64 
L E V 
L E V 
lowered by means of a mi! led-headed screw t 
K, which works through a collar in the lower 
end of the tube g ; the rest of the tube h.as a 
triangular hole through it, in which slides a 
bar k, which is part of the Y ; O the female 
screw is cut within this bar, and the screw 
works into it, so that by turning the milled 
head cr.e way, the Y is raised, and by re- 
versing the motion, it is lowered. The axis 
which connects the compass-box and the 
other apparatus, has a collar upon it just 
above where it enters the ball, fig. 5, which 
is embraced by a clamp P, fig. 6, w hicb is 
closed by a screw C, so as to hold the collar 
of the axis quite tight ; and when the screw is 
turned back, its own elasticity opens it so as 
to allow the axis of the compass-box to turn 
round freely within it; on the opposite side of 
the clamp is a projecting arm /, carrying the 
nut m of the screw Q, which screw works in a 
stud n, fixed to the upper plate G, tigs. 7 and 
6; by this means, when G is loosened, the 
telescope can be turned quite round, but 
when it is fastened, it can only be moved by 
turning the screw Q. The level-lube Z is 
fastened to the under side of the telescope 
by a screw q at one end and a bar r at the 
other : the use of these are to adjust it so 
that it shall be exactly parallel to the axis of 
the telescope-tube. The level, as best ex- 
plained in the section, tig. 1, is a tube of 
glass ss, nearly filled with spirits of wine, but 
so as to leave a bubble of air in it ; if the tube 
is of exactly the same diameter in every part, 
the bubble will rest in the middle of the tube 
when it is level. In some of the best levels 
made by Ramsden, the inside of the tube is 
bent into a segment of a circle, 100 feet dia- 
meter, and the inside is ground, which causes 
tiie bubble to adhere together; if the tube is 
straight, it is liable to divide into several 
small ones. The internal parts of the tele- 
scope are explained in fig. 1 : RR is the ex- 
ternal tube of brass plate; within this slides 
another tube ss ; ft has two glasses r, zv, 
screwed into the outer end, called object- 
glasses, and it lias two divisions x, y, called 
tbaphagram, with small holes in them ; their 
u is to collect the prismatic rays with 
which the objects would otherwise he tinged; 
the tube ss has a rack t fixed nearly in the 
middle of it, which takes into a pinion on 
the axis of the milled head T, figs. 1 and 7 ; 
by turning this, the glasses v, zv, can be 
moved nearly to, or farther from, the eye to 
adjust the focus ; to the tube R at v are 'fixed 
the cross wires, whose intersection is exactly 
in the centre of the tube. The manner of 
fixing these is explained in fig. 3: A is a 
brass box, which fits into the end of the tele- 
scope-tube, and is held there by four small 
screws; within this box is placed a brass 
plate B, carrying the wires, which are fasten- 
ed by screwing four screws down upon their 
ends; when the plate B is in the box, a ring 
D is screwed in upon it, which prevents its 
falling out, but at the same time leaves it at 
liberty to move about in the box; the sides 
of the box, and also the telescope-tube, lias 
four rectangular holes in it, through which 
four screws are passed into the edges of the 
piece B, so as to hold it in any position: 
these screws come through the external tube, 
and have square heads, to be turned by a 
key, so as to adjust the interactions in the 
-centre: the box A lias a female screw in the 
irout, into which is screwed the eye-piece 
L E V 
Vv r ; 3 is the tube which screwed to the te- 
lescope ; within this slides a tube, containing 
two glasses 4, 5 ; by sliding the glasses in or 
cut of the tube 3, they < an be ad; listed sd as 
to adapt their focus to the cross w ires. This 
eye-piece is convenient on account of its 
shortness; but as it reverses the objects, it is 
sometimes more convenient 1o use the eye- 
piece fig. 2, which is much longer, but does 
not reverse objects, a is the tube, which is 
screwed to the telescope; within this slides 
another tube bb, having at one end a tube 
(Id, containing two glasses cf, and a diap ha- 
gram g, and at the other end a tube hh, con- 
taining two glasses ik, and a diaphagram : 
vr is a cap screwed on to the end to prevent 
the tubes coming out. When the instrument 
is to be carried, the level is unscrewed from 
the legs and packed in a ca'se; the legs are 
shut up and kept so by the rings, as before 
described. The manner of using this instru- 
ment is as follows: When the difference of 
level between any two places is required, the 
observer with the level goes to the highest of 
the two, and his assistant goes to the lowest 
with the target, which is a long pole of wood 
with a groove in it, in which slides a small rod 
carrying a round piece # of wood, called a 
sight, which is to be observed through the 
telescope; the observer opens the legs of the 
instrument, and sets them on the ground; 
the level is next screwed to them at E, as 
shewn in fig. 7 ; the telescopeds then brought 
nearly to a level by the screws If 11I1H, as 
before described ; the screw c is then turned 
so as to release the clamp P, fig. 6 ; and the 
telescope is turned about, so as to point to 
the target; the clamp P is then closed, the 
observer looks through the telescope, and by 
turning the nut T, the focus is adjusted : the 
screw Q is then turned (ill the cross wires are 
brought to coincide with the object, in an 
horizontal plane; he then takes his eye from 
the telescope, and works the screw N till he 
brings the bubble of air in the level-tube ex- 
actly in the middle, which shews that the te- 
lescope is perfectly horizontal; the observer 
then makes signals to the assistant to raise or 
lower the sight on the slider of the target, till 
it is brought to coincide with the intersection 
of the cross wire, which shews that the tele-: 
scope and the sight of the target are on the 
same level ; the height which the sight is 
from the ground where the target stands, de- 
ducted from the height the telescope stands 
from the ground, is the difference of level 
required. 
LEVELLING, the art or act of finding a 
line parallel to the horizon at one or more 
stations, to determine the height or depth of 
one place with respect to another; for laving 
out grounds even, regulating descents, drain- 
ing morasses, conducting water, &c. 
Two or more places are on a true level 
when they are equally distant from the centre 
O! the earth. Also one place is higher than 
another, or out of level with it, when it is far- 
ther from the centre of the earth; and a line 
equally distant from that centre in all its 
points, is called the line of true level. Hence, 
because the earth is round, that line must be 
a curve, and make a part of the earth’s cir- 
cumference, or at least parallel to it, or con- 
centrical with it; as the line BCFG (Plate 
Misc. fig. 152), which has all its points equally 
distant from A, the centre of the earth, con- 
sidering it as a perfect globe. 
But the line of sight BDE, &c. given by 
the operations of levels, is a tangent, or a 
"S™ lniti perpendicular to tide scinidiaiTieter 
of the earth at the point of contact B, rising 
always higher above the true line of level” 
tnc farther the distance is, is called the appa- 
rent line of level. r llms, CD is the height 
of the apparent level above the true level 
at the distance BC or BD ; also EF is the 
excess of height at F, and GlJ at G, kc, 
1 he d.ffei ence, it is evident, is always equal 
to, the excess of the secant of the arch of dis- 
tance above the radius of the earth. 
The common methods of levelling are suf- 
ficient for laying pavements of walks, or for 
conveying water to small distances, &c. ; but 
in more extensive operations, as in levelling 
rhe bottoms of canals, which are to convey 
water to the distance of many miles, and such 
kke, the difference between 'the true and the 
apparent level must be taken into the ac- 
count. 
Now the difference CD between the true and 
apparent level, at any distance EC or bD, may 
be found thus : By a well-known property of 
the circle, 2AC -j- CD ; BD BD ; CD ; or 
because the diameter of the earth is" so great 
with respect to the line CD at all distances to 
whicn an operation of levelling commonly ex- 
tends, that SAC may be safely taken for SAC 
CD in that proportion without any sensible 
error, it will be SAC ; BD ; ; BD ; CD, which 
therefore is _ - -, or - nearly ; that is, the 
difference between the true and apparent level, 
is equal to the square of the distance between 
the places, divided by the diameter of the earth ; 
and consequently it is always proportional to 
the square of the distance. 
Now the diameter of the earth being nearly 
7958 miles ; if we first take BC = I mile, then 
.v »c 2 , 1 
the excess becomes of a mile, which 
is 7.962 inches, or almost 8 inches, for the height 
of the apparent above the true level at the dis- 
tance of one mile. Hence, proportioning the 
excesses in altitude according to the squares of 
the distances, the following Table is obtained, 
shewing the height of the apparent above the 
ti ue level for every 100 yards of distance on 
the one hand, and for every mile on the other. 
Dist. 
or BC. 
Dif. of Level, 
or CD. 
Dist. 
or BC. 
Dif. of Level, 
or CD. 
Yards. 
Inches. 
Miles. 
Feet. 
Inc. 
100 
0.026 
X 
0 
OF 
200 
0.103 
i 
0 
2 
800 
0.231 
0 
H 
400 
0.411 
1 
0 
8 
500 
0.643 
2 
2 
8 
600 
0.925 
3 
6 
0 
700 
1.260 
4 
10 
7 
800 
1.645 
5 
16 
7 
900 
2.081 
6 
23 
11 
1000 
2.570 
7 
32 
6 
1100 
3.110 
8 
42 
6 
1200 
3.701 
9 
53 
9 
1800 
4.344 
10 
66 
4 
1400 
5.038 
11 
80 
3 
1500 
5.784 
12 
95 
7 
1600 
6.580 
13 
112 
2 
1700 
7.425 
14 
130 
1 
By means of tables of reductions, we 
can now level to almost any distance at one 
operation, which the antients could not do 
but by a great multitude; tor, being unac- 
quainted with the correction answering to 
any distance, they only levelled from one 20 
