opposites, may suffice to plot the same from the landmarks, Å, B, C, &c. as well as those taken on the land: or, indeed, by the course and distance, as in navigation, if the water be smooth and without a current.

In sea shoals, it is convenient to note at each observation the depth of the water found by the lead, and the drift and setting of the current by the log and compass, while the boat is at anchor, which may be done with ease and expedition enough. For while the boat rides at an anchor, her stern points out the setting of the current, and the log and glass will measure its drift.

And these ought to be noted on the draught, which may be thus:

The currents may be shown, by drawing a dart pointing out its setting, and its drift by the Roman capital letters, the depth of the water by the small figures, and rocks by little crosses, &c.

SECTION IX.

OF LEVELLING.

PL. 13. fig. 2.

LEVELLING is the art of ascertaining the perpendicular ascent or descent of one place (or more) above or below the horizontal level of another, for various intentions, and of marking out courses for conveyance of water, &c.

The true level is a curve conforming to the surface of the earth; as ABG.

The apparent level is a tangent to that curve; as ADE.

The correction or allowance for the earth's curvature is the difference between the apparent level and the true; as BD. The quantity of this correction may be known by having in the right-angled triangle CAD the two legs AC = the semidiameter of the earth (=1267500 perches), and AD = the distance of the object, to find the hypothenuse CD, from which taking CB (=CA), the remainder will be the correction BD; but it may be obtained more practically thus:

Square the

distance in

four-pole chains, and divide by 800,) for the coror in perches, and divide by 12800 rection in or in miles, and multiply by 8 inches.

EXAMPLE.

Required the correction for 20 four-pole chains = 80 perches

=

mile.

That is, .5, or inch, the correction required.

But, to save the trouble of calculation, we insert the following table of corrections.

The first thing necessary in levelling is the adjusting of the level, which may be performed several ways. The following is very easy and practical.

Choose some ground which is not above 4 or 5 feet out of the level, for the distance of 8 or 10 chains in length, and suppose it be AB (fig. 3), and find the middle between A 'and B, which suppose to be C; plant the intstrument at C, direct the tube to a station-staff held up at A, and elevate or depress the tube till the bubble is exactly in the middle of the divisions; then by signals direct your assistant at A to raise or depress the vane sliding on the station-staff till the horizontal hair in the glass cuts the middle of that vane; then see how many feet, inches, and parts are cut by the upper part of the vane, which suppose to be 3 feet 4 inches and 6 tenths.

In like manner direct to the other staff at B, and suppose the upper edge of that vane to be cut at the height of 6 feet 5 inches and 2 tenths, then will these two vanes be on a level.

From 6 feet 5.2 inches subtract 3 feet 4.6 inches, and reserve the remainder 3 feet 0.6 inches.

Now remove the instrument as close to the higher stationstaff as you can; so that the middle of the telescope may almost touch it. Then bring the telescope as near to a level as the judgment of the eye will direct.

Measure from the ground the height of the top of the telescope; and also of the bottom in feet, inches, and parts; suppose them to be 4 feet 10.5 inches, and 5 feet 0.3 inches; then half the sum of the heights 4 feet 11.4 inches is the height of the centre of the glass; and to this add half the breadth of the vane, which suppose to be 1 inch and 5 tenths, and to the sum 5 feet 0.9 inches add the preceding remainder 3 feet 0.6 inches; then let the person at B move his vane till the upper edge cut 8 feet 1.5 inches, the sum of the preceding numbers.

Now so elevate or depress the hair of the bubble till the hair cut the middle of the vane at B, and at the same time the bubble stands at the middle of the divisions; and then will the instrument be duly adjusted.

If you have a mind to be more accurate, repeat the operation; but when you place the instrument at C, turn the tube at right angles to the line AB, and there set it level; then proceed with a repetition of the work. Only observe to crosslevel it in this adjustment, and in all future uses whatsoever.

Or the level may be adjusted thus: As before, first plant the instrument in the middle between A and B (fig. 4), and observe the heights on the station-staves, which suppose to be as above; and consequently their difference, as before, is 3 feet 0.6 inches. Now measure from C towards the highest ground

A, some distance that comes almost to A, suppose 4 chains to D; and DB will be 9 chains, and DA one chain; then plant the instrument at D, direct the telescope to A, and setting the bubble to the middle of the division direct your assistant to move the vane till the hair cuts the middle of it, and note down the feet, inches, and parts cut by the upper edge of the vane, which suppose to be 3 feet 8.4 inches: to this add the difference 3 feet 0.6 inches, and the sum 6 feet 9 inches reserve.

Now direct the telescope to the staff at B, level it, and direct your assistant to move the vane till the hair cuts the middle thereof; and then if the upper edge of the vane cuts the foregoing sum 6 feet 9 inches, the hair and bubble are truly adjusted. But if not, say, as BD less AD is to the difference between the numbers cut by the upper edge of the vane and the number 6 feet 9 inches, so is the distance AD to a number which, added to that cut by the vane when less than 6 feet 9, and subtracted from the number cut by the vane when it is greater than 6 feet 9, will give a number, to which let the assistant fix the vane; then so elevate or depress the hair or the bubble till the hair cuts the middle of the vane at B, and the bubble stands in the middle of the divisions; for then the level will be adjusted. The operation may be again repeated, and at every station. cross-levelled, which will confirm the former adjustment.

Or it will be still better to set the station-staves equally distant from the instrument (suppose about 16 or 20 perches each) at an angle of about 60°, or so as to form nearly an equilateral triangle therewith, and level the two vanes (A and B, fig. 5), as before, which will be then both in the same horizontal level, whether the instrument be rightly adjusted or not, because one will be as much above or below the true level of the instrument as the other, being in the same distance from it; then remove the instrument as near as may be to one of them, suppose A, and raise or lower the vane A to the exact level of the visual ray in the instrument, noting precisely how much it is moved, and have the other vane B moved just as much, in order to bring them again to a level, allowing for the correction of the apparent level if it be a sensible quantity; then adjust the instrument to the level of the vane at B.

To adjust the rafter-level (plate 13, fig. 6), which may be 10, 12, or 14 feet in the span AB; set it on a plank or hard ground nearly level, and mark where the plumb line cuts the beam mn, suppose at c; then invert the position by setting the foot A in the place of B, and B in that of A, marking where the line now cuts, as at e; the middle point between c and e will be the true levelling mark,

To continue a level course with this instrument, set the foot A to the starting place, and move B upward or downward towards D or E, till the point B be determined and marked for a level with A; then carry the instrument forward in the direction of C, till the foot A rests at B, whence the point C is levelled as before, &c. Sights may be placed at r and s, and the instrument adjusted to them, as before, by reversing them in the direction of some distant object.

After the instrument is duly adjusted, you may proceed to use it. Let the example be this annexed (fig. 7), where A everywhere represents the level, and B the station-staves; and suppose the route be made from a to e: first plant the instru ment between the staves a and b; at A direct the level to aB, bring the bubble to the middle of the divisions, and instruct your assistant so to place the vane that the hair in the telescope cuts the middle of the vane; then in a book divided into two columns, the one entitled Back-sights, the other Fore-sights, enter the feet, inches, and parts cut by the upper edge of the vane at aB in the column entitled Back-sights.

Then look towards the other staff bB, bring the bubble to the middle of the divisions, and direct your assistant to place the vane so that the hair cuts the middle of the vane; then enter the feet, inches, and parts cut by the upper edge of the vane in the column of Fore-sights.

Now plant the instrument at A2, still keeping the staff Bb exactly in the same place, and carry the staff aB forward to the place cB; now look back to the staff bB, and enter the numbers cut by the vane there under the title. Back-sights; then look forwards to cB, and enter the observation under the title Fore-sights. Do the like when the instrument is planted at A3, A1, &c., always taking care to keep the staff in the same place when you looked at it for a fore-sight, till you have also taken with it a back-sight.

Having finished your level, add up the column of backsights into one sum, and the column of fore-sights also into one sum; and the difference between these sums is the ascent or descent required. And if the sum of the fore-sights be greater than the sum of the back-sights, then e is lower than a; but if the sum of the fore-sights be less than the sum of the back-sights, e is higher than a. For example, let the numbers be as in the following table.