the sights toward C, and let the assistant at C slip his vane up or down till the white line appear through the sights, as at E; and note CE. Turning the instrument about, look toward F till, through the sights, you see the white line at G, and note FG; in the mean time let the assistant at C remove to I, and placing the instrument at R, direct it backward toward F and forward toward K. And so proceed, from station to station, to the end. And set down the back heights AB, CE, FO, and the fore heights CD, FG, IK, in their proper columns. Then add the columns, and take the difference of the sums; and if the fore heights exceed, the line is a descent; but if the back heights exceed, it is an ascent. If they be equal, it is an apparent level.

Stations. Back Heights.

ft.

Fore Heights.

3

Hence, as the fore heights are greater, there is a descent, below the apparent level, of 3 feet 5 inches from A to I.

But to reduce this to the difference of true heights, the distances from each station of the level, both to the back and fore stations of the staves, must be measured, and the heights corrected, by the last Problem, when necessary; then, the columns of corrected heights being added, the difference of their sums will be the difference of true heights.

NOTE

NOTE I. The operation may also be performed by placing the Level first at one place, as A, and then successively at other convenient stations, taking fore observa tions only, till a height at the other, as I, is found.

NOTE 2. If the distances of the instrument from the back station staff be every where equal to its distances from the corresponding fore station staff, there will be no need of correction for curvature.

NOTE 3. The velocity of running water depends on the fall. Where the fall is only 3 or 4 inches in a mile, the velocity is very small. Some canals have been cut with a fall from 4 to 6 inches.

1

END OF SURVEYING.

NAVIGATION.

NAVIGATION teaches to conduct a ship on the sea from one port or place to another.

In Navigation there are four principal things; two of which being given, the rest are thence determined.

1. Difference of latitude.

2. Difference of longitude.

3. Distance, or length of the run.

4. Course, or rhumb line, on which the ship sails. The distance is measured by the Log line; and the thumb is shewn by the Compass.

PLANE CHART.

It is absolutely necessary to a traveller, that he should be acquainted with the situation of those places, to which he intends to go. And as the situations of places on the earth are known from their latitudes and longitudes, a sufficiently

tance.

sufficiently correct and copious table of latitudes and longitudes, or an equivalent to such a table, is one of the helps, which a navigator ought not to be without. A table of this kind is susceptible of the advantage of denoting the situation of places to any required degree of accuracy; but, at the same time, it must be confessed, that names and numbers convey a very imperfect notion of these situations to the imagination; and this purpose is more ef fectually answered by the use of maps or charts, which, in general, are drawings or pictures of the face of the earth and sea, as they would appear to an eye at a sufficient disThose may be called true charts, which are either globes or delineations according to the rules of perspect ive; but neither of them is used at sea, because of the few straight lines they contain. The charts, used at sea, are either plane charts, or Mercator's charts. In the plane chart the meridians and parallels of latitude are right lines, at right angles to each other; consequently, it has all its meridians parallel to each other, and all its parallels of latitude equal. It is, therefore, useful only in small spaces of the earth's surface, which do not much differ from planes; such, for example, as a ship's run in a day, or the extent of a bay or harbour. This kind of chart may be used for several degrees of latitude on each side of the equator, because the meridians are there almost parallel. Mercator's chart is similar to the plane chart, excepting that the degrees of the meridian are not equal, but enlarged toward the poles; by which contrivance it acquires many valuable properties. It will be further considered in another place.

PROBLEM.

A

44

43

42

41

40

39

38

37

PROBLEM.

To construct a plane chart.

11 12 13 14 15 16 17 18 19 20 21 22 B

44

43

4.2

41

40

39

38.

37

36

36

C II 12 13 14 15 16 17 18 19 20 21 22 D

Draw two right lines parallel to each other across the paper, one at the top, and the other at the bottom, AB, CD. At right angles to these, draw two other parallel lines, one near the right, and the other near the left extremity of the paper, AC, BD. Divide the two first lines, each into a like number of equal parts, within the points of intersection formed by the crossing of the other two right lines. And divide the other two right lines in like manner into parts, each equal to a part of the first lines. Then the two first lines will represent the extreme parallels of latitude, and the two latter the extreme meridians of the intended chart; and the subdivisions, on each, will represent degrees, miles, leagues, or any other measure, which may best suit the purpose of the designer. If one of the parallels be supposed to represent the equator, the divisions of the meridians must be numbered thence ; if not, the divisions must be reckoned from the latitude

VOL. II.

L L

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of