Feet. Inches. Tenths. Feet. Inches. Tenths.

1. And if the distances thus taken are short, the curvature of the earth may be rejected. For, if the distance from the instrument be everywhere about 100 yards, all the curvatures in a mile's work will be less than half an inch.

2. If the distance from the instrument to the hindermost staff be everywhere equal to the distance from the instrument to the corresponding staff, the curvature of the earth and the minute errors of the instrument will both be destroyed. Hence it will be much better to set the instrument as equally distant from both staves as may be,

3. If the distances of the instrument from the staves be very unequal and very long, the curvatures must be accounted for, and the distances, in order thereto, must be measured.

4. Therefore it appears, that the best method to take a level is, to measure the several distances from the instrument to the back and forward station-staves; and enter them in the fieldbook, according to the titles of their several columns, as in the following example; and correct the heights from the table of allowances, which may be done at home when you are about to sum up the heights.

Distan. Height. Corrected. Distan. Height. Corrected.

So that the fall in 68 chains is about 11 inches and of an inch.

Lastly, though hitherto we have considered the level with one telescope only, the same observations may be applied to a level with a double telescope; and I would advise those who use the double telescope, at every station to turn that end of the telescope forward which before was the contrary way.

A more general method of levelling, adapted to the surveying of roads and hilly ground, is exhibited in the following example, in which the measures are given in links.

EXAMPLE.

PL. 13. fig. 8.

Required the bearing and distance of the place B from A, and its perpendicular ascent or descent above or below the horizontal level of A.

As 100 links: 66 feet: 217.6 links: 143.6 feet, the descent

B below the level of A.

Hence, B bears N. 79° 54′ E. from A.

Nearest horiz. dist. 3547 links.

Sum of obl. dist. 3948 links.

Sum of horiz. dist. 3783 links.

Perp. desc. 217.6 links=143.6ft.

Answer.

With the angular elevation or depression in the third column, and the oblique distance in the fourth (as course and distance) are found the horizontal distance in the fifth, and the perpendicular ascent or descent on the sixth, for each station (as difference of latitude and departure): then, with the bearing and horizontal distance, we get the difference of latitude and departure in the last two columns.

The ascents and descents in the sixth column are distinguished by the letters E and D in the third, signifying elevation or depression; and being added separately, the difference of their sums 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.

PROMISCUOUS QUESTIONS.

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 ?

acre.

Ans. 2.626 feet. 2. Two sides of a triangle are respectively 20 and 40 perches; required the third, so that the contents may be just an Ans. 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. Ans. 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? Ans. 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 encloses, and how much it stands upon.

Ans. It encloses 4A. 6P., and stands on 1760 square feet. 6. Required the dimensions of an elliptical acre with the greatest and least diameters in the proportion of 3 to 2.

Ans. 17.479 by 11. 653 perches.

7. The paving of a triangular court at 18d. per foot, came to 100%. 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 161 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?

Ans. 92A. 1R. 28P. Cheshire; 67A. 3R. 25 P. Irish. 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 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. Ans. 117A. 2R. 28P. 11. Required the dimensions of an oblong garden containing three acres, and bounded by 104 perches of pale fence. Ans. 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? Ans. 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? Ans. 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 may.

it

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

Ans. 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.

PART III.

Containing the astronomical methods of finding the latitude, 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 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

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