In the preceding examples the bearings and distances of all the boundaries are given; but when the field-work is accurately performed, the area may be calculated, if any two of the bearings or distances, or one bearing and distance be omitted. The method of doing this in the cases most likely to occur in practice, is exemplified in the three following examples. Either of the preceding rules may be used in the calculation.

EXAMPLE 1.

In taking a survey of a tract of land bounded by six straight sides, I was prevented going directly from the 3rd to the 4th corner by a pond of water. I therefore set up two stakes near the edge of the pond, and took the bearing and distance from the 3rd corner to the first stake, from the first stake to the second, and from the second to the 4th corner, and noted them in my field-book as all belonging to the 3rd station of the survey. The field-notes being as follow, the bearing and distance of the 3rd side, and the area of the survey are required.

To find the bearing and distance of the 3rd side, Fig. 80.

Find the difference of latitude and departure for each of the devious courses, EA, AB, and BC. Then the difference between the sums of the north and south latitudes, and the difference between the sums of the east

and departure corresponding to the 3rd side, and of the same name with the less sums respectively.

Draw CD parallel to NS, and on it let fall the perpendicular ED; then will CD be the difference of latitude, and ED the departure corresponding to the 3rd side, ard the angle DCE will be the bearing, which will be between the north and east in going from C to E. Therefore by trigonometry,

To the tang. of DCE, or bearing of

CE, N. 10° 47' E.

9.28000

Consequently the bearing of EC is S. 10° 47′ W.

The bearing and distance of the 3rd side is therefore

Sta.

Courses.

Dist.

N.

S.

E.

W.

Cor. S. Cor. W.

N.

S.

E.

W.

N. Area.

S. Area.

1

North,

7.81

7.81

.01 .01

7.80

.01

.0780

EXAMPLE 2.

In a survey of which the following are the field-notes, the bearing and distance of the last side were not taken on account of obstacles in the way; but depending on the accuracy of the others, it is required to find them and the area of the survey.

With the given bearings and distances find their corresponding latitudes and departures, and what they want of balancing will be the difference of latitude and departure of the closing line. The area may then be found as in the preceding examples.

1.7979

2)671.1313

335.56565

With the difference of latitude and departure of the closing line, its bearing and distance may be found as in the preceding example. Thus,

The bearing and distance of the last side is therefore

S. 60° 8 W. 12.27 ch.