"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 rightangled triangle CAB, 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 correction in inches. EXAMPLE. 8, Required the correction for 20 four-pole chains =80 perches-mile. *800)20×20=400(.5 12800)80×80=6400(.5 1.25, and .25×25×8=.5 that is,.5, or inch, the correction required. But, to save the trouble of calculation, we insert the following table of corrections. A Table of Corrections! The distances in four-pole chains. Distar Correc. DistanCorre^ 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. 3.) and 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 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 preced-. ing numbers. Now, so elevate or depress the hair or the bub ble, 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 soever. 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 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 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 2 vanes (A and B fig. 5.) as before, which will be then both in the same horizontal level, whether the instrument be right 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 move 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 P P |