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or half a brick thick: what will this piece of work come to at 51. 10s. per statute rod? Ans. 20. 11s. 71⁄2d.

QUEST. 18. How many bricks will it take to build a wall, 10 feet high, and 500 feet long, of a brick and half thick; reckoning the brick 10 inches long, and 4 courses to the foot in height? Ans. 72000.

QUEST. 19. How many bricks will build a square pyramid of 100 feet on each side at the base, and also 100 feet perpendicular height: the dimensions of a brick being supposed 10 inches long, 5 inches broad, and 3 inches thick? Ans. 3840000.

QUEST. 20. If, from a right-angled triangle, whose base is 12, and perpendicular 16 feet, a line be drawn parallel to the perpendicular, cutting off a triangle whose area is 24 square feet; required the sides of this triangle?

Ans. 6, 8, and 10. QUEST. 21. The ellipse in Grosvenor-square measures 840 links across the longest way, and 612 the shortest,within the rails: now the walls being 14 inches thick, what ground do they enclose, and what do they stand upon?


Senclose 4 ac. Or. 6 p. stand on 1760 sq. feet.

QUEST. 22. If a round pillar, 7 inches over, have 4 feet of stone in it: of what diameter is the column, of equal length, that contains 10 times as much?

Ans. 22.136 inches.

QUEST. 23. A circular fish-pond is to be made in a garden, that shall take up just half an acre; what must be the length of the chord that strikes the circle? Ans. 273 yards.

QUEST. 24. When a roof is of a true pitch, or making a right angle at the ridge, the rafters are nearly of the breadth of the building: now supposing the eaves-boards to project 10 inches on a side, what will the new ripping a house cost, that measures 32 feet 9 inches long, by 22 feet 9 inches broad on the flat, at 15s. per square?

Ans. 81. 15s. 91d. QUEST. 25. A cable, which is 3 feet long, and 9 inches in compass, weighs 221b; what will a fathom of that cable. weigh, which measures a foot about? Ans. 783 lb.

QUEST. 26. My plumber has put 281b. per square foot into a cistern, 74 inches and twice the thickness of the lead long, 26 inches broad, and 40 deep: he has also put three stays across it within, of the same strength, and 16 inches


deep, and reckons 22s. per cwt. for work and materials. I, being a mason, have paved him a workshop, 22 feet 10 inches broad, with Purbeck stone, at 7d. per foot; and on the balance I find there is 3s. Ed. due to him; what was the length of the workshop, supposing sheet lead of of an inch thick to weigh 5.899lb. the square foot?

Ans. 32 feet, 03 inch.

QUEST. 27. The distance of the centres of two circles, whose diameters are each 50, being given, equal to 30; what is the area of the space enclosed by their circumferences?

Ans. 559.119.

QUEST. 28. If 20 feet of iron railing weigh half a ton, when the bars are an inch and quarter square; what will 50 feet come to at 31d. per lb, the bars being of an inch square? Ans. 201. Os. 2d. QUEST. 29. The area of an equilateral triangle, whose base falls on the diameter, and its vertex in the middle of the arc of a semicircle, is equal to 100: what is the diameter of the semicircle? Ans. 26.32148.

QUEST. 30. It is required to find the thickness of the lead in a pipe, of an inch and quarter bore, which weighs 14lb. per yard in length; the cubic foot of lead weighing 11325 ounces? Ans. 20737 inches.

QUEST. 31. Supposing the expense of paving a semicircular plot, at 2s. 4d. per foot, come to 10%.; what is the diameter of it? Ans. 14.7737 feet. QUEST. 32. What is the length of a chord which cuts off of the area from a circle whose diameter is 289?

Ans. 278.6716.

QUEST. 33. My plumber has set me up a cistern, and, his shop-book being burnt, he has no means of bringing in the charge, and I do not choose to take it down to have it weighed; but by measure he finds it contains 64 square feet, and that it is precisely of an inch in thickness. Lead was then wrought at 217. per fother of 194 cwt. It is required from these items to make out the bill, allowing 65 oz. for the weight of a cubic inch of lead? Ans. 4. 11s. 2d.

QUEST. 34. What will the diameter of a globe be, when the solidity and superficial content are expressed by the same number? Ans. 6.

QUEST. 35. A sack, that would hold 3 bushels of corn, is 224 inches broad when empty; what will another sack


contain, which, being of the same length, has twice its breadth, or circumference? Ans. 12 bushels.

QUEST. 36. A carpenter is to put an oaken curb to a round well, at 8d. per foot square: the breadth of the curb is to be 74 inches, and the diameter within 3 feet; what will be the expense? Ans. 5s. 2 d.

QUEST. 37. A gentleman has a garden 100 feet long, and 80 feet broad; and a gravel walk is to be made of an equal width half round it: what must the breadth of the walk be, to take up just half the ground? Ans. 25.968 feet.

QUEST. 38. The top of a may-pole, being broken off by a blast of wind, struck the ground at 10 feet distance from the foot of the pole; what was the height of the whole maypole, supposing the length of the broken piece to be 26 feet? Ans. 50 feet,

QUEST. 39. Seven men bought a grinding stone, of 60 inches diameter, each paying part of the expense; what part of the diameter must each grind down for his share? Ans, the 1st 4-4508, 2d 4.8400, 3d 5:3535, 4th 6-0765, 5th 7.2079, 6th 9.3935, 7th 22.6778 inches.

QUEST. 40. A maltster has a kiln, that is 16 feet 6 inches square: but he wants to pull it down, and build a new one, that may dry three times as much at once as the old one; what must be the length of its side? Ans. 28 feet 7 inches.

QUEST. 41. How many 3-inch cubes may be cut out of a 12-inch cube?

Ans. 64.

QUEST. 42. How long must the tether of a horse be, that will allow him to graze, quite around, just an acre of ground? Ans. 394 yards.

QUEST. 43. What will the painting of a conical spire come to, at 8d. per yard; supposing the height to be 118 feet, and the circumference of the base 64 feet? Ans. 147. Os. 83d.

QUEST. 44. The diameter of a standard corn bushel is 16 inches, and its depth 8 inches; then what must the diameter of that bushel be, whose depth is 7 inches? Ans. 19 1067 inches. QUEST. 45. Suppose the ball on the top of St. Paul's church is 6 feet in diameter; what did the gilding of it cost at 3 per square inch? Ans. 237/. 10s. ld,

QUEST. 46. What will a frustum of a marble cone come to, at 12s. per solid foot; the diameter of the greater end being 4 feet, that of the less end I, and the length of the slant side 8 feet? Ans. 30. 15. 101⁄4d,

QUEST. 47.

QUEST. 47. To divide a cone into three equal parts by sections parallel to the base, and to find the altitudes of the three parts, the height of the whole cone being 20 inches? Ans. the upper part 13.867.

the middle part 3·605. the lower part 2-528.

QUEST. 48. A gentleman has a bowling green, 300 feet long, and 200 feet broad, which he would raise 1 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 every where 8 feet? Ans. 7 feet. QUEST. 49. How high above the earth must a person be raised, that he may see of its surface?

Ans. to the height of the earth's diameter. QUEST. 50. A cubic foot of brass is to be drawn into wire, of of an inch in diameter; what will the length of the wire be, allowing no loss in the metal?

Ans. 97784-797 yards, or 55 miles 984-797 yards.

QUEST. 31. Of what diameter must the bore of a cannon be, which is cast for a ball of 24lb. weight, so that the diameter of the bore may be of an inch more than that of the ball? Ans. 5.647 inches.

QUEST. 52. Supposing the diameter of an iron 9lb. ball to be 4 inches, as it is very nearly; it is required to find the diameters of the several balls weighing 1, 2, 3, 4, 6, 12, 18, 24, 32, 36, and 42lb, and the caliber of their guns, allowing of the caliber, or of the ball's diameter, for windage. Answer


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QUEST. 53. Supposing the windage of all mortars to be

of the caliber, and the diameter of the hollow part of the shell to be of the caliber of the mortar: it is required to determine the diameter and weight of the shell, and the quantity or weight of powder requisite to fill it, for each of the several sorts of mortars, namely, the 13, 10, 8, 58, and 4.6 inch mortar.

Calib.of Diameter Wt. of shell mort. of shell.


Wt. of

Wt. of shell




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QUEST. 54. If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches; it is required to determine how much water will run over ?

Ans. 26-272 cubic inches, or nearly of a pint. QUEST. 55. The dimensions of the sphere and cone being the same as in the last question, and the cone only full of water; required what part of the axis of the sphere is immersed in the water? Ans. 546 parts of an inch.

QUEST. 56. The cone being still the same, and full of water; required the diameter of a sphere which shall be just all covered by the water? Ans. 2 445996 inches.

QUEST. 57. If a person, with an air balloon, ascend vertically from London, to such a height that he can just sèe Oxford appear in the horizon; it is required to determine. his height above the earth, supposing its circumference to be 25000 miles, and the distance between London and Oxford 49.5933 miles ? Ans. of a mile, or 547 yards 1 foot.

31I 1000

QUEST. 58. In a garrison there are three remarkable objects A, B, C, the distances of which from one to another are known to be, AB 213, AC 424, and BC 262 yards; I am desirous of knowing my position and distance at a place or station s, from which I observed the angle ASB 13° 30′, and the angle CSB 29° 50', both by geometry and trigonometry.


AS 605-7122;
BS 429.6814;

CS 524-2365.

QUEST. 59.

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