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is set at the bottom of the column with the name of the greater, and shows 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.
1. The perambulator, or surveying wheel, is so contrived as to turn just twice in the length of
a pole or 16; feet; what then is the diameter Answ. 2.626 feet.
2. Two sides of a triangle are respectively 20,
and 40 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. 5. The ellipse in Grosvenor Square measures 840 links the longest way, and 612 the shortest, within the rails: now the wall being 14 inches thick, it is required to find what quantity of ground it incloses, and how much it stands upon.
Answ. it incloses 4A, 6P. and stands on 1760; square feet. -
6. Required the dimensions of an elliptical acre with the greatestand least diameters in the propor
tion of 3 to 27 f Answ. 17,479 by 11,653 perches.
7. The paving of a triangular court at 18q. per foot, came to 100l. The longest of the three sides was 88 feet: what then was the sum of the other two equal sides! * * - Ans. 106.85 feet.
8. In 110 acres of statute measure, in which the pole is 16; 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. 1R. 28P. Cheshire; 67P. 3R. 25P. Hrish.
9. The three sides of a triangle containing 6A. 1R. 12P. are in the ratio of the three numbers, 9, 8, 6, respectively; required the sides? * Ans. 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 31 15, 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 2 Answ. 117A. 2R. 28B.
11. Required the dimensions of an oblong gar
den containing three acres, and bounded by 104 perches of pale fence
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. 14A. 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 circumference 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 r
- - 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 ! Ans. 1A. 3R.
Containing the Matronomical methods of finding the Latitude, Variation of the Compass, &c. with a description of the instruments used in these ofterations.
D AY and night arise from the circumrotation 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 which 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,
Note. The ancients having no instruments by which they could make observations with any tolerable degree of accuracy, supposed the length of the year, or annual motion of the earth, to be completed in 360 days: and hence arose the division of the circumference of a circle into the same number of equal parts, which they called degrees.
The Meridian of any place, is a semicircle passing through that place, and terminating at the Poles of the Equator. The other half of this circle is called the opposite Meridian.
The Latitude of any place, is that portion of the Meridian of that place, which is contained between the Equator and the given place; and is either North or South, according as the given place is in Northern or Southern Hemisphere, and therefore cannot exceed 90°.
The Parallel of Latitude of any place, is a circle passing through that place, parallel to the Equator. -
The Difference of Latitude between any two places, is an arch of a meridian intercepted between the corresponding parallels of latitude of those places. Hence, if the places lie between the Equator and the same Pole, their difference of latitude is found by subtracting the less latitude from the greater: but if they are on opposite sides of the Equator, the difference of latitude is equal to the sum of the latitudes of both places.
The First Meridian is an imaginary semicircle, passing through any remarkable place, and is therefore arbitrary. Thus, the British esteem that