be revolved in the Y's, the bubble will continue at the middle point of the tube. It is, however, difficult to make the first part of this adjustment, while the axis of the level is considerably inclined to the line of collimation: for, allowing the level to be truly horizontal in one position of the telescope, after it is reversed, there will be but one corresponding position in which the bubble will stand at the middle of the tube. This suggests the necessity of making the first part of the adjustment with tolerable accuracy; then, having made the second with care, re-examine the first, and proceed thus till the adjustment is completed. Third adjustment. To make the level CD and the line of collimation perpendicular to the axis of the instrument, or parallel to the horizontal bar EE. Loosen the clamp screw S, and turn the bar EE, until the level DC comes directly over two of the levelling screws. By means of these screws, make the level DC truly horizontal. Then, turn the level quite round; if, during the revolution, it be still horizontal, it must be at right angles to the axis of the instrument about which it has been revolved. But if, after the revolution, the level DC be not horizontal, rectify half the error with the screw N, and half with the levelling screws. Then place the bar EE over the other two levelling screws, and make the same examinations and corrections as before ; and proceed thus, until the level can be turned entirely around without displacing the bubble at the centre. When this can be done, it is obvious, that the level DC and the line of collimation, are at right angles to the axis of the instrument about which they revolve; and since the axis is carefully adjusted by the maker, at right angles to the bar EE, it follows, that the line of collimation, the level DC, and the bar EE, are parallel to each other. These adjustments are, however, made on the supposition, that the parts of the telescope which come in contact with the Y's are portions of the same cylinder. To ascertain if they be so, let the telescope be reversed in the P's, and then turned half round; if the level DC continue horizontal, and the interboth positions of the telescope, the adjustments are accurate. If otherwise, such alterations must be made in the places of the spider's lines, by the screws which govern their slides, that, in both positions of the telescope, their intersection shall be directed to the same point, the level DC continuing at the same time horizontal. The level is now adjusted. When used, however, it is best to re-examine it every day or two, as the work will be erroneous unless the adjustments are accurate. OF LEVELLING STAVES. 202. The levelling staves are used to determine the points at which a given horizontal line intersects lines that are perpendicular to the surface of the earth, and the distance of such points of intersection from the ground. They are thus constructed. AB (Pl. 9, Fig. 3) is a rectangular piece of wood, in the middle of which is a groove abcd. Into this groove a slide Inst enters, and is worked freely along the groove. At the upper end of the slide is a rectangular index fhgi, called a vane, six inches, in the direction hi. The vane is divided into four equal parts, by the lines fg, hi : the two rectangles fh, ig, are usually painted black, and the other two, if, hg, white, so that the lines fg and hi may be distinguished with great accuracy. The slide from fg to In is of the same length with the body of the staff AB: hence, when the line fg coincides with bc, the lower end of the slide in will coincide with ad. The pins p and q, which work in grooves, and are largest at the ends p and q, are pressed in to hold the slide in any position at which it may be placed. The length of the staff is generally six feet, and it is usually divided into eighths or tenths of an inch. The slide is divided in the same way. The longer lines show the feet, the shorter the inches. The object to be attained by these divisions is, to ascertain the distance of the line fg from the ground. When the line fg is brought to the top of the staff, to coincide with bc, the lower line wio, of the vane, coincides with the line marked 6, on the left of the staff: which shows, the staff standing upright, that the line the lower end of the staff, is, indeed, but 5 feet 9 inches; but the line fg is three inches above the line wio, so that fg is six feet from the ground. If, from the last position, the slide be run up until the line wio coincides with the division marked 1, on the left of the staff, the line fg will be six feet and one inch from the ground: if till it coincides with bc, it will be six feet and three inches, the inches being marked both on the staff and slide. If it be still run up, until 7 on the slide coincides with be, the line fg will be seven feet from the ground. In the figure, the line fg is seven feet from the bottom of the staff. The count above 6 feet 3 inches is always made on the slide. The manner of counting off, for the parts of an inch, is too plain to require particular explanation. Having run down the slide till the upper line h, of the vane, coincides with bc, place bB on the ground, and the staff vertical. It is now plain, that the line fg is three inches above the ground. These three inches are marked on the right of the staff. If the slide be run up till the lower line h coincides with 1 on the right of the staff, the line fg will be one foot from the ground, and similarly until six feet be shown at the other end of the staff. The feet are marked 1, 2, 3, &c., from the upper end, and are reversed in the present position of the staff; but are upright when the staff is placed for use. In this position of the staff, the count is made at the lower line of the vane. 203. There is yet a method of ascertaining if the level be truly adjusted, which ought not to be neglected, since all the results depend on the accuracy of the instrument. The method is this:— The line of collimation being first adjusted, place the level A (Fig. 4) at any convenient place, as G. At equal distances of about 100 yards, on either side, and in the same line with the level, place the levelling staves CE, BF. Make the level horizontal with the levelling screws. Then, turn it towards either staff, as BF, and run the vane up or down, as required, until the intersection of the hairs strikes its centre : then make the slide fast, and note carefully the height of the Turn the level half round, and do the same in respect of vane. Sight again to the staff BF, and move the vane, until the intersection of the hairs shows its centre; and note the exact height. Let the telescope be now turned half round, and the same done in respect of the staff CE. If the staves are equidistant from the level, the difference between the two observed heights of the vane of the staff BF, will be equal to the difference of the observed heights on the staff CE; and if the staves are at unequal distances from the level, the differences of the observed heights will be proportional to those distances, BG, GC. Let gAf be the true horizontal line, and Ad the first line of sight. When the level is turned half round, the corresponding line will be Ab. The level being reversed in the Y's, the line of sight becomes Aa, and turning the level half round, the corresponding line is AE. Now, Bd and Ba are the observed heights .on one staff, and CE, Cb on the other. Moreover, if GB and GC are equal, it is evident, that the two triangles Ada, AEb will also be equal; and consequently, da=Eb. It is also evident, that Aa is as much above the horizontal line Ag, as Ad is below it: so that, if da, the difference of the two heights, be divided by 2, the quotient will show how far the vane must be elevated from its first position, or depressed from its second, to bring it to the horizontal line passing through A. Let the index be so elevated, or depressed. Then turn the screw N (Fig. 2), until the intersection of the hairs rests on the centre of the vane: the axis of the telescope is then horizontal, and by means of the screw h, the level DC is made parallel to it. The line of collimation and the level CD are then to be made parallel to EE, as in the third adjustment. It is perhaps too obvious to be mentioned, that, if the level be truly adjusted in the beginning, the points d and a will coincide with g, and the points E and b with f. 204. Having described the instruments used in levelling, it remains to show the manner of using them in the practical operations on the field. When it is proposed to find the difference of level of any two objects, or stations, all levels made in the direction of the station at which the work is begun, are, for the sake of distinc tion merely, called back-sights; and levels taken in the direction of the other station, fore-sights. Before going on the field with the level, rule three columns, as below, and head them, Stations, Back-sights, Fore-sights. the vane 205. To find the difference of level between any two points, as A and G. (Pl. 9, Fig. 5.) The level being adjusted, place it at any point B, as nearly in the line joining A and G as may be convenient. Place a levelling staff at A, and another at N, a point lying as near as may be in the direction of G. Make the level horizontal by means of the levelling screws; turn the telescope to the staff at A, and direct the person at the staff to slide up until the horizontal line ab cuts its centre; then note the distance Ab, (equal to 10 feet in the present example,) and enter it in the column of back-sights, opposite station 1. Sight also to the staff at N, and enter the distance Na, equal to 3 feet, in the column of fore-sights, opposite station 1. Take up the level, and place it at some other convenient station, as C, and remove the staff at A to M. Having levelled the instrument, sight to the staff at N, and enter the distance Nd, 11 feet 6 inches, in the column of back-sights, opposite station 2: sight also to the staff at M, and enter the distance Mf, equal 0, in the column of fore-sights, opposite station 2. Let the level be now removed to any other station, as D, and the staff at N, to some other point, as P. Let the dis |