The girt is the circumference of the tree in the middle, and is conveniently taken with a piece of string, or a common measuring tape. The content is best found by the Sliding Rule. This rule contains a line called the "girt-line," which with the slide will furnish the solidity in feet with great rapidity. The rule is :-Set the length on C to 12 on D, then opposite the quarter girt on D is the content on C.

THE ANCHOR RING.

XLV.

To find the surface of an anchor ring.

Multiply the mean diameter of the ring by the thickness; then multiply twice by 22 and divide by 49.

Ex. Find the surface of an anchor ring whose inner diameter is 14 inches, and thickness 4 inches.

To find the solidity of an anchor ring.

Multiply the square of the thickness by the mean diameter of the ring; then multiply twice by 11 and divide

by 49.

Ex.

Find the solidity of an anchor ring whose thickness is 3 inches, and inner diameter 9 inches.

EXAMPLES.

1. Find the surface of an anchor ring whose inner diameter is 8 ft. 5 in., and thickness 15 inches.

2.

Ans. 11952, feet.

Find the cost of painting a fly-wheel whose inner diameter is 18 feet, and thickness 20 inches, at id. per foot. Ans. £1. 6s. 113d.

3. Find the solidity of an anchor ring whose thickness is 24 inches, and inner diameter 63 inches. Ans. 112

4. Find the weight of a fly-wheel whose thickness is 9 inches, and outer diameter 12 feet.

Ans. 3 tons. I qr. 2 lbs.

THE WEDGE.

XLVII.

To find the solidity of a wedge.

To twice the length of the thick end of the wedge add the length of the thin end; then multiply by the breadth of the thick end, and by the perpendicular from the thin end upon the base, and divide by 6.

Ex. The length and breadth of the thick end of a wedge are 15 and 6 inches, the breadth at the thin end

12 inches, and the perpendicular from the thin end upon the thick end 18 inches; find the solidity.

15

2

30

12

42

6

252

18

2016

252

64536

756 Ans.

FRUSTUM OF WEDGE.

XLVIII.

To find the solidity of the frustum of a wedge.

The frustum is equal to two wedges whose bases are the thick and thin ends, and heights the common distance between them.

These rules are useful in measuring haystacks, stoneheaps, &c.

EXAMPLES.

I. The length and breadth of the thick end of a wedge are 18 and 4 inches, the breadth at the thin end 16 inches, and the perpendicular from the thin end upon the thick end 12 inches; find the solidity. Ans. 416.

2. The length and breadth of the thick end of the frustum of a wedge are 10 and 4 feet, of the thin end 14 and 2 feet, and the perpendicular from the thin end upon the thick end 12 feet; find the solidity.

Ans. 424 feet.

3. The lower part of a stack of hay is the frustum of a wedge whose height is 3 yards, the length and breadth of the upper end 8 and 6 yards; and of the lower end 7 and 5 yards; the upper part is a complete wedge whose height is 2 yards, the length of the ridging being 61 yards; find the solidity. Ans. 1801 yards.

4. The base of a stone-heap measures 18 feet by 12 feet, the upper section 13 ft. 6 in. by 7 ft. 6 in., and the thickness of the heap is 2 ft. 3 in. ; find the cost of breaking at 10d. per yard. Ans. 115. 332d.

SIMILAR SOLIDS.

XLIX.

The volumes of similar solids are to one another as the cubes of their like dimensions. The corresponding edges of similar parallelopipedons are proportional; but the volume of one parallelopipedon is to the volume of the other as the cube of an edge of the former is to the cube of the corresponding edge of the latter. If a cone be cut by a