cafe truly level. In this facile mode of adjustment confifts the new improvement of the inftrument; and it is hereby capable of being adjusted by only one ftation and one object, which will at the fame time determine it to be in a true level. If by change of weather, accident, or otherwise, the inftrument should have loft its level adjustment or ftate, it may thus be readily reftored and readjusted at the first station; which is an advantage none of the inftruments formerly made have been capable of. The two fupporters DE, on which the level rests and turns, are fhaped like the letter Y. The telescope refts within the upper part of them; and the inner fides of each of these Ys are tangents to the cylindric tube of the telescope, which is turned to a true cylinder, and each touches it but at one place only.

The lower end of these fupporters are inferted into a ftrong brass plate (FE), and fo as to ftand perpendicularly on it. One is kept faft by a tightening fcrew G, and to the other is applied a fine threaded fcrew H, to adjust the tube when on its fupporters to a true level. To the fupporter D is fometimes applied a line of tangents as far as 12 degrees, in order to take an angle of depreffion or elevation to that extent. Between the fupporters is also sometimes fixed a compafsbox I, divided into 360 degrees, and again into four 90°; having a centre pin and needle, and trigger, at d, to throw off the needle from the centre when not used; fo in this manner it conftitutes a perfect circumferenter, connected with all the foregoing improvements. This plate is fixed on a conical brafs ferrel K, which is adapted to the bell-metal fruftum of a cone at top of the brass head of the ftaves, having a ball and focket, with three bell-metal joints, two ftrong brafs parallel plates LL, the four fcrews eeee for adjusting the horizontal motion, a regulating fcrew M to this motion, and a fastening screw N to lighten it on the cone when neceffary. The faftening fcrew N, and the regulating fcrew M, by which the whole inftrument is moved with accuracy through a small space in an horizontal direction, was an addition of Mr Ramfden's.

The manner of adjusting the fpirit-level at the first flation. The whole level being now placed fteadily on its ftaves, it must be rendered parallel to the axis of the telescope before you adjust the horizontal motion. To this end the telescope must be placed in a line with two of the fcrews ee, and then levelled thereby till the bubble of air in the fpirit-tube keeps its pofition in the middle, while turned about to three points, making nearly right angles at the centre to one another.

The horizontal motion being thus adjusted, the rims ff of the Ys are to be opened, the telescope taken off and laid the contrary way upon the fupporters. If the bubble of air then refts exactly the fame, the level and telescope are adjusted rightly to one another; but if the bubble does not remain the fame, the end to which the air bubble goes must be noticed, and the diftance of it from the telescope altered; correcting one half the error by the screws cc, and the other half by the fcrews ee.

Now the intersection of the wires being directed to any distant object, it may be one of the vanes of the staves hereafter defcribed: if they continue to be VOL. X. Part I.

against it precisely while the telescope is turned round Levelling. on its Ys, it proves, as before mentioned, that the axis of the telescope coincides with the interfection of the wires, and that the inftrument will give the true level direction.

The operation of levelling being of a very accurate and important nature, and the best inftrument when out of its adjustment being of little ufe, it is quite neceffary that every perfon ufing fuch an inftrument fhould have it readily in his power to correct it; and the one above described appears to be the best adapted for that purpose of any hitherto contrived.

LEVELLING may be defined, the art which inftructs us in finding how much higher or lower any given point on the furface of the earth is than another; or, in other words, the difference in their distance from the centre of the earth.

The practice of levelling therefore confifts, 1. In finding and marking two or more points that fhall be in the circumference of a circle whofe centre is that of the earth. 2. In comparing the points thus found with other points, to afcertain the difference in their diftances from the earth's centre.

With regard to the theory of levelling, we muft obferve, that a plumb-line, hanging freely in the air, points directly towards the centre of the earth; and a line drawn at right angles, croffing the direction of the plumb-line, and touching the earth's furface, is a true level only in that particular fpot; but if this line which croffes the plumb be continued for any confiderable length, it will rife above the earth's furface, and the apparent level will be above the true one, be cause the earth is globular; and this rifing will be as the fquare of the distance to which the faid right line is produced; that is to say, however much it is raised above the earth's furface at one mile's distance, it will rife four times as much at the diftance of two miles, nine times at the distance of three, &c. This is owing to the globular figure of the earth; and this rifing is the difference betwixt the true and apparent levels; the real curve of the earth being the true level, and the tangent to it the apparent level. Hence it appears, that the less distance we take betwixt any two ftations, the truer will be our operations in levelling; and fo foon does the difference betwixt the true and apparent levels become perceptible, that it is neceffary to make an allowance for it if the distance betwixt the two ftations exceeds two chains in length. The following is an infallible rule for determining the allowance to be made:

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Multiply the number of Gunter's decimal ftatute Leach's In chains that are contained in length between any two land navistations where the levels are to be taken by itself, andgation. the product arifing therefrom again by 124; which is a common multiplier for all manner of diftances for this purpose on account of the earth's curvature: then divide the fecond product arifing therefrom by 100,000; or, which is alfo the fame, with the dash of the pen cut off five figures on the right hand fide of the product, and what remains on the left fide is inches, and the five figures cut off decimal parts of an inch."

fhows that B is three fe t lower than A.

If the station-points of the level are above the line of fight, as in fig. 2. and the diftance from A to C be fix feet, and from B to D nine feet, the difference will ftill be three feet which B is higher than A.

As an example of compound levelling, fuppofe it were required to know the difference of height between the point A on the river Zome, and N on the river Belann, fig. 3. (As our author could find no fatiffactory examples in any English author, he copied this and the following ones from M. le Febure). In this operation stakes should be driven down at A and N, exactly level with the furface of the water; and thefe ftakes fhould be fo fixed, that they may not be changed until the whole operation be finished: a plan of the ground between the two rivers fhould then be made, by which it will be difcovered, that the fhorteft way between the rivers is by the dotted line AC, CH, HN; from whence alfo the number of ftations neceffary to be taken will be determined. The operator will also be enabled to diftribute them properly according to the nature and fituation of the ground. In the figure 12. ftations are marked. Stakes ought then to be driven in at the limits of each station, as A, B,C,D, &c. They ought to be about two or three inches above the ground, and driven 18 inches into it. Stakes fhould also be driven in at cach station of the inftrument, as 1, 2, 3, 4, &c.

The operation may be begun in the following man. Levelling. ner. Let the first ftation be at 1, equally distant from the two points A and B, which themselves are distant 166 yards. Write down then in one column the first limit A; in another, the number of feet, inches, and tenths; with the points of fight indicated on the stationftaff at A, viz. 7. 6. o. In the third column, the fecond limit B; in the fourth, the height indicated at the ftation-ftaff B, viz. 6. o. o. Lastly, in the fifth co lumn, the distance from one ftation-ftaff to the other; which in this cafe is 166 yards. Remove now the level to the point marked 2, which is in the middle between B and C, the two places where the ftationftaves are to be held; obferving that B, which was the fecond limit in the former operation, is the firft in this. Then write down the obferved heights as before; in the first column B; in the fecond 4. 6. o; in the third C; in the fourth 5. 6. 2; in the fifth 560, the diftance between B and C.

It being impoffible, on account of the inequality of the ground at the third station, to place the inftrument in the middle between the two ftation-ftaves, find the moft convenient point as at 3; then measure exactly how far this is from each ftation-ftaff, and you will find that from 3 to C is 160 yards; from 3 to D, 80 yards; and the remainder of the operation will be as in the preceding flation.

In the fourth operation, we muft endeavour to compenfate for any error which might have happened in the laft. Mark out, therefore, 80 yards from the flation-staff D to the point 4; and 160 yards from 4 to E; and this must be carefully attended to, as by fuch compenfations the work may be much facilitated. Proceed in the fame manner with the eight remaining ftations, obferving to enter every thing in its proper column; and when the whole is finished, add the fums of each column together, and then subtract the leffer from the greater; the difference, which in the present cafe is 5. 4. 8. fhows the ground at N to be thus much lower than the ground at A.

To obtain a fection of this level, draw the dotted line o, fig. 4. either above or below the plan; which may be taken for the level or horizontal line. Let fall then perpendiculars upon this line from all the stationpoints and places where the station-staves were fixed. Beginning now at A, fet off 7 feet 6 inches upon the line from A to a: for the height of the level-point determined on the staff at this place, draw a line through a parallel to the dotted line ao, which will cut the third perpendicular at b, the second station-staff. Set off from this point downwards fix feet to B, which shows the fecond limit of the firft operation; and that the ground at B is one foot fix inches higher than at A: place your inftrument between these two lines at the height of the level line, and trace the ground according to its different heights. Now fet off, on the second stationftaff B, four feet fix inches to C, the height determined by the level at the fecond station; and from C draw a line parallel to 00, which will cut the fifth perpendicular at d, the third station-staff. From this point fet off 5 feet 6 inches downwards to C, which will be our fecond limit with refpect to the preceding one and the third with respect to the firft. Then draw your inftrument in the middle between B and C, and delineate the ground with its inequalities. Pro

ceed