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TO FIND THE

CONTENT OF LAND,

BY

CALCULATION.

THE foregoing method of dividing a map into Triangles and Trapeziums, although it appears to be demonstrably true in theory, it is not to be depended on in practice, where accuracy is required; for a map may be so divided several ways, and will generally give as many different areas; therefore I shall not enlarge upon it here, but proceed to shew how the true Area may be found, by difference of latitude and departure.

DEFINITIONS.

1. Meridians are North and South lines supposed to pass through every station, parallel to each other.

2. The difference of Latitude, or Northing or Southing of any line, is the distance that one end of the line is North or South from the other-Thus in the following figure

S

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Suppose NS to be a meridian line, passing through the point A, of the line AB; then is AD the difference of latitude or southing of the line AB.

3. The Departure of any line, is the nearest distance from one end of a line to a meridian passing through the other end; thus DB is the Departure or Westing of the line AB.

Reverse this line, and call it BA; then will BC be the Difference of Latitude or Northing of the line BA, and CA the Departure or Easting of the same line.

4. That meridian which passes through the first station, is called the first meridian.

The meridian distance of any line, is the distance there

POSITION.

In every survey, which is truly taken, the sums of the Northings and Southings will be equal; and the sums of the Eastings and Westings will be equal.

For, if I depart from any place, suppose A, in the annexed figures, it is evident, that when I return to the same spot, I must have made as much Northing as Southing, and Easting as Westing, let my traverse be ever so irregular.

A

To take out of the Tables of Latitude and Departure, the Difference of Latitude and Departure, answering to any Course and Distance.

RULE.

If the integral number exceeds not 100, it is found in the right and left hand columns marked, Dist. And if the degrees be less than 45, they are found at the top of the page; and in the columns marked Lat. and Dep. is the latitude and departure answering thereto; but if the degrees exceed 45, they are found at the bottom of the page, and the latitude and departure in the columns so marked at the bottom. Then, opposite to the given distance, and under, or over the given degrees, will be the Latitude and Departure required. And if a decimal number be annexed, proceed with it as if a whole number, only observe, in taking out the difference of Latitude and Departure, to move the decimal point as many figures to the left, as are in the given decimal: and these last numbers, added to the former, will be those sought; but if the distance exceeds 100, it must be taken out at two or more times, and the results added together.

EXAMPLES.

Suppose the course to be N. 34° E. and distance 14.64 chains.

Opposite to 14, and under 34° 1, I find

Opposite to 64, and under the same de

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grees, moving the decimal point two 00.52

figures to the left, I find

0.36

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