QUA 
declination, be of contrary names, (that is, 
if the sun, or star, comes to the meridian in 
the north, and has south declination, or per 
contra), the zenith-distance, added to the 
declination, gives the latitude of the place 
of observation; the designation will be 
north, or south, according as the declina- 
tion may be. 
g. When the zenith-distance, and the de- 
clination, are of the same name, that is, 
when the sun, or star, comes to the meri- 
dian in the north, and has north declination ; 
or, per contra ; then subtract the lesser 
from the greater ; and the remainder is the 
latitude. 
This general rule decides whether it be 
north or south. When the declination is 
greater than the zenith distance, the latitude 
is of the same name with the declination ; 
but if less, the latitude is on the opposite 
side of the equator. For further particu- 
lars, see Latitude. 
Quadrant of altitude, is a thin piece of 
metal, in general applied to the globe, and 
masked with the degrees, from 0 to 90“ : 
when laid upon the meridian of anyplace, 
it shows its latitude, or distance from the 
equator. 
Quadrant of a circle, or the fourth 
part of its circumference, is contained un- 
der two radii standing at right angles. The 
quadrant contains ninety degrees, and is 
the parent of various lines of the greatest 
utility in many branches of the mathema- 
tics, such as the lines of chords, of sines, of 
latitude, &c. See Mathematical histru- 
inents, and Dialling. 
Quadrants, gunner's, are made in va- 
rious manners, some of them having levels ; 
but the most simple construction, with 
Which we are acquainted, is that made 
with a staff about a foot in length, having 
on one side a quadrant, which, by means of 
a pendulum of metal, shows the exact an- 
gle made by the chase, or bore. The staff 
being put into the muzzle of a mortar, or 
howitzer, so as to lay, in contact, evenly 
with its lower side, and the quadrant part 
being turned down, immediately beyond 
the muzzle, the pendulum- wire, which is 
fixed to a small pivot in the right angle, ex- 
actly at the centre, whence the quadrant 
was described, will be kept perpendicular 
by the weight attached thereto ; and will 
thus indicate the exact elevation of the 
piece. The point of oscillation, i. e. the 
pivot, must, however, be always kept 
very smooth ; that there may not be the 
QUA 
least roughness ; else the action would be 
affected, and the index prove erroneous. 
QUADRAT, a mathematical instrument, 
called also a geometrical square, and line 
of shadows ; it is frequently an additional 
member on the face of thq common quad- 
rant, as also on those of Gunter’s and Sut- 
ton’s quadrant; but we shall describe it by 
itself, as being a distinct instrument. 
It is made of any solid matter, as brass, 
wood, &c. or of any four plain rules joined 
together at right angles, as represented in 
Plate XIII. Miscell. fig. 2, where A is the 
centre, from which hangs a thread with a 
small weight at the end, serving as a plum- 
met. Each of the sides, B E and D E, is 
divided into an hundred equal parts ; or, if 
the sides be long enough to admit of it, into 
a thousand parts ; C and F are two sights, 
fixed on the side A D. There is, moreover, 
an index, G H, which, when there is occa- 
sion, is joined to the centre. A, in such a man- 
ner as that it can move freely round, and 
remain in any given situation ; on tliis in- 
stfument are two sights, K L, perpendicu- 
lar to the right line going from the centre of 
the instrument. The side D E is called 
the upright side, or the line of the direct or 
upright shadows ; and the side B E is 
termed the reclining side, or the line of the 
versed or back shadows. 
To measure an accessible height, A B, 
(fig. 3) by the quadrat, let the distance, B D, 
be measured, which suppose = 96 feet, and 
let the height of the observer’s eye be 6 
feet; then holding the instrument with a 
steady hand, or rather resting it on a sup- 
port, let it be directed towards the summit 
A, so that it may be seen clearly through 
both sights ; the perpendicular, or plum-line, 
mean while hanging free, and touching the 
surface of the instrument : let novv the per- 
pendicular be supposed to cut off on the up- 
per side, K N, 80 equal parts ; it is evident, 
that L K. N, A C K, are similar triangles, 
and (by prop. 4. lib. 6. of Euclid) N K : 
R L : : K C (i. e. B D) : C A ; that is, 
80 rlOO : ; 96 : C A : therefore, by the rule 
of three, C A = = 120 feet ; and 
oU 
C B = 6 feet being added, the whole 
height B A is 126 feet. 
If the observer’s distance, as D E, be 
such, that, when the instrument is directed 
as formerly towards the summit A, the per- 
pendicular fall on the angle P, and the dis- 
tance, B E or C G, be 120 feet, C A will 
also be 120 feet : for P G : G H : : G C : 
