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Square the distance in
for the correction in inches.
Required the correction for 20 four-pole chains=80 perches=\ mile.
15.25, and .25x.25x8=.5 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 length, and suppose it be AB (fig. 128.) and find the middle between A and B, which suppose to be C; plant the instrument at C; direct the tube to a stationstaff, 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 assistants 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 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 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 1.05 inches, and 5 feet 0.3 inches; then half the sum of these 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 or the bubble, till the hair cut the middle of the vane at B, and at the same time the bubble stands in the middle of the divi. sions ; and then will the instrument be duly adjusted.
If you have a mind to be 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 the repetition of the work. Only observe to cross-level 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. 129.) and observe the heights on the stationstaves, which suppose to be as above; and conse
Now measure from C towards the highest ground A, some distance that comes almost to A ; suppose + 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.