 4 0 | 46 6 32 ---- | 3 0 | 34 1 24 ---- | 2 0 | 25 5 18 ---- | 1 8 | 19 15¹⁄₂ 12 ---- | 1 0 | 10 15 9 ---- | 0 13 | 7 6 6 ---- | 0 8 | 5 8¹⁄₂ 4 ---- | 0 6 | 3 14¹⁄₂ 3 ---- | 0 0 | 2 10¹⁄₂ ¹⁄₂ ---- | 0 ³⁄₄ lead| 8³⁄₄ -----------+-------------+------------