534 
QUA 
QUA 
QUA 
Q 
or q, the sixteenth letter of our alpha- 
^5 bet. As a numeral it stands for 500 ; and 
with a dash over it, thus Q^ for 500000. Used 
as an abbreviature, q signifies quantity, or 
quantum : thus, among physicians, q. pi. is 
quantum placet, i. e. as much as you please 
of a thing ; and q. s. quantum sufficit, i. e. as 
much as is necessary. Q. E. D. among ma- 
thematicians, is quod erat demonstrandum, 
e. which was to be demonstrated ; and Q. 
E. F. quod erat faciendum, i. e. which was to 
be done. Q. D. among grammarians, is 
quasi dictum, i. c. as if it was said, or, as who 
should say. In the notes of the antients, Q 
stands for Quintus, orQuintius; Q. B. V. for 
quod bene vertat; Q. S. S. S. for quae supra 
scripta sunt; Q. M. for Quintus Mutius, or 
quomodo; Quint, for Quintilius ; and Quaes, 
for quaestor. 
QUADRANGLE, in geometry, the same 
with a quadrilateral figure, or one consisting 
of four sides and four angles. 
QUADRANS, the quarter or fourth part 
of any thing, particularly the as, or pound. 
QUADRANT, in geometry, is either the 
quarter or fourth part of a circle, or the fourth 
part of its circumference; the arch of which 
therefore contains 90 degrees. 
Quadrant also denotes a mathematical 
instrument, of great use in astronomy and 
navigation, for taking the altitudes of the sun 
and stars, as also taking angles in surveying, 
heights and distances, ike. 
This instrument is variously contrived, and 
furnished with different apparatus, according 
to the various uses it is intended for; but they 
have all this in common, that they consist' of 
the quarter of a circle, whose limb or arch is 
divided into 90°, &c. Some have a plummet 
suspended from the centre, and are furnished 
either with plain sights, or a telescope to look 
through. 
The principal and most useful quadrants 
are as follows : 
Quadrant, the common, or surveying. 
1 his instrument ABC, fig. 1. Plate Quadrants, 
is made of brass, or wood, &c. : the limb or 
arch of which BC is divided into 90°, and 
each of these is farther divided into as many 
equal parts as the space will allow, either dia- 
gonally or otherwise. To one of the radii 
AC, are fitted two moveable sights; and to 
the centre is sometimes also annexed a label, 
or moveable index, AD, bearing two other 
sights ; but instead of these last sights, there is 
sometimes fitted a telescope. Also from the- 
centre hangs a thread with a plummet ; and 
on the under side or face of the instrument 
are fitted a ball and socket, by means of which 
it may be put into any position. The general 
use of it is for taking angles in a vertical plane, 
comprehended under right lines going from 
the centre of the instrument, one of which 
is horizontal, and the other is directed to 
some visible point. But besides the parts 
above described, there is often added on the 
face, near the centre, a kind of compartment 
EF, called a quadrat, or geometrical square, 
which is a kind of separate instrument, and is 
particularly useful in altimetry and longi- 
metry, or measuring heights and distances. 
This quadrant may be used in different 
situations ; in each of them, the plane of the 
instrument must be set parallel to that of the 
eye and the objects whose angular distance is 
to be taken. Thus, for observing heights’ or 
depths, its plane must be disposed vertically, 
or perpendicular to the horizon ; but to talce 
horizontal angles or distances, its plane must 
be disposed parallel to the horizon. 
Again, heights and distances may be taken 
two ways, viz. by means of the' fixed sights 
and plummet, or by the label ; as also, either 
by the degrees on the limb, or lay the quadrat. 
1 hus, fig. 2 shews the manner of taking an 
angle of elevation with this quadrant ; the eye 
is applied at C, and the instrument turned 
vertically about the centre A, till the object 
R is seen through the sights on the radius 
AC ; then the angle of elevation RAH, made 
with the horizontal line KAH, is equal to the 
angle BAD, made by the plumb line and the 
other radius of the quadrant, and the quantity 
of it is shewn by the degrees in the arch BD 
cut off by the plumb line AD. 
Quadrant, astronomical. See Obser- 
vatory. 
Quadrant, Coles, is a very useful in- 
strument, invented by Mr. Beniamin Cole. 
It consists of six parts, viz. the stalf AB, fig. 3 ; 
the quadrantal arch DE; three vanes A, B, 
C ; and their vernier FG. The staff is a 
bar of wood about two feet long, an inch and 
a quarter broad, and of a sufficient thickness 
to prevent it from bending or warping. The 
quadrantal arch is also of wood, and is divided 
into degrees and third parts of degrees, to a 
radius of about nine inches; and to its ex- 
tremities are fitted two radii, which meet in 
the centre of the quadrant by a pin, about 
which it easily moves. The sight-vane A is a 
thin piece of brass, near two inches in height 
and one broad, set perpendicularly on the 
end of the staff A, by means of tw r o screws 
passing through its foot. In the middle of 
this vane is drilled a small hole, through which 
the coincidence or meeting of the horizon 
and solar spot is to be viewed. The horizontal 
vane B is about an inch broad, and two inches 
and a half high, having a slit cut through it 
of near an inch long, and a quarter of an inch 
broad ; this vane is fixed in the centre-pin of 
the instrument, in a perpendicular position, 
by means of two screws passing through its 
foot, by which its position with respect to the 
sight-vane is always the same, their angle of 
inclination being equal to 45 degrees. 'The 
shade- vane C is composed of twrn brass plates. 
The one which serves as an arm, is about 
4-§ inches long, and f of an inch broad ; being 
pinned at one end to the upper limb of the 
quadrant by a screw, about which it has a 
small motion ; the other end lies in the arch, 
and the lower edge of the arm is directed to 
the middle of the centre-pin. The other plate, 
which is properly the vane, is about two inches 
long, being fixed perpendicularly to the other 
plate, at about half an inch distance from that 
end next the arch ; this vane may be used 
either by its shade, or by the solar spot cast 
by a convex lens placed in it. And because 
the wood- work is often subject to warp or 
twist, therefore this vane may be rectified by 
means of a screw, so that t ire warping of the 
instrument may occasion no error in the ob- 
servation, which is performed in the following 
manner: set the line G on the vernier against 
a degree of the upper limb of the quadrant ; 
and turn the screw on the backside of the 
limb forward or backward, til! the hole in the 
sight-vane, the centre of the glass, and the 
sunk spot in the horizon-vane, lie in a right 
line. 
To find the sun's altitude by this instrument. 
Turn your back to the sun, holding the staff 
of the instrument with the right hand, so that 
it is in a vertical plane passing through the 
sun ; apply one eye to the sight-vane looking 
through that and the horizon-vane till the 
horizon is seen; with the left hand slide the 
quadrantal arch upwards, till the solar spot 
or shade, cast by the shade-vane, falls directly 
upon the spot or slit in the horizon-vane; 
then will that part of the quadrantal arch 
which is raised above G or S (according as 
the observation respects either the solar spot 
or shade), shew the altitude of the sun at that 
time. But for the meridian altitude, the ob- 
servation must be continued ; and as the sun 
approaches the meridian, the sea wi 11 appear 
through the horizon-vane, which completes 
the observation; and the degrees and minutes, 
counted as before, will give the sun’s me- 
ridian altitude; or the degrees counted from 
the lower limb upwards, will give the zenith 
distance. 
Quadrant, Collins’s or Sutton’s, fig. 4, 
is a stereographic projection of one quarter 
of the sphere between the tropics, upon the 
plane ot the ecliptic, the eye being in its north 
pole ; and fitted to the latitude of London. 
The lines running from right to left, are pa- 
rallels of altitude; and those crossing them 
are azimuths. The smaller of the two circles 
bounding the projection, is one quarter of the 
tropic of Capricorn ; and the greater is a 
! quarter of the tropic of Cancer. The two 
ecliptics are drawn from a point on the left 
edge of the quadrant, with the characters of 
the signs upon them ; and the two horizons 
are drawn from the same point. The limb is 
divided both into degrees and time; and by- 
having the sun’s altitude, the hour of the day 
may here be found to a minute. The qua- 
drantal arches next the centre contain the 
j calendar of months; and under them, in ano- 
; ther arch, is the sun’s declination. On the 
projection are placed several of the most re- 
markable fixed stars between the tropics ; and 
