L O E 
toe 
L G G 79 
bolt of common locks, Mr. Stansburv uses a 
piece J, which has a spindle going through 
the plate ot the lock, and projecting from the 
door with a handle on it, by w hich its arm 
/can be moved up and down,' when the door 
is to be bolted ; this handle is turned so that 
the knob g on the arm/may fail in the notch 
cut in the bolt to receive it ; this prevents the 
bolt being moved back by the pusher, til! 
the arm J is first removed. ' The. e is a spring 
at the back of this arm, which pressing against 
the plate ol the lock, by its friction keeps it 
from falling by accident K is the main bolt 
of the lock ; it is kept steady by a rectangu- 
lar opening, through which a screw passes, 
'i he bolt is moved by a circular iron plate, 
moving round a pin It, which is riveted into 
a circular bridge N, screwed to the plate 
shewn separately in fig. 3; tins bridge has a 
circular opening i in it, through which a pin 
e, riveted to the plate L, moves; this pin 
takes into a notch m the bolt, so as to move 
it backwards and forwards, when the plate is 
turned round its centre. The locking part 
is performed thus: the wheel L has a. certain 
number of holes drilled in if, as at m ; the 
bridge has the same number of similar holes 
in ft, and in (he same position; each hole in 
the bridge has a small pin in it, which is 
pushed In by a slight spring n it n, fig. 3 ; 
when the holes in the plate coincide with the 
holes in the bridge, the springs it n a push up 
the pins through the plate, and lock them 
both together. The key, fig. 2, has the same 
number of pins projecting from its lower end, 
as the pin-holes iii the bridge, and in the 
same position ; the length of the pins is the 
same as the thickness of the plate L, fig. 4. 
When it is to be unlocked, the key is intro- 
duced, and as it is turned round, it is pushed 
gently forward against the . plate; when the 
pins and key come opposite the pin-holes 
and pins, the force applied overcomes the 
resistance of the springs n n n, the pins are. 
pushed out, and the key gets hold of the plate 
L, when being turned round, it draws the 
bolt back by the pin b, fig. 3. 
LOCUS geometricus, denotes a line 
by which a local or indeterminate problem is 
solved. 
A locus is a line, any point of which may 
equally solve an indeterminate problem. Thus, 
if a l ight line suffice for the construction of the 
equation, it is called locus ad rectum', it a circle, 
locus ad circulum ; if a parabola, locus ad parabolam ; 
if an ellipsis, locu ad ellipsin ; and so of the rest of 
the conic sections. The loci of such equations 
as are right lines, or circles, the ancients called 
plane loci ; and of those that are parabolas, hy- 
perbolas, Sec. solid loci Eut Wolfius, and others 
among- the moderns, divide the loci more com- 
modiously into orders, according to the number 
of dimensions to which the indeterminaie quan- 
tities rise. Thus, it will be a locus of the first 
order, if the equation is a- = — - ; a locus cf the 
C 
second or quadratic order, if y 2 — ax, or y 2 — 
a 1 — x 2 ', a locus of the third or cubic order, if 
— a 2 x, or y' — ax 2 — ,v J , Sec. 
All equations whose loci are of the first or- 
der, may be reduced to some one of the four 
following formulas r 1. y — — . 2.v = — -Lc. 
a a ' 
tv 
where the un- 
known quantity y, is supposed always to be freed 
from fractions, and the fraction that multiplies 
the other unknown quantity x, to be reduced 
to this expression — , and all the known terms 
a 
to c. 
All loci of (he second degree are conic sec- 
tions, viz. either the parabola, the circle, el- 
lipsis, or hyperbola : if an equation, the refbre, 
is given, whose locus is of the second degree, 
and it is required to draw the conic section 
which is the loeui thereof, first draw a para- 
bola, ellipsis, or hyperbola, yo as that the 
equation ; expressing the natures thereof may 
be as compound as possible, in order to ge*t 
general equations or formulas, by examining 
the peculiar properties whereof we may 
know which of these formulas the given 
equation ought to have regard to ; that is, 
which of the conic sections will be the locus 
of the proposed equation. This known, com- 
pare all the terms of the proposed equation 
with the terms of the general formula of that 
conic section, which you have found will be 
the locus of the given equation; by which 
means you will find howto draw the section 
which is the locus of the equation giveh. 
Is an equation, whose locus is a conic sec- 
tion, is given, and the particular section 
-whereof it is the locus is required ; all the 
terms of the given equation being brought 
over to one side, so that the other is equal to 
nothing, there will be two cases. 
Case f. 'W hen the rectangle x 1/ is not in 
the given equation. 1. If either )/// or xx 
is isi the same equation, the locus will be a 
parabola. 2. If both x x and ijy are in the 
equation with the same signs, the locus will 
be an ellipsis or a circle. 3. If x x and yy 
have different signs, the locus will be an hy- 
perbola, or the opposite sections regarding 
their diameters. 
Case II. When the rectangle x y is in the 
given equation. 1. If neither of the squares 
xx or yy, or only one of them, is in the 
same, the locus ot it will be an hyperbola 
between the asymptotes. 2. If y y and x x 
is therein, having different signs, 'the locus 
will be an hyperbola regarding its diameters. 
3. If both the squares x x and yy are in the 
equation, having the same signs, you must 
free the square yy from fractious ; and then 
the locus will be an Hyperbola, when the 
square of % the fraction multiplying xy, is 
equal to the fraction multiplying x x ; an el- 
lipsis, or circle, when the same is less ; and 
an hyperbola, or the opposite sections, re- 
garding their diameters, when greater. 
LOCUST. See Gryllus. 
LODGMENT, in military affairs, is a 
work raised with earth, gabions, fascines, 
woolpacks, or mantelets, to cover the be- 
siegers from the enemy’s fire, and to prevent 
their losing a place which they have gained, 
and are resolved, if possible, to keep. For 
this purpose, when a lodgment is to be made 
on the glacis, covered way, or in the breach, 
there must be great provision made of fas- 
cine-, sand-bags, &c. in the trenches; and 
during the action, the pioneers with fascines, 
sand-bags, &c. should be making tire iodg- 
ment, in order to form a covering in as ad- 
vantageous a manner as possible from the 
opposite bastion, or the place moot to be 
feared. 
LOEFLINGIA, a genus of the class and 
order triandria monogynia. The calvx is 
live-leaved ; corolla live-pet ailed ; capsule 
one-celled, three-valved. There is one spe- 
cies, an annual of Spain. 
LGESELIA, a genus of the didynamia 
angiospermia class of plants, the flower of 
which is monopetalous and qurnquelxl at the 
limb; the fruit is a tiilocular capsule, with se- 
veral angulated seeds in each cell., I here is 
one species, a herb of South America. 
LOG, in naval affairs, is a flat piece of 
wood, shaped somewhat like a flounder, with 
a piece of lead fastened to its bottom, which 
makes it stand or swim upright in the water. 
To this log is fastened a long line, called the 
log-line; and this is commonly divided into 
certain spaces 30 feet in length by knots, 
which are pieces of knotted twine inreeved 
between the strands of the line; which shew, 
by means of a half-minute glass, how many 
ot these spaces or knots are run out in half a 
minute. ] hey commonly begin to be count- 
ed at the distance of about 10 fathoms or do 
feet from the log; so that the log, when it is 
hoven overboard, may be out of the eddy of 
the ship’s wake before they begin to count : 
and for the ready discovery of this point of 
commencement, there isjcommonly fastened 
at it a red rag. 
The log being thus prepared, and hoven 
overboard from the poop, and the line veered 
out by the help of a reel, as fast as the ship 
sails from it, will shew how far the ship has 
run in a given time, and consequently her 
rate of sailing. 
Hence it is evident, that as the distance of 
the knots bears the same proportion to a mile 
as halt a minute does to an hour, whatever 
number of knots the ship runs in half a mi- 
nut'e, the same number of miles she will run 
in an hour, supposing her to run with the 
same degree of velocity during that time; 
and therefore, in order to know her rate of 
sailing, it is the general way to heave the leg 
every hour; but if the force or direction of 
the vine! varies, and does not continue the 
same during the whole hour, or if there has 
been more sail set, or any sail handed in, by 
which the ship has sailed faster or slower than 
she did at the time of heaving the log, there 
must then be an allowance made for it ac- 
cordingly. 
Lfec-EOARD, a table generally divided 
into five columns, in the first of which is en- 
tered the hour of the day ; in the second the 
course steered ; in the third, the number of 
knots run oil the reel each time of heaving 
the log; in the fourth, from what point the 
wind blows; and in the fifth, observations on 
the weather, variation of the compass, See. 
Log-book, a book ruled in columns like 
the log-board, into which the account 011 the 
log-board is transcribed every day at noon ; 
whence, after it is corrected, Sec. it is entered 
into the journal. See Navigation. 
Log-wood, in commerces See FIjema- 
toxylum. v 
Logwood is used by dyers for dying blacks 
and blues. 
LOGARITHMIC, in general, something 
be’ inging to logarithms. See Logarithms. 
Logarithmic curve. < If on the line 
AN (Plate Miscek, tig. 155.) both ways in- 
definitely extended, be taken, AC, €E,‘ EG, 
GI, IL, on tile- right hand, and A g, g- P, 
Sec. on the left, all equal to one another, 
and if at the points P, g, A. C, E, G, 1. I,, 
be erected to the right hue AN, the perpen- 
dkuiau PS, AB, CD, EF, Gii, IK, 
