Plane trigonometry with practical applications, by Leonard E. Dickson.

Ch. VII]

LAND SURVEYING

87

latter two triangles and the negative of the trapezoid is equal to
the negative of ABC. As the sign before the area obtained for
the field is of no interest and is changed by passing around the
field in the reverse sense, it is ignored. The double areas of the
three auxiliary figures are found by the following multiplications:
Course Lat. Double Double area
mer. dist.
AB +AM 2FD 2ABM
BC -PM 2HIG -2MBCP Alg. sum
CA +PA 2KJ 2PAC J =-2ABC
Hence, if we multiply the latitude of each course by its double
meridian distance, paying attention to their signs, and divide the
algebraic sum of these products by 2, we obtain the area of the
closed field.
We shall now illustrate the rules given in the last two sections
by performing the computations necessary to find the area of the
triangle in Arts. 63, 64 obtained after balancing its survey.
Double
Course Lat. Dep. mer.dis Double area
AB +13.02 +22.56 +22.56 13.02X22.56 = +293.73
+22.56
- 9.69
BC -29.56 - 9.69 +35.43 -29.56X35.43 = -1047.30
- 9.69
-12.87
CA +16.54 -12.87 +12.87 16.54X12.87 = +212.87
d-506.60 +506.60
2)540.70
270.35
As a check, the double meridian distance +12.87 for CA is
the negative of its departure. If the given distances are in chains,
the area is 27.035 acres.