PROBLEM II.

To find the level of two places; or the ascent or decent from

one to the other.

This is best done with a spirit level, having telescopic sights; which may be set horizontally by screws, that raise or lower the ends of the tube; and station staves with sliding vanes.

To take a level from A to I-let one assistant stand at A and another at C, and at a convenient place, as P, between A and C, place the level, and set it horizontally by means of the screws. Let the assistant at A hold the staff upright in his hand at A, while from P you look through the sights toward A, and direct him to slip the vane up or down till the white line at B be level with the sights; then note AB. Direct the other assistant to stand at C, and to hold the staff upright, then turning the instrument round at P, and looking toward C, direct him to raise or lower the vane till, through the sights, you can see the white line at D; then note the height above the ground, CD. And the difference of the heights, AB and CD, is the ascent or decent with respect to the apparent level, if there be no other station,

But, if there be many stations, make a table with two columns, one for the back stations, and the other for the fore stations. Now to proceed, set down the two heights AB, CD; and let the assistant at A go to F with his staff, and remove the instrument to Q, and level it; then direct

assistant at C slip his line appear through the Turning the instrument

the sights toward C, and let the vane up or down till the white sights, as at E; and note CE. 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. is an apparent level.

If they be equal, it

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 1. 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 observations 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 ef 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.

NAVIGATION.

NAVIGATION

AVIGATION 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 rhumb is shown 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 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 situ-ations 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 distance. Those may be called true charts, which are either globes or delineations according to the rules of perspective; 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 harbor. 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 farther considered in another place.