tuse angle the greater, then will n=s S r, and r

a2+2nR-a as before; but if both be acute, n—str

and x-a-a2-2nR and these theorems will afford

the most expeditious solution that the above useful problem can admit of.

Note 2. The quantity a2+2nR or a2—2nR ses the length of the division line a b.

expres

EXAMPLE II.

To divide off 50 acres by a right line, parallel to DC in the same survey with the preceding examples.

Here the angle D=64 45' its Co. tang. -1.471630 C=138° 00' its Co. tang. -1.110606

EXAMPLE III.

It is required to cut off 80 acres adjoining and rallel to BC, in the same survey.

pa

Here the angle B is 94° 15', Co. tang. angle C is 138°00', Co. tang.

.07431

1.11061

a=39.20; and a2+2nR=ab = 58.582

12

hence a2+2nR-a-x is found-16.36

n

hence Cc-24.45 and Bb = 16.40/1/

To divide off 120 acres, adjoining and parallel to AD.

As S. D:x:: Rad.: Db = 18.15
As S. ZA:x:: Rad.: Aa

= 18.43

If it were required to cut off from a given farm any number of acres by a line, having a given bearing, the problem might be solved from the precepts already given; for by drawing a line from any convenient angle in the direction required, find its length, by the foregoing problem, and then the content it incloses ; which done, the last problem will give the position of the line required.

EXAMPLE.

Let it be required to cut off 100 acres from the N. end of the foregoing survey, by a line running north

From C, draw CE, North East; then since DC is S. 37° 45' E. the angle DCE must be 7° 15' and the angle D is 64° 45', therefore angle E is 108° 00'.

As S. E.: DC:: S. D: CE 39.94 = a

=

hence the triangle DCE = 105.85 chs.

area to be cut off = 1000.

SECT. VIII.

CONTAINING THE SURVEYING OF HARBOURS, &c. AND LEVELLING.

Of surveying Harbours, Shoals, Sands, &c.

THERE

HERE are three methods whereby this may be performed; for the observations may be made either on the water or on the land. Those made on the water are of two kinds, one by the log-line and compass (as in plane sailing) measuring the course and distance round the sand; and then to be plotted as a large