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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. 27d. 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 maya pole, 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 4 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?

QUEST. 42. How long must the tether of a horse be, that will allow hiin 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. 141. Os. 8 d.

QUEST. 44. The diaineter of a standard corn bushel is 182 inches, and its depth 8 inches; then what must the diameter of that bushel be, whose çlepth is 74 inches?

Ans. 19:1067 inches. QUEST. 45. Suppose the ball on the top of St. Paul's church is 6 feet in diaineter; what did the gilding of it cost at 34 per square inch?

Ans. 2371. I os. ld, Quest. 46. What will a frustpim 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 1, and the length of the siant side 8 feet?

Ans. 301. 1s. 1011,

QUEST. 47,

Ans. 64;

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 į 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 45 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 241b. weight, so that the diameter of the bore may be to 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 421b, and the caliber of their guns, allowing of the caliber, or 's of the ball's diameter, for windage.

Answer

[blocks in formation]

QUEST. 53. Supposing the windage of all mortars to be to of the caliber, and the diameter of the hollow part of the shell to be to 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, 5:8, and 4.6 inch mortar.

Answer

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

powder. filled.

4.6 5.8 8 10 13

4.523 50703 7.867 9.833 12:783

8.320 16.677 43.764 85.476 187.791

0:583 1:168 3.065 5.986 13:151

8.903 17.845 46.829 910462 200.942

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. 26272 cubic inches, or nearly of a pint. Quest. 55. The dimensions of the sphere and cone being the saine 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 froni London, to such a height that he can just see 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 ? Aris. 70's of a mile, or 547 yards 1 foot.

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.

Answer,
AS 605.7122;
BS 429•6814;
CS 524-2365,

QUEST. 59. QUEST. 59. Required the same as in the last question, when the point B is on the other side of ac, supposing AB 9, AC 12, and BC 6 furlongs; also the angle ASB 33° 45', and the angle BSC 22° 30'.

Answer,
As 10'64, BS 15.64, cs 14.01.

B

As

S QUEST. 60. It is required to determine the magnitude of a cube of gold, of the standard fineness, which shall be equal to a sum of 480 million of pounds sterling; supposing a guinea to weigh 5 dwts 94 grains. Ans. 18.691 feet.

Quest. 61. The ditch of a fortification is 1000 feet long, 9 feet deep, 20 feet broad at bottom, and 22 at top; how inuch water will fill the ditch ?

Ans. 1158127 gallons nearly. QUEST. 62. If the diameter of the earth be 7930 miles, and that of the moon 2160 miles: required the ratio of their surfaces, and also of their solidities : supposing them both to be globular, as they are very nearly?

Ans. the surfaces are as 13, to I nearly;

and the solidities as 491 to 1 nearly,

PRACTICAL EXERCISES CONCERNING SPECIFIC

GRAVITY.

The Specific Gravities of Bodies are their relative weights contained under the same given magnitude; as a cubic foot, or a cubic inch, &c.

The specific gravities of several sorts of matter, are expressed by the numbers annexed to their names in the Table of Specific Gravities, at page 231; from which the numbers are to be taken, when wanted.

Note. The several sorts of wood are supposed to be dry. Also, as a cubic foot of water weighs just 1000 ounces avoirdupois, the numbers in the table express, not only the specific gravities of the several bodies, but also the weight of a cubic foot of each in avoirdupois ounces; and hence, by proportion, the weight of any other quantity, or the

quantity quantity of any other weight, may be known, as in the fol, lowing problems,

PROBLEM I.

To find the Magnitude of any Body, from its Weight,

As the tabular specific gravity of the body,
Is to its weight in avoirdupois ounces,
So is one cubic foot, or 1728 cubic inches,
To its content in feet, or inches, respectively,

EXAMPLES.

Exam. 1. Required the content of an irregular block of common stone, which weighs lcwt. or 1121b.

Ans. 1228 cubic înches. Exam. 2. How many cubic inches of gunpowder are there in ilb weight?

Ans. 29cubic inches nearly, Exam. 3. How many cubic feet are there in a ton weight of dry oak?

Ans. 3813 cubic feet,

PROBLEM II.

To find the Weight of a Body from its Magnitude,
As one cubic foot, or 1728 cubic inches,
Is to the content of the body,
So is its tabular specific gravity,
To the weight of the body.

EXAMPLES.

Exam. 1. Required the weight of a block of marble, whose length is 63 feet, and breadth and thickness each 12 feet; being the dimensions of one of the stones in the walls of Balbeck ?

Ans. 683 77 ton, which is nearly equal to the burden

of an East-India ship. EXAM. 2. What is the weight of 1 pint, ale measure, of gunpowder ?

Ans. 19 oz. nearly. EXAM. 3. What is the weight of a block of dry oak, which measures 10 feet in length, 3 feet broad, and 24 feet deep?

Ans. 133574|b.

PROBLEM

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