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1. A circular fish-pond is to be dug in a garden, that shall take up just half an acre ; what must be the length of the cord that strikes the circle ? Ans. 27.75 yards.,
2. Two sides of a triangle are 20 and 40 perches respectively ; required the third side, so that the content may be just an acre.
Ans. Either 23.099 or 58.876 perches.
3. In 110 acres of statute measure, in which the pole is 5.5 yards, hofv 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. IR. 29P. Cheshire ; 67A. 3R. 25P. Irish.
4. The ellipse in Grosvenor square, London, measures 840 links the longer way, and 612 the shorter, 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 4 A. OR. 6 P. and stands on 1760,
5. Required the dimensions of an elliptical acre, with the greater and less diameters in the ratio of 3 to 2.
Ins. 17.481 by 11.654 perches.
equal to the difference between the lengths of the longer side and the diagonal; hence the sides are required.
Ans. 21 and 28 chains.
18. The boundaries of a tract of land are as follow : Ist. N. 14° W. 15.20 ch. 2nd. N. 70°į E. 20.43 ch. 3rd. S. 6° E. 22.79 ch. 4th. N. 86°; W. 18 ch, to the place of beginning ; within the tract there is a spring, the bearing and distance of which, from the 2nd corner, is S. 75° E. 7.90 ch. It is required to cut off 10 acres from the west side of this tract by a straight line running through the spring; what must be the distance of the division line from the 1st corner, measured on the fourth side?
Ans. 4.6357 chains.
19. The boundaries of a quadrilateral tract of land are as follow : Ist. N. 3501 E. 23 ch. 2nd. N. 7501 E. 30.50 ch. 3rd. S. 301 E. 46.49 ch. and 4th N. 66°1 W. 49.64 ch., to the place of beginning. This tract is to be divided into four equal parts by two straight lines, one of which is to run parallel to the 3rd side ; required the distance of the parallel division line from the first corner, measured on the 4th side ; also the bearing of the other division line and its distance from the same corner, measured on the 1st side.
Ans. Distance of the parallel division from the first corner 32.50 chains, the bearing of the other, S. 88° 22' E. and its distance from the same corner 6 chains.
LATITUDE AND DEPARTURE;
FROM 1 To 10,000;
ARTIFICIAL SINES, TANGENTS, AND
PUBLISHED BY JOHN RICHARDSON, No. 31, MARKET-STREET.