bottom, then at anchor, was 35°; what was its distance from the bottom of the wall? Ans. 204.2 feet.

8. There are two columns left standing upright in the ruins of Persepolis; the one is 64 fect above the plane, and the other 50; in a right line between these stands an ancient statue, the head of which is 97 feet from the summit of the higher, and 86 from that of the lower column; and the distance between the lower column and the centre of the statue's base is 76 feet: required the distance between the tops of the columns.

Ans. 157 feet.

SURVEYING.

CHAPTER I.

ON THE DIMENSIONS OF A SURVEY.

1. SURVEYING is the art of measuring, laying out and dividing land.

2. A Four-Pole Chain is an instrument used for measuring the boundaries of a survey. It is, as its name imports, 4 poles or 66 feet in length, and is divided into 100 equal parts or links. The length of a link is therefore 7.92 inches.

Note.-A Four-pole Chain is frequently called simply a chain.

3. A Two-pole Chain is 2 poles or 33 feet in length, and is usually divided into 50 equal parts or links. When it is thus divided, the links are of the same length as in a four-pole chain; and the measures taken with it are reduced to four-pole chains previous to using them in calculation.

Sometimes the two-pole chain is divided into 40 links; in which case, each two links is the one-tenth of a perch. Measures taken with a two-pole chain, thus divided, are usually expressed in perches and tenths.

4. The Distance of a line in surveying, is its length, estimated in a horizontal direction. It is generally expressed either in chains and links, or in perches and tenths.

5. A Meridian or Meridian Line is any line that runs due north or south.

Note.-All the meridians passing through any survey of moderate extent may be considered as straight lines, parallel to one another.*

6. The Bearing or Course of a line, is the angle which it makes, with a meridian passing through one end; and it is reckoned from the North or South Points of the horizon towards the East or West Points.

Thus, supposing the line NS, Fig. 77, to be a meridian, and the angle SAB to be 50°; then the bearing of AB from the point A, is 50° to the east of south; which is usually expressed thus: S, 50° E., and read, south, fifty degrees east.

7. The Reverse Bearing of a line is the bearing taken from the other end of the line.

Note. The bearing and the reverse bearing of a line, are angles of the same magnitude,† but lying between

* The meridians are, in reality, curve lines which meet in the north and south poles of the earth. No two of them are therefore exactly parallel; but in usual surveys their deviation from parallelism is so very small, that there is no sensible error in considering them so.

As the meridians are not exactly parallel, this is not strictly true, except

directly opposite points. Thus, if the bearing of AB, from the end A, is S. 50° E., the bearing of the same line from the end B, is N. 50° W.

8. A Circumferentor or Surveyor's Compass, is an instrument used to take the bearings of lines.

The circumference of its face is divided into degrees, and in some of the larger ones into half degrees, in such manner that two opposite points may be exactly in the direction of the sights with which the instrument is furnished. These points are the north and south points of the instrument. Midway between them, on the circumference, are the east and west points. The degrees are numbered from 0° to 90°, each way from the north and south points to the cast and west ones. In the centre of the face is a pin, finely pointed, which supports a Magnetic Needle, moving freely within the instrument. The instrument, when used, is placed on a staff, having a pointed iron at the bottom, and a ball and socket at the top.

The Chain and Compass are the instruments with which the dimensions of surveys in this country are generally taken. It is important to have them accurately made. In the selection of a compass, particular attention should be directed to the settling of the needle. If, when the needle has been moved out of its natural position, it settles very soon, it is defective; either its magnetic virtue is weak, or it does not move with sufficient freedom on the pin.

9. The Difference of Latitude, or the Northing or

the latitude of Philadelphia the greatest difference between the bearing and reverse bearing of a line, a mile in length, is only 44". In higher latitudes the difference is greater.

Southing of a line, is the distance that one end is further north or south than the other end; or it is the distance which is intercepted on a meridian passing through one end, between this end and a perpendicular to the meridian, from the other end.

Thus, if NS, Fig. 77, be a meridian passing through the end A, of the line AB, and Bb be perpendicular to NS, then is Ab the difference of latitude or southing of AB.

10. The Departure or the Easting or Westing of a line is the distance that one end is further east or west than the other end; or it is the distance from one end, perpendicular to a meridian passing through the other end.

Thus Bb, Fig. 77, is the departure or easting of the line AB.

But if ns be a meridian, and AC perpendicular to it, and if the bearing of the line be taken from B to A, then is BC the difference of latitude or northing, and AC the departure or westing, of the line AB.

Note.-It is evident from the definitions, that the Distance, Difference of Latitude, and the Departure form the sides of a right-angled triangle; in which, considering the departure as the base, the perpendicular is the difference of latitude, the hypothenuse is the distance, and the angle at the perpendicular is the bearing.

11. The Meridian Distance of any station, is its dis tance from a meridian passing through the first station of the survey, or any other assumed point.