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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.
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.
I more general method of levelling, adapted to the
surveying of roads and hilly grounds, exhibited in the following example, in which the measures are given in links.
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.
Course or Elev. or Obl. Hor. Perpen. Dif. De-
Lat. part. IN E 79° 15' D 170 151738 705 218.9 131 692 2N E 75 00 D 21 45 684 635 253.4! 164 613 3N E 50 30 E 14 00 976 947 236.1 602 730 4S E 85 15 D 11 30 930 911185.4 75 908 5S E 70. 00 E 19 15 620 585 204.0 200 549
3948|37831217.6) 622 3492
Desc. N. E.
As Dif. Lat. 622
Is to radius S. 90°, So is Dep. 3492
To T. Bear. 79° 54'.
As S. Bear. 79° 54'
Is to Dep. 3492,
To Dist. 3547.
As 100 links : 66 feet :: 217.6 links : 143.6 feet, the descent of 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 in 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 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.
1. The perambulator, or surveying wheel, is so contrived as to turn just twice in the length of a pole or 16į 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. 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 Grovesnor 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. 16P. and stands on 17601 square feet.
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?
8. In 110 acres of statute measure, in which the pole is 164 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 ; 67A. 3R. 25P. 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;
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.
11. Required the dimensions of an oblong garden, 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. 4A. 2R. 11P.