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Level. cale truly level. In this facile mode of adjustment against it precisely while the telescope is turned round Levelling.

confifts the new improvement of the instrument; and on its Ys, it proves, as before mentioned, that the axis
it is hereby capable of being adjusted by only one fta- of the telescope coincides with the intersection of the
tion and one object, which will at the same time de- wires, and that the instrument will give the true level
termine it to be in a true level. If by change of wea- direction.
ther, accident, or otherwise, the instrument should have The operation of levelling being of a very accurate
loft its level adjustment or state, it may thus be readily and important nature, and the best instrument when
restored and readjusted at the first station; which is an out of its adjustment being of little use, it is quite ne-
advantage none of the instruments formerly made have cessary that every person using such an instrument
been capable of. The two supporters DĖ, on which should have it readily in his power to correct it; and
the level rests and turns, are Maped like the letter Y. the one above described appears to be the best adapted
The telescope rests within the upper part of them; and for that purpose of any hitherto contrived.
the inner sides of each of these Ys are tangents to the LEVELLING may be defined, the art which in-
cylindric tube of the telescope, which is turned to a structs us in finding how much higher or lower any
true cylinder, and each touches it but at one place given point on the lurface of the earth is than another;

or, in other words, the difference in their distance from
The lower end of these supporters are inserted into the centre of the earth.
a strong brass plate (FE), and so as to stand perpen- The practice of levelling therefore confifts, 1. In
dicularly on it. One is kept fast by a tightening screw finding and marking two or more points that shall be
G, and to the other is applied a fine threaded screw in the circumference of a circle whose centre is that of
H, to adjust the tube when on its supporters to a true the earth. 2. In comparing the points thus found
level. To the supporter D is sometimes applied a with other points, to ascertain the difference in their
line of tangents as far as 12 degrees, in order to take distances from the earth’s centre.
an angle of depression or elevation to that extent. Be- With regard to the theory of levelling, we must ob-

the supporters is also sometimes fixed a compass- serve, that a plumb-line, hanging freely in the air,
box I, divided into 360 degrees, and again into four points directly towards the centre of the earth; and a
90°; having a centre pin and needle, and trigger, at d, line drawn at right angles, croffing the direction of
to throw off the needle from the centre when not used; the plumb-line, and touching the earth's surface, is a
so in this manner it constitutes a perfect circumferen- true level only in that particular spot; but if this line
ter, connected with all the foregoing improvements. which crosses the plumb be continued for any confi-
This plate is fixed on a conical brass ferrel K, which derable length, it will rise above the earth's surface,
is adapted to the bell-metal frustum of a cone at top and the apparent level will be above the true one, be«
of the brass head of the staves, having a ball and sock- cause the earth is globular; and this rising will be as
et, with three bell-metal joints, two strong brass pa- the square of the distance to which the said right linc
rallel plates LL, the four screws eeee for adjusting the is produced ; that is to say, however much it is raised
horizontal motion, a regulating screw M to this mo- above the earth's surface at one mile's distance, it will
tion, and a fastening screw N to lighten it on the cone rise four times as much at the distance of two miles,
when necessary. The fastening screw N, and the regu- nine times at the distance of three, &c. This is owing
lating screw M, by which the whole inftrument is to the globular figure of the earth; and this rising is
moved with accuracy through a small space in an the difference betwixt the true and apparent levels ;
horizontal direction, was an addition of Mr Rams- the real curve of the earth being the true level, and

the tangent to it the apparent level. Hence it ap-
The manner of adjusting the spirit-level at the fir Pation. pears, that the less distance we take betwixt any two
The whole level being now placed steadily on its staves, itations, the truer will be our operations in levelling ;
it must be rendered parallel to the axis of the telescope and so soon does the difference betwixt the true and
before you adjust the horizontal motion. To this end apparent levels become perceptible, that it is necessary
the telescope must be placed in a line with two of the to make an allowance for it if the distance betwixt
fcrews ce, and then levelled thereby till the bubble of the two stations exceeds two chuins in length. The
air in the spirit-tube keeps its position in the middle, following is an infallible rule for determining the al-
while turned about to three points, making nearly lowance to be made :
right angles at the centre to one another.

Multiply the number of Gunter's decimal statute Leacb's lice The horizontal motion being thus adjusted, the rims chains that are contained in length between any two land naviff of the Ys are to be opened, the telescope taken off stations where the levels are to be taken by itself, and patien. and laid the contrary way upon the supporters. If the the product arising therefrom again by 124; which is bubble of air then rests exactly the same, the level and a common multiplier for all manner of distances for telescope are adjusted rightly to one another ; but if this purpose on-account of the earth's curvature: then the bubble does not remain the same, the end to which divide the second product arising therefrom by 100,000; the air bubble goes must be noticed, and the distance or, which is also the fame, with the dash of the per of it from the telescope altered; correcting one half cut off five figures on the right hand side of the prothe error by the screws cc, and the other half by the duct, and what remains on the left side is inches, and screws ee.

the five figures cut off decimal parts of an inch.”
Now the intersection of the wires being directed
to any diftant object, it may be one of the vanes of
the staves hereafter described : if they continue to be
Vol. X. Part I.













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Levelling. The following is A Table of Curvature of the Earth

The operation may be begun in the following man. Levelling. and shows the quantity below the apparent level at

Let the first station be at 1, equally distant from
the end of every number of chains to 100.

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 station.
staff at A, viz. 7. 6. o. In the third column, the se-

cond limit B; in the fourth, the height indicated at
1 0.00125 140.2427 0.91

40 2.00

the station-Itaff B, viz. 6. O. O. Lastly, in the fifth co
20.005 15|0.28. 280.98 45 2.28 lumn, the distance from one station-staff to the other ;
30.01125) 160.32 29'1.05 50 3.12 which in this case is 166 yards. Remove now the le-
40.02 170.36 30'1.12 55: 3.781 vel to the point marked 2, which is in the middle be-
180.40 31.1.19 60 4.50 tween B and C, the two places where the station-

ftaves are to be held ; observing that B, which was the
60.04 1910.45 32 1.27

second limit in the former operation, is the first in this.
20 0.50:33:1.351 70 6.12 Then write down the observed heights as before ; in
8 0.08 210.55 34'1.44 75 7.03 the first column B; in the second 4. 6. O; in the third
22 0.60 35'1.53

80 8.00 C; in the fourth 5. 6. 2; in the fifth 560, the di-
230.67 36 1.62
85 9.03

stance between B and C.

It being impossible, on account of the inequality of II 0.15 24,0.72 37 1.711 90 10.12 the ground at the third station, to place the instrument 12 0.18 250.78 38,1.80' 95 11.28 in the middle between the two station-staves, find the

130.21 26'0.84 39 1.91 100 12.50 most convenient point as at 3; then measure exactly Levelling is either simple or compound. The for- how far this is from each ftation-staff, and you will mer is when the level points are determined from one

find that from 3 to C is 160 yards; from 3 to D, 80 ftation, whether the level be fixed at one of the points yards; and the remainder of the operation will be as or between them. Compound levelling is nothing more

in the preceding station.
than a repetition of many simple operations.

In the fourth operation, we must endeavour to com-
An example of fimple levelling is given Plate pensate for any error which might have happened in
CCLXXI. fig. 1. where A B are the station points

the last. Mark out, therefore, 80 yards from the sta-
of the level ; C D the two points ascertained. Let tion-staff D to the point 4; and 160 yards from

4 the height

E; and this must be carefully attended to, as by fuch

Feet. Inches. compensations the work may be much facilitated. Pro-
From A to C be


ceed in the same manner with the eight remaining staFrom B to D be


tions, observing to enter every thing in its proper co

lumn; and when the whole is finished, add the sums of The difference


each column together, and then subtract the lesser from
shows that B is three fe t lower than A.

the greater ; the difference, which in the present case is
If the station-points of the level are above the line 5. 4. 8. shows the ground at N to be thus much low-
of fight, as in fig. 2. and the distance from A to C be er than the ground at A.
fix feet, and from B to D nine feet, the difference will To obtain a section of this level, draw the dotted
ftill be three feet which B is higher than A.

line on, fig. 4. either above or below the plan ; which
As an example of compound levelling, suppose it may be taken for the level or horizontal line. Let fall
were required to know the difference of height be- then perpendiculars upon this line from all the station-
tween the point A on the river Zome, and N on the points and places where the station-staves were fixed.
river Belunn, fig. 3. (As our author could find no fatif- Beginning now at A, set off 7 feet 6 inches upon the

factory examples in any English author, he copied line from A to a : for the height of the level-point de-
this and the following ones from M. le Febure). In termined on the staff at this place, draw a line through
this operation stakes should be driven down at A and a parallel to the dotted line 00, which will cut the third
N, exactly level with the surface of the water ; and perpendicular at b, the second station-staff. Set off from
these stakes should be so fixed, that they may not be this point downwards fix feet to B, which shows the se-
thanged until the whole operation be finished : a plan cond limit of the firft operation ; and that the ground
of the ground between the two rivers should then be at B is one foot fix inches higher than at A: place
made, by which it will be discovered, that the short- your instrument between these two lines at the height
eft way between the rivers is by the dotted line AC, of the level line, and trace the ground according to its
CH, HN; from whence also the number of stations different heights. Now set off, on the second station-
necessary to be taken will be determined. The ope- ftaff B, four feet fix inches to C, the height deter-
rator will also be enabled to distribute them properly mined by the level at the second ftation ; and from C
according to the nature and situation of the ground. draw a line parallel to 00, which will cut the fifth per-
In the figure 12. stations are marked. Stakes ought pendicular at d, the third station-staff. From this point
then to be driven in at the limits of each ftation, as A, set off 5 feet 6 inches jo downwards to C, which will

B,C,D, &c. They ought to be about two or three be our second limit with respect to the preceding one
inches above the ground, and driven 18 inches into it. and the third with respect to the first. Then draw
Stakes should also be driven in at each itation of the your instrument in the middle between B and C,
inftrument, as 1, 2, 3, 4, &c.

and delineate the ground with its inequalities. Pro


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feet i. A 21

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E 16 3 3591


F 10

OH 19
OK 47

H 5

Levelling. ceed in the same manner from flation to station, till work ; by which it is easy to form a just estimation of Levelling,

you arrive at the last N, and you will have the profile the land to be dug away, in order to form the canal,
of the ground over which the level was taken. by adding the depth to be given to it.

This method answers very well where only a gene- Fig: 6. gives an example of compound levelling,
ral profile of the different stations is required, but where the situation is so steep and mountainous, that the
where it is necessary to have an exact detail of the staves cannot be placed at equal distances from the in-
ground between the limits, we must then go to work strument, or where it is even impossible to make a re-
more particularly. Suppose, therefore, the level to ciprocal levelling from one station to the other. Thus
have been taken from A to N by another route, but suppose the point K to be the bottom of a bason where
on more uniform ground, in order to form a canal it is required to make a fountain, the reservoir being
marked O, P, Q, R, S, T, U, X, Y. Draw at plea- at A ; so that, in order to know the height to which
sure a line 2, Y, fig. 5. to represent the level, and re- the jet d'eau will rise, it is necessary to know how high
gulate the rest; then let fall on this line perpendicu- the point A is above K.
lars to represent the staves at the limits of each station, In great heights such as this, it will be necessary to
taking care that they be fixed accurately at their re- proceed by small descents, as from A to D. The initru-
spective distances from each other. The difference be- ment must be adjusted with all poffible care ; and it
tween the extreme limits, in this case, ought to be the will even be proper, in some part of the work, to use
same as in the former, viz. 5 feet 4 inches . Set off a smaller instrument.

instrument. The following is a table of the
this measure upon the perpendicular o the first limit; and different operations used in making this level, it having
from 0, prolonging the perpendicular, mark off at a been taken from M. le Febure's practice.
the height determined at the first station-staff; then

fect. 10.;yards.
do the same with the second and third, and so on with


9 901 the following, till this part of the work is finished;


3 40 there remains then only to delineate in detail the ground


3 9 between the station-staves, the diftances in this example


5 17 9 250 being assumed larger on account of the detail.



To obtain the section of the ground between 0 and


0 300
P, place your inftrument at one of the limits, as P,

3 1000
fixing it fo that the cross hairs may answer to the point
C; then look towards the first limit 0, raising or de-

95 o 106 9240;

pressing the vane till it coincides with the intersection
of the cross hairs ; and the line of sight from one point In this case only two levellings are made between
to the other will mark the level or horizontal line. A and D, though more would have been necefTary;

To set off the height of the brink of the river above but they are omitted to avoid confufion. In the
the first limit, drive a stake down close to the ground fourth station the height found was 16 feet 8 inches;
at a; and place your station-staff upon it, observing where but on account of the great length, it was requisite to
the hairs intersect the vane, which will be at


reduce the apparent level to the true one, which is alinches; then, laying off upon the line oz the distance ways necessary where the length is considerable. At the from the first to the last stake, let fall from thence a last limit we get the height from N to o; then from o to perpendiculas, and set off thereon 4. 10. O to a, which I; from I to K, fig. 7. &c.; all which added together, gives the height at the first stake ; or, which is the and then corrected for the curvature, gives 47 feet

3 same, the height from the edge of the river above the inches. Now, by adding each column together, and surface of the water, as is evident from the section. subtracting one from the other, we have 51 feet

9 Drive a second stake at 6, in a line between the limits; inches for the height which the point A is above the place the itation-staff upon this stake, and observe the bottom of the bafon, and which will cause the jet height 4. 6. interfected by the cross hairs, the instru- d'eau to rise about 45 feet. The general section of ment still remaining in the same situation.

Set off on this operation is shown at fig. 7, 8. but an exact profile the level-line the distance from the first stake a to the of the mountain is more difficult, as requiring many second b; and then let fall a perpendicular, and mark operations ; though some of these might be obtained upon it 4.6 to b, which gives the height of the ground by measuring from the level line without moving the at this place.

instrument. The small hollow c is marked out by driving down The latt example given by our author is likewise a third stake even with the ground, in the middle of it from M. le Febure, and includes a length of near five at c; but the exact distance of the second stake b from German miles (25 of ours) in a straight line, and 9 or the third must be marked upon the level line : then 10 (45 or 50 English) including the tụrnings and let fall a perpendicular from c, and set off upon it windings. In this the declivity of the river Faynox 6. 8. 9, pointed out by the cross hairs on the staff, was measured from Lignebruk to Villebourg. The which determines the depth of the hollow, as appears first operation was to drive stakes at several parts of from the figure. As the distances between the stakes the river even with the water's edge; the first of are now very short, they can eatily be marked by the which a little above the mills of Lignebruk showed operator, who can settle any little inequalities by a the upper water-mark, and another showed the lower comparison with those already ascertained. Proceed water-mark at the same mills. Two stakes above and thus with the other stations till you arrive at the laft, below the mills of Mazurance, somewhat more than and you will always obtain an accurate section of your half way between Lignebruk and Villebourg, pointed

B 2


feet 10

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