EXAMPLE II.

by subtracting the lesser Areas from the greater, the true content frequently calculated twice over, and sometimes oftener; therefore,

of the Field is obtained.

Area of the Field, as in the second Example.

the difference of the sum of these Products would be double the ed by the respective Northings or Southings standing against them, upper numbers in the Column of Meridian Distances, were multipliIf, instead of making a Column of half Meridian Distances, the

See next page.

It will be observed, that in this Example, the Columns of Latiitude and Departure are carried to but one place of Decimals, which can generally be done without making a difference of, perhaps, one Square Rod, in 20 Acres of Land, and the Additions, Subtractions, and Multiplications are greatly diminished.

The preceding is called the Pennsylvania method of calculation. Another system of Rectangular Surveying, differing but little from this, and frequently used by practical Surveyors, is that adopted by MR. FLINT in his "TREATISE ON SURVEYING," a specimen of which is given below.

From the Traverse

Table

take

the Northings, Southings, East

ings, and Westings, and balance the Columns as before directed, after which, instead of forming a Column of Meridian Distances

proceed to form a Departure Column, the numbers, in which, show how far the end of each Side of the Field is East or West of the Station, where the Calculation begins. This Column is formed by a continual addition of the Eastings and subtraction of the Westings; or by adding the Westings and subtracting the Eastings. See Example 4.

In this Survey the Calculation begins at the Second Station; the Easting against this Course, 17 is the first number to be placed in the first Departure Column; to this add 16,52 the next Easting, which make 16,69 for the next Departure; to this add,17 the next Easting which make 16,86 the next Departure; to this add 5,58 and 22,44 is the next Departure; to this add 1,11 and 23,55 is the next Departure; to this add 2,12 and 25,67 is the next Departure; to this add 1,31 and 26,98 is the next Departure. From this subtract 26,98 the Westing and 00,00 remains to be set against the remaining or first Course.

In the next place form a second Departure Column, the numbers in which, like the upper numbers in the Column of Meridian Distances, in the Pennsylvania method, show the sum of the Distances at each end of every Line from the first Meridian, or from a North and South Line passing through the Station where the Calculation begins.

The number which begun the first Departure Column must be set against the same Course to begin the second Departure Column ; to which add the second number, in that Column, for the second in this; for the third, add the second and third; and for the fourth, add the third and fourth, and so on till the Column be completed

The first number to be placed in the second Departure Column is,17; to this add 16,69 which make 16,86 for the second number; to 16,69 add 16,86 which make 33,55 for the third number; to 16,86 add 22,44 which make 39,30 for the fourth number; to 22,44 add 23,55 for the next number; to 23,55 add 25,67 for the next number; to 25,67 add 26,98 for the next number; and to 26,98 add 00,00 for the upper number.

The work being thus prepared, multiply the several numbers in the second Departure Column by the Northings or Southings standing against them respectively; place the products of those multiplied by the Northings in the Column of North Areas, and of those multiplied by the Southings in the Column of South Areas; add up these two Columns and subtract the less from the greater, the remainder will be double the Area of the Field in Square Rods, or Square Chains and Links, according to the measure used in the Survey.