then run the line AH, it will cut off from the land the required area.

REMARK I. If the part cut off by the first closing line, should exceed the given area, the division line will fall on the left of AC.

REMARK II. If the difference between the given area and the first area cut off, divided by half the perpendicular AG, gives a quotient larger than the course CD; then, draw a line from A to D, and consider it as the first closing line, and let fall a perpendicular on DE.

REMARK III. When the point from which the division line is to be drawn, falls between the extremities of a course, dividing the course into two parts, consider one of the parts as an entire course, and the other as forming a new course, having the same bearing. The manner of making the calculation will then be the same as before.

X SECTION IV.

PUBLIC LANDS-VARIATION OF THE NEEDLE.

1. Soon after the organization of the present government, several of the states ceded to the United States large tracts of wild land, and these, together with the lands since. acquired by treaty and purchase, constitute what is called the public lands, or public domain. Previous to the year 1802, these lands were parcelled out without reference to any general plan, in consequence of which the titles often conflicted with each other, and in many cases, several grants covered the same premises.

In the year 1802, the following method of surveying the public lands, was adopted by Colonel Jared Mansfield, then surveyor-general of the North-Western Territory.

2. The country to be surveyed is first divided by

again, by a system of east and west lines, also six miles from each other. The country is thus divided into equal squares, which are called townships. Hence, each township is a square, six miles on a side, and contains thirty-six

square miles.

3. For the purpose of illustration, we have obtained from the general land office the accompanying map, which represents a considerable portion of the State of Arkansas.

The principal meridian in this Survey is called the 5th meridian, and passes through the point of junction of the White river and the Mississippi. The principal base line, running east and west, intersects this meridian a little to the east of White river; and from the meridian and base line, reckoned from this point of intersection, all the ranges of townships are laid off.

For example, 1 North, will apply to all the townships lying in the first row north of the base line: 1 South, will apply to all the townships in the first row south of the base line. Range 1 East, will apply to all the townships lying in the first row, east of the 5th meridian: and range 1 West, will apply to all lying in the first row to the west of it. The small figures designate the rows of townships, reckoned north and south from the base line, and the ranges reckoned east and west from the 5th meridian. Thus, township 1 North, range 4 West, has its exact place designated, and may be immediately located.

4. The principal meridians, and the principal base lines are established by astronomical observation, and the lines of subdivision run with the compass.

For convenience in making surveys, and for the purpose of designating particular localities, a state or large tract, is often divided into parts called "Districts." There are three such districts in the map before us, the boundaries of which are designated by the full dark lines.

5. Each township is divided into equal squares, by meridians one mile apart, and by east and west lines at the same distance from each other. Hence, each township is

a section.

The sections of a township are numbered from

1 to 36, beginning at the north-east angle, and each contains 640 acres.

The diagram exhibits the 36 sections of a township.

To describe a section accurately, we say, section number 5, in township number 4 north, in range 3d west of a known meridian; the one, for example, drawn through the mouth of White river. The description fixes precisely the place of the section. Go to the 3d range of townships, west of the known meridian, find township number 4 north, in this range, and lastly, section number 5 of that township. The corners of the sections should be marked by permanent corner-posts, or by lines blazed on trees.

6. The sections are divided into half sections, quarter sections, and even into eighths of sections. The following table shows the contents of a township, and its subdivi sions:

VARIATION OF THE NEEDLE.

7. The angle which the magnetic meridian makes with the true meridian, at any place on the surface of the earth, is called the variation of the needle at that place, and is east or west, according as the north end of the needle lies on the east or west side of the true meridian.

8. The variation is different at different places, and even at the same place it does not remain constant for any length of time. The variation is ascertained by comparing the magnetic, with the true meridian.

9. If we suppose a line to be traced through those points on the surface of the earth, where the needle points directly north, such a line is called the line of no variation. At all places lying on the east of this line, the variation of the needle is west; at all places lying on the west of it, the variation is east.

10. The public is much indebted to Professor Loomis, for the valuable results of many observations and much scientific research, on the dip and variation of the needle, contained in the 39th and 42d volumes of Silliman's Journal.

The variation at each place was ascertained for the year 1840; and by a comparison of previous observations and the application of known formulas, the annual motion, or change in variation, at each place, was also ascertained, and both are contained in the tables which follow.

11. If the annual motion was correctly found, and continues uniform, the variation at any subsequent period can be ascertained by simply multiplying the annual motion by the number of years, and adding the product, in the algebraic sense, to the variation in 1840. It will be observed that all variations west are designated by the plus sign; and all variations east, by the minus sign. The an

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