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find the middle between A and B, which suppose to be C; plant the instrument 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 rise 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 cut at the height of 6 feet 5 inches and two 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 station-staff 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 tentbs, 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 or 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 cross-level it in this adjustment, and in all future uses what
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 D A 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 outs 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 adjust
ed. 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 adjustments
Or it will be still better to set the station-staves equally distant froin 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 2 vanes (A and B fig. 5.) as before, which will be then both in the same horizontal level, whether the instrument he right adjusted or not, because one will be as much above or below the true level of the instruinent, 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 с, 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 toward 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 instrument 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 sighls.
Then look toward the other staff 6B, 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 forwards to the place cB; now look back to the staff bB, and enter the numbers cut by the vane there under the title Back säghts ; then look forwards to cB, and enter the observation under the title Fore sights. Do the like when the instrument is planted at A', A', &c. always taking care to keep the staff in the same place wben 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 Back sights into one sum, and the column of Fore sights also into one sum; and the difference between these suuns 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.