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bottom of the column with the name of the greater, and shews the perpendicular descent of B below the horizontal level of. A.

In like manner the northings and southings in the seventh column are distinguished by the letters N and S in the second, &c.

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The perambulator, or surveying wheel, is so contrived as to turn just twice in the length of a pole or 164 feet; what then is the diameter?

2,626 feet.

2. Two sides of a triangle are respectively 20 and 10 perches ; required the third so that the content may be just an acre ?

Answ.either 23. 099 or 58.876 perches.

3. I want the length of a line by which my gardener may strike out a round orangery that shall contain just half an acre of ground.

Answ. 273 yards.

4. What proportion does the arpent of France, which contains 100 square poles of 18 feet each, bear to the American acre, containing 160 square poles of 16.5 feet each, considering that the length of the French foot is to the American as 16 to 15 ?

Answ. as 512 to 605

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8. In 110 acres of statute measure, in which the pole is IC feet, how many Cheshire acres, where the customary pole is 6 yards, and how many of Ireland, where the pole in use is 7 yards?

Answ. 92A. IR. 28P. Cheshire; 67A. 3R. 25P. Irish.

9. The three sides a triangle containing 6A. 1R. 12P. are in the ratio of the three numbers, 9, 8, 6, respectively; required the sides?

Answ. 59.029, 52.47, and 39.353.

10. In a pentangular field, beginning with the south side, and measuring round towards the east, the first or south side is 2735 links, the second 3115, the third 2370, the fourth 2925, and the fifth 2220; also the diagonal from the first angle to the third is 3800 links, and that from the third to the fifth 4010; required the area of the field?

Answ. 117A. 2R. 28P.

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11. Required the dimensions of an oblong garden containing three acres, and bounded by 104 perches of pale fence 119

Answ. 40 perches by 12.

12. How many acres are contained in a square meadow, the diagonal of which is 20 perches more than either of its sides.

Answ. 4A. 2R. 11P.

13. If a man six feet high travel round the earth, how much greater will be the circumference described by the top of his head than by his feet?

Answ. 37.69 feet. N. B. The required difference is equal to the cit. cumference of a circle 6 feet radius, let the magnitude of the earth be what it may.

14. Required the dimensions of a parallelogram containing 200 acres, which is 40 perches longer than wide ?

Answ. 200 perches by 160.

15. What difference is there between a lot 28 perches long by 20 broad, and two others, each of half the dimensions ?

Answ. 1A. 3R

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PART III.

Containing the Astronomical methods of finding the Latijude, Variation of the compass,&c. with a description of the instruments, used in these operations,

SECTION I.

INTRODUCTORY PRINCIPLES.

Day and night arise from the circumrotation

AY of the Earth. That imaginary line about which the rotation is performed, is called the Axis, and its extremities are called Poles. That towards the most remote parts of Europe is called the North Pole, and its opposite the South Pole. The Earth's Axis being produced will point out the Celestial Poles.

The Equator is a great circle on the Earth, every point of wbich is equally distant from the Poles ; it divides the Earth into two equal parts, called Hemispheres : that having the North Pole in its centre is called the Northern Hemisphere-and the other, the Southern Hemisphere. The plane of this circle being produced to the fixed stars, will point out the celestial Equator or Equinoctial. The Equator, as well as all other great circles of the sphere, is divided into 360 equal parts, called degrees ; each degree is divided into 60 equal parts, called minutes, and the sexagesimal division is continued.

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