L E V. 
L E V 
;-yards to another, when they had occasion to 
continue the work to some considerable ex- 
tent. 
This table will answer several useful pur- 
poses. dims, first, to find the height ot the 
apparent level above the tru i, at any distance. 
If the given distance is in the table, the cor- 
[ rection of level is found on the same line 
; with it: thus at the distance of 1000 yards, 
the correction is 2 57, or two inches and a 
half nearlv ; and at the distance of 1 0 miles, 
it is 66 feet 4 inches. Rut if the exact dis- 
[■ tance is not found in the table, then multiply 
the square of the distance in yards by 2\>7, 
| and divide by 1,000,000, or cut off six places 
i on the right tor decimals ; the rest are inches : 
[ or multiply the sejuare-of the distance in miles 
bv 66 feet 4 inches, and divide by 100. 
2diy, To find the extent of the visible ho- 
rizon, or how far can be seen from any given 
l height, on a horizontal plane, as at sea, &c. 
I Suppose the eye of an observer, on the top 
: of a slfip’s mast at sea, is at the height of 130 
i feet above the water, he will then see about 
14 miles all around. Or from the top of a 
cliff by the sea-side, the height of which is 66 
'I l'ect, a person may see to the distance of near 
10 miles on the surface of the sea. Also, 
when the top of a hill, or the light in a light- 
■ house, or such like, whose height is 130 feet, 
| first comes into the view of an eye on board 
1 a ship, the table shews that the distance of 
I the ship from it is 14 miles, if the eye is at 
! t'ae surface of tiie water; but if the height of 
the eye in the ship is 80 feet, then the dis- 
ij tance will be increased by near 1 1 miles, 
making in all about 25 miles distance. 
3d!y, Suppose a spring to be on one side 
I of a h'i:l, and a house on an opposite hill, with 
I a valley between them, and that the spring 
I seen from the house appears by a levelling 
I instrument to be on a level with the fourida- 
i ti :n of the house, which suppose is at a mile 
j distance from it; then is the spring eight 
j inches above the true level of the house ; and 
i tyis difference would be barely sufficient for 
I the water to be brought in pipes from the 
i spring to the house, the pipes being laid all 
the way in the ground. 
4th; If the height or distance exceed the 
limits of the table, then, first, if the distance 
be given, divide it by 2, or by 3, or by 4, 
i &c. till the quotient come within the dis- 
tances in the table ; then take out the height 
answering to the quotient, and multiply it by 
the square of the divisor, that is, by 4, or. 9, 
j or id, &c. for the height required: .so if the 
top of a hill is just seen at the distance of 40 
miles, then 40 divided by 4 gives 10, to 
which in tiie table answer 66§- feet, which 
being multiplied by 16, the square of 4, gives 
1 06 1 y feet for the height of the hill. But 
when the height is given, divide it by one of 
these square numbers 4, 9, 16, 25, &c. till 
the quotient come within the limits of the 
table, and multiply the quotient by the 
square root of the divisor, that is bv 2, or 3, 
or 4, or 5, &c. for the distance sought: so 
when the top of the peak of Tenerilife, said 
to be almost 3 miles, or 15840 feet high, just 
c oines into view at sea, divide 15840 by 225, 
or the square of 15, and the quotient is 70 
nearlv; to which in the table answers by pro- 
portion nearly 102. miles; then multiplying 
102 . by 15, gives 154 miles and 2., for the 
distance of the hill. 
VOL. II. 
The operation of levelling is as follows : 
Suppose the height of the point A (Plate 
Miscel. fig. 153.) on the top of a mountain, 
above that ot B at the foot of it, is required. 
Place the level about the middle distance at 
D, and set up pickets, poles, or stall's at A 
and B, where persons must attend with sig- 
nals for raising and lowering, on the Said 
poles, little marks of pasteboard or other 
matter. r i lie level having been placed ho- 
rizontally by the bubble, &c. look towards 
the staff AT, and cause the person there to 
raise or lower the mark till it appears through 
the telescope or sights, &c. at K : then mea- 
sure exactly the perpendicular height of the 
point I'd above the point A, which suppose 
5 feet 8 inches, and set it down in your book. 
Then turn your view the other way towards 
the pole B, and cause the person there to 
raise or lower ins mark, till it appears in the 
visual line as before at C ; and measuring 
the height of C above B, which suppose 15 
feet 6 inches, set this down in vour book 
also, immediately above the number of the 
first observation. Then subtract the one 
from the other, and the remainder 9 feet 10 
inches will be the difference of level between 
A and B, or the height of the point A above 
the point B. 
If the point D, where the instrument is 
fixed, is exactly in the middle between the 
points A and B, there will be no necessity for 
reducing the apparent level to the true one, 
the visual ray on both sides being raised 
equally above the true level. But if not, 
each height must be corrected or reduced 
according to its distance, before the one cor- 
rected height is subtracted from the other. 
VY hen the distance is very considerable or 
irregular, so that the operation cannot be 
effected at once placing of the level, or when 
it is required to know if there is a sufficient 
descent for conveying water from the spring 
A to the point B (fig. 154.), this must be 
performed at several operations. Having 
chosen a proper place lor the first station, 
as at I, fix a pole at the point A near the 
spring, with a proper mark to slide up and 
down it, as L ; and measure the distance 
from A to I. Then the level being adjusted 
in the point T, let the mark L be raised or 
lowered till it is seen through the telescope or 
sights of the level, and measure the height 
AL. Then having fixed another pole at H, 
direct the level to it, and cause the mark G to 
be moved up or down till it appears through 
the instrument; then measure the height 
GH, and the distance from 1 to H, noting 
them down in the book. This done, remove 
the level forwards to some other eminence as 
E> from whence the pole H may be viewed, as 
also another pole at D ; then having adjusted 
the level in the point E, look back to the pole 
II; and managing the mark as before, the 
visual rav will give the point F; then mea- 
suring the distance HE and the height IIF, 
note them down in the book. Then, turning 
the level to look at the next pole D, the 
visual ray will give the point D ; there mea- 
sure the height of D, and the distance EB. 
entering them in the book as before. And 
thus proceed from one station to another till 
the whole is completed. 
But all these heights must be corrected or 
reduced by the foregoing table, according to 
their respective distances ; and the whole, 
both distances and heights, with their eorrec- 
1 
LEY 65 
lions, entered in the book in the following 
manner: 
Cors. 
inc. 
7 0 
2.2 
O] 
Cb 
CM 
CO 
d nt - 
O ci 
o 
A ^ h,o 
_ 
r-< 
K * - ~ 
CM 
A ch 
O 6 
O I 
1 • rr-A 'V 4 
q> 
% 2 ‘ 
CM I 
1 a <5 
i 
Having summed up all the columns, add 
those of the distances together, and the whole 
distance from A to B is 4755 yards, or two 
miles and three quarters nearly. Then the 
sums of the corrections taken from the sums 
of the apparent heights, leave the two cor- 
rected heights ; the one of which being taken 
from the other, leaves 5 feet 11*1 inches for 
the true difference of level sought between 
the two places A and B, which is at the rate- 
of an inch and a half nearly to every 100 
yards, a quantity more than sufficient to 
cause the water to run from the spring to the 
house. 
Or the operation may be otherwise per- 
formed, thus: Instead of placing the level 
between every two poles, and taking both 
back-sights and lore-sights, plant it first at 
the spring A, and from thence observe the 
level to the first pole; then remove it to this 
pole, and observe the second pole ; next 
move it to the second pole, and observe the 
third pole; and so on, from one pole to ano- 
ther, always taking foreward sights or obser- 
vations only. And then at the last, add all 
the corrected heights together, and the sura 
will be the whole difference of level sought. 
Levelling-staa^es, instruments used in 
levelling, serving to carry the marks to be 
observed, and at the same time to measure 
the heights of those marks from the ground. 
They usually consist each of two long wooden 
rulers, made to slide over one another, and 
divide into feet, inches, &c. 
LEVER. See Mechanics. 
LEVIGATION. See Pharmacy. 
LEVISANUS, a genus of the class and 
order pentandria monogynia. The flowers 
are aggregate ; corolla one-leafed, superior, 
five-cleft; filaments inserted into the base of 
the perianthium ; styles two, conjoined ; seeds 
live or six. There are five species, shrubs of 
the Cape. 
LEYDEN PIIIAL. See Electricity. 
LEYSERA, a genus of the polygamia 
superfiua order, in tiie syngenesia class of 
plants, and in the natural method* ranking 
under the 49th order, composite. The re- 
ceptacle is naked; the pappus paleaceous; 
