RULE 3.

1. Find the latitude and departure corresponding to each course and distance, and correct them as directed in rule 1.

2. Beginning at the first or any other convenient station of the survey, place the departure for the corresponding lower meridian distance, and mark it with the same name as the departure; take the sum or difference of this meridian distance and the next departure, according as they are of the same or different names, and place it for the upper meridian distance of the next horizontal column, marking it with the same name as the meridian distance and departure when they are alike, but with the name of the greater when they are different. Proceed to find the remaining meridian distances, products, and area in every respect as directed in the last rule*.

Note. In working by this rule there is one multiplication less to make than by either of the preceding, because the last meridian distance, which always comes out nothing, is an upper one.

*By drawing a meridian line to bisect the side whose departure is made the first meridian distance, the demonstration of this rule may be formed nearly in the same manner as the one preceding.

Note. It may not be improper here to remark that the three preceding rules are only some of the different cases of one general rule that might have been given. But it was thought better to give them thus distinctly, as they are thereby rendered plainer.

EXAMPLES.

The field-notes being the same as in the last example, the area

is required by the above rule.

100.6992

13.26W

190.53 57.57 57.85 61.68] 61.93| .28 .25 57.70 57.70 61.8061.80

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.

Ch. 7.81

S. 76°1 E. 18.15 S. 52 W. 10.70 3. S. 7 W. 13.92

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 west departures, will be the difference of latitude

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, and the angle DCE will be the bearing, which will be between the north and east in going from C to E. trigonometry,

Therefore, by

CE, N. 10° 47′ E.

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

The bearing and distance of the 3rd side is therefore

S. 10° 47′ W. 28.42 Ch.

R