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of each station by the corresponding Northing or Southing, and place the product in the North or South area, according as the latitude is north or south, the difference of the sum of these products will give twice the area, half of which gives the area of the survey.
The most westerly point of the survey being made the first station, and the several meridian distances being calculated, &c. the foregoing table will stand thus: - \
* The meridian distances, in this column, are the sum of two adjacent meridian distances; but at the most westerly point, the meridian distance is nothing, hence the first Dep. is the first meridian distance, and, in like manner, the last Dep. is the last meridian distance.
# This is not the first station in the actual survey, but only the most west. erly point of the survey as calculated by the foregoing method from the field. #. which, for convenience sake, I call the first station in making out this "Fabie:
The difference of latitude and departure being found and corrected as in the preceding rule.
As, beginning at the most northerly or most southerly point of the survey, admits of a continual addition of the one and subtraction of the other; make choice of either of these points in order to calculate the area of the survey.
1. It is necessary to calculate the several latitudes in order to find the most northerly or most southerly point of the survey, which may be done from Table 1. thus:
The first Lat. is .02 south, which is the difference of latitude between the second point of the survey and the first, when the survey is corrected,
from the next departure 3.93 which is N. subtract .02, and their difference 3.91 is equal to the difference of latitude between the third point and the first which is N. and 3.91—2.02=1.89–the difference of lat. between the fourth point and the first; which is also N. But as the next difference of lat. is south, therefore 5.71—1.89 = 3.82= the difference of lat. S. between the fifth point and the first ; and 3 82+2.99–681 = the difference of lat. S. between the sixth point and the first; and 6.81 +265=9.46=the difference of lat. S. between the seventh point and the first; and 9.46—5.77= 3.69= the difference of lat. S. between the eighth point and the first ; and 3.69—3.69=0; hence it is evident that 9.46 is the greatest lat. S = the dif. ference of lat. between the seventh point and the first; therefore, the seventh point of the survey is the most southerly point; and, in like manner, 3.91=the difference of lat. between the third point
and the first, is the greatest lat. north; hence, the third point is the most northerly point of the survey.
Now, by calling the most southerly point of the survey the first station, and proceding to find the latitudes for the several lines in the order in which they were surveyed; that is, the first difference of lat. will be the first lat. which place in the column of latitudes, opposite the said difference of fatitude; to the same lat. add the said difference of lat. to which sum add the next difference of lat. if it be of the same name, but subtract if of a different name, and place it in the column of latitudes, in like manner continue to add or subtract the difference of lat. twice, and the last lat. comes out nothing, if the additions and subtractions are rightly performed. Multiply each of the upper numbers in the column of latitudes by the correspond. ing dep, and place the products in the column
of east or west area, according as the dep, is E. or W. The difference of these columns will be equal to twice the area, half of which will give the area of the survey: as in the following Table.
* Each of the numbers in the column of latitudes is twice the mean latitude of two adjacent latitudes; but at the most southerly point the latitude is nothing; hence the first difference of latitude is the #. lat. and in like manner, the last difference of lat. is the last latitude. It is also to be remarked that the first station used in this Table is not the first station in the actual survey; but the most southerly point of the survey, as calculated by the forsgoing method from Table K.