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1. And if the distances thus taken are short, the curvature of the earth may be rejected. For, if the distance from the instrument he every where 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 every where 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 best to set the instrument as equally dįstant from both staves as may be.
3. If the distances of the instrument from the staves, be very unequal and very long, the eurvatures 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 field-book, 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,
Course or Elev. or Obl. Hor.(Perpen. Dif. De-
NE 50 30 E 14 00 976 947 236.1 602 730
3948 3783) 217.6 622 3492
Desc. N. E.
As Dif. Lat. 622
Is to radius S. 20°, So is Dep. 3492
TO T. Bear. 79° 54'.
As S. Bear. 79° 45'
Is to Dep. 3492,
To Dist. 3547.
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.
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 weget the difference of latitude and departure in the two last 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 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.
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. 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. 27 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 Grovesner 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 ineloses, and how much it stands upon. Answ. it incloses 4A. 6P. and stands on 17604
6. Required the dimensions of an elliptical acre with the greatest and least diameters in the proportion of 3 to 2?
Answ. 17.479 by 11.653 perches.
7. The paving of a triangular court at 18d. per foot, came to 1001. The longest of the three sides was 88 feet: what then was the sum of the other two equal sides?
Answ. 106.85 feet.
8. In 110 acres of statute measure, in which the pole is 1C1 leet, 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 of a triangle containing 6A. IR. 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 2920; 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.