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Bearing S. 53°W. Distance 26.17 chains.

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Opposite to 26, and over 53° 4, I find

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Opposite to 17, moving the point two figures to the left, I find

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The numbers required,

15.66 20.97

Bearing, N. 28° 3 W. Distance, 146.8 perches.

Lat. Dep.

Opposite to 100, and under 28° 3, I find 87.67
Opposite to 46, in the same columns,

48.10

I find

} 40

40.33 22.13

}

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Opposite to 8, moving the point one

figure to the left hand,

Give, as required,

128.70 70.61

If the given distance be less than 10, and only one decimal figure, then the difference of latitude and departure may be taken at one view, by finding the two figures in the side column, as if they were a whole number; and in taking out the latitude and departure, move the decimal point one figure to the left.

Suppose the bearing to be S. 18° E. Distance 7.40 chains.

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Opposite to 74, and under 18°, moving

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the point one figure to the left, I find

Thus proceed with every course and distance in the survey, and place the numbers in their respective columns, in tables ruled for that purpose, as in the Examples following. Then add up each column, and if they balance, as mentioned in the preceding position, the work is right.

But in real practice, it but rarely happens, that the columns of latitude and those of departure, will balance on first being added up, for little inaccuracies will arise, both in taking the observations, and in chaining; to adjust which, Observe,

That in small surveys, if the difference amounts to 5 links for every station, there must have been some error com-. mitted in taking the survey; and the best way to rectify it, will be by a re-survey on the ground, or at least so much of it as will discover the error. But if the differences be within these limits, the work may be balanced, by adding one half of the differences to the numbers in the less columns, and subtracting it from those in the greater, in such a manner, that the numbers may be altered nearly in proportion to their corresponding distances, as in the following example.

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Field Notes.

No.

From the Tables.

Balanced.

Courses. Chains N. L. | S. L. E. D. | W. D. N. L. | S. L. ¡E. D. | W. D.

1 S. 40 W. 17.50

2 N. 45 W.22.25 15.74

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3 N. 36 E. 312 525.28

18.37

25.27

18.36

4

North. 13.60 13.60

13.60

5 S. 81 E. 46.50

7.27 45.92

7.2845.91

6 S. 8 W. 34.25

3

4.76

33.92

4.77

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difference of latitude and

departure

to every course and distance, and balanced the columns, if necessary, then find the meridian distances, by choosing such a place in the columns of Eastings or Westings, as will admit of a continual double addition of the one, and subtraction of the other; and this will end in 0, 0, or a cipher, if the additions and subtractions be right; because there is just as much added as subtracted, which will become easy and familiar by a little practice, and instruction from the teacher.

Then multiply each upper meridian distance into its respective Northing or Southing, and place the products in their respective columns of North or South area, and half the difference between the sums of these columns will be the area of the map, in such measure as the distances were taken in. As exemplified in the following examples.

I shall now proceed to find, by calculation, the area of each of the preceding surveys.

Note. In the following example, the columns of difference of latitude and departure, will not balance on first adding up.

EXAMPLE 1.

No Bearings. D. Ch. N. L.JS. L.E. D. W. D. [E.M.DN. Area.

S. Area.

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Proved by making West Meridian Distance.

No Bearings. D. Ch. N. L.IS. L. E. D. W. D. | WMD N. Area

S. Area

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Ab or DC, is the east departure of the first distance AO; and AD or bC the north difference of latitude, gh

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