23. A May-pole, whose top was broken off by a blast of wind, struck the ground at 15 feet distance from the bottom of the pole what was the height of the whole May-pole, supposing the length of the broken piece to be 39 feet? Ans. 75 feet.

24. What will the diameter of a globe be, when the solidity and superficial content thereof are represented by the same number?

Ans. 6.

25. How many three inch cubes can be cut out of a 12 inch cube?

Ans. 64.

26. A farmer borrowed part of a hay-rick of his neighbor, which measured 6 feet every way, and paid him back again by two equal cubical pieces, each of whose sides was three feet: Query, whether the lender was fully paid?

Ans. He was paid part only.

27. What will the painting of a conical church spire come to at 8d. per yard; supposing the circumference of the base to be 64 feet, and the altitude 118 feet?

Ans. 147. Os. 8ąd.

28. What will a marble frustrum of a cone come to at 12s. per solid foot; the diameter of the greater end being 4 feet, that of the less end 14 feet, and the length of the slant side 8 feet? Ans. 30%. 1s. 11ąd.

29. The diameter of a legal Winchester bushel is 18 inches, and its depth 8 inches: what must the diameter of that bushel be whose depth is 7 inches?

Ans. 19.1067.

30. Suppose the ball at the top of St. Paul's Church is 6 feet in diameter; what did the gilding of it come to at 34d. per square inch? Ans. 2377. 10s. 1d.

31. A person wants a cylindric vessel of 3 feet deep, that shall hold twice as much as a vessel of 28 inches deep, and 46 inches in diameter: what must be the diameter of the vessel required? Ans. 57.37 inches.

32. Two porters agreed to drink off a quart of strong beer between them, at two pulls, or a draught each; now the first having given it a black eye, as it is called, or drank till the surface of the liquor touched the opposite edge of the bottom, gave the remaining part of it to the other: what was the difference of their shares, supposing the pot was the frustrum of a cone, the depth being 5.7 inches, the diameter at the top 3.7 inches, and that of the bottom 4.23 inches? Ans. 7.05 cubic inches.

33. The monument erected in Babylon by Queen Semiramis at her husband Ninus's tomb, is said to have been one solid block of marble in the form of a pyramid; the base was a square whose side was 20 feet; and the height of the monument was 150 feet; now suppose this monument was sunk in the Euphrates, what weight would be sufficient to raise the apex of it to the surface of the water, and what weight would raise the whole of it above the water?

Ans. To raise it to the surface would require 948

tons, to raise it out would require 150638 tons, (which is the same as the weight of the monument.)

34. If the pyramid described in the last example were divided into three equal parts by planes parallel to its base, what would be the length of each part, beginning at the top? Ans. 104.0042, 27.0329 and 18.9629 respectively. 35. How high above the surface of the earth must a person be raised to see of its surface?

of

Ans. To the height of the earth's diameter.

36. A cubical foot of brass is to be drawn into a wire of an inch in diameter; what will be the length of

the wire, allowing no loss in the metal?

Ans. 97784.5684 yards, or near 56 miles.

37. A gentleman has a bowling green, 300 feet long, and 200 feet broad, which he would raise one foot higher by means of the earth to be dug out of a ditch that goes round it; to what depth must the ditch be dug, supposing its breadth to be everywhere 8 feet?

Ans. 78 feet.

X

38. Of what diameter must the bore of a cannon be, which is cast for a ball of 24lbs. weight, so that the diameter of the bore may be of an inch more than that of the ball? Ans. 5.647 inches.

39. One end of a certain pile of wood is perpendicular to the horizon, the other is in the form of an inclined plane: the length of the pile at the bottom is 64 feet, length at the top 50 feet, height 12 feet, length of the wood 5 feet; required the number of cords it contains ?

Ans. 2633.

40. The ellipse in Grosvenor-square measures 840 links across the longest way, and 612 the shortest, within the walls now the walls being 14 inches thick, it is required to find what ground they inclose, and what they stand upon. Ans. They inclose 4ac. Oro. 6 po. and stand on 17601 square feet.

41. If a heavy sphere whose diameter is 4 inches, be put into a conical glass, full of water, whose diameter is 5, and altitude 6 inches: it is required to know how much water will run over?

Ans. of a pint nearly, or 26.272 inches.

42. Suppose it be found by measurement, that a man-ofwar, with its ordnance, rigging and appointments, draws so much water as to displace 50,000 cubic feet of water; required the weight of the vessel?

Ans. 1395 tons.

43. One ev'ning I chanc'd with a tinker to sit,
Whose tongue ran a great deal too fast for his wit:
He talked of his art with abundance of mettle;
So I ask'd him to make me a flat-bottom'd kettle.
Let the top and the bottom diameters be,
In just such proportion as five is to three:
Twelve inches the depth I propos'd, and no more;
And to hold in ale gallons seven less than a score.
He promis'd to do it, and straight to work went;
But when he had done it he found it too scant.

U

He alter'd it then, but too big he had made it;
For though it held right, the diameters fail'd it;
Thus making it often too big and too little,
The tinker at last had quite spoiled his kettle;
But declares he will bring his said promise to pass,
Or else that he'll spoil every ounce of his brass.
Now to keep him from ruin, I pray find him out
The diameter's length, for he'll ne'er do't, I doubt.

Ans. The bottom diameter is 14.4401, and the top diameter 24.4002.

44. If the above-mentioned frustrum of the cone were to hold as much again, what would be the length of the part added to the greater end?

Ans. 6.384 in. nearly.

A

TABLE

OF THE

AREAS OF THE SEGMENTS OF A CIRCLE,

Whose diameter is Unity, and supposed to be divided into 1000

equal Parts.

.021659

.066 .022154

.019 .003471 .042 .011330 .065
.020 .003748 .043 .011734
.021 .004031 .044 .012142
.022 .004322 .045 .012554
.023 .004618 .046 .012971

.067 .022652 .068 .023154

.069 .023659