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

Ch. VII]

LAND SURVEYING

85

the errors of measurement. This adjustment of the errors is
known as balancing the survey.
Consider the following survey of a triangular field (Fig. 45),
in which the data in the first three columns are taken from the
field notes of the survey, while the entries in the next four columns
have been read off from the traverse table:

Lat. Dep. Balance
Course Bearing Dist. -N-. S p. Balance
_________ N S E W Lat. Dep.
AB N 60010'E 26 12.94 22.56 +13.02 +22.56
BC S 18~ 5' W 31.2 29.66 9.68 -29.56 - 9.69
CA N 38~ W 20.9 16.47 ____12.87 +16.54 -12.87

Sum of Dist. = 78.1 29.41 29.66 22.56 22.55
29.41 22.55
Error in Lat. = 0.25 0.01 = error in Dep.
We have added the north latitudes, then the south latitudes, etc.
If the survey had been exact (which is not to be expected in view
of errors of measurement in the field), the sum of the north latitudes would have been equal to the sum of the south latitudes.
In our example, the latter sum exceeds the former by 0.25, which
is called the error in latitude. This error is distributed among
the individual latitudes in proportion to the lengths of the courses,
the proportionate parts of the error 0.25 being
26 31.2 20.9
8X.25=.08, 781 X.25=.10, 78 X.25=.07.
The partial errors in the north latitudes are here to be added to
them, while the partial error in the south latitude is to be subtracted from it. The corrected latitudes are entered in the first of
the columns headed "Balance"; to the north latitudes prefix the
sign +, and to the south latitudes the sign -, thus enabling us
to put all of them in a single column. Moreover, these signs are
needed in the further problem to find the area of the field.
Similarly we obtain the corrected departures and prefix the sign
+ to the east departures and the sign - to the west departures.