EQU 
e a u 
E a u 
643 
nations, or the expression denoting this equal- 
ity ; -which is done by setting the one in op- 
position to the other, with the sign of equality 
(~) between them : thus 3s.=36d., or 3 feet 
1 yard. Hence, if we put a for a foot, and b 
tor a yard, we will have the equation 3u=b, 
in algebraic characters. See Algebra. 
Equation of a curve, an equation ex- 
pressing the nature of a curve, the relation 
between an abciss and a corresponding ordi- 
nate, or -the relation of their fluxions. See 
-Curve. 
Equation of time, in astronomy and 
chronology, the reduction of the apparent 
time or motion of the sun, to equable, mean, 
or true time. See Astronomy. 
EQUATOR, iii geography, a great circle 
of the terrestrial globe, equidistant from its 
poles, and dividing it into two equal hemi- 
spheres; one north, and the other south. See 
Globes, use of. , 
EQUATORIAL, universal, or Porta- 
ble Observatory, is an instrument in- 
tended to answer a number of useful pur- 
poses in practical astronomy, independant of 
any particular observatory. It may be em- 
ployed in any steady room or place, and it 
performs most of the useful problems in the 
science of astronomy. See Observatory. 
EQUERRY, in the British customs, an 
oflicer of state under the master of the horse. 
There are live equerries, who ride abroad 
with his majesty; for which purpose they 
give their attendance monthly, one at a time, 
and are allowed a table. As to the equerries 
of the crown-stable, they have this distinct 
appellation, as being employed in mounting, 
managing, and Leaking, the saddle-horses 
for his majesty’s use, and holding his stirrup. 
EQU ES auratus, is used for a knight 
bachelor, called auratus, q. d. gilt, because 
antiently none but knights were allowed to 
beautify their armour, or other habiliments of 
war, with gold. This term is not used in law, 
but instead of it miles and chevalier are 
made use of. 
EQUESTRIAN statue, signifies the 
statue of a person mounted on horseback. 
Equestrian order, among the Romans, 
signified their knights or equites, as also 
their troopers or horsemen in the held; the 
first of which orders stood in contradistinction 
to the senators, as the last did to the foot, 
military, or infantry : each ot these distinc- 
tions was introduced into the state by Ro- 
mulus. 
EQUIANGULAR, in geometry, an epi- 
thet given to figures whose angles are all 
equal : such are a square, an equilateral tri- 
angle, &c. 
EQUIDIFFERENT numbers, in arith- 
metic, are of two kinds. 1. Continually equi- 
'different is when, in a series of three numbers, 
there is the same difference between the first 
and second, as there is between the second 
and third ; as 3, 6, 9- And 2. Discretely 
equidilTerent is when, in a series of four num- 
bers or quantities, tire re is the same difference 
between the first and second as there is be- 
tween the third and fourth. : such are 3, 6, 
7, 10. 
EQUIDISTANT, an appellation given to 
things placed at an equal distance from some 
fixed point, or place, to which they are re- 
ferred. 
^QU [LATERAL, in general, something 
thutffias eqaial sides, as an equilateral triangle. . 
Equilateral hyperbola, one whose 
transverse diameter is equal to its parameter ; 
and so all the other diameters, equal to their 
parameters ; in such an hyperbola, the asymp- 
totes always cut one another at right angles 
in the centre. Its most simple equation, with 
regard to the transverse axis, is y 1 —. r 2 — a 2 ; 
and, with regard to the conjugate, if=x 2 X a 2 , 
when* is the semitransverse, or semiconju- 
gate. The length of the curve cannot be 
found by means of the quadrature of any 
space, of which a conic section is any part ot 
the perimeter. 
EQUILIBRIUM, in mechanics, is when 
the two ends of a lever or balance hang so 
exactly even and level, as neither to as- 
cend nor descend, but keep in a position paral- 
lel to the horizon; which is occasioned by 
their being both charged with an equal weight. 
EQUIMULTIPLES, in arithmetic and 
geometry, are numbers or quantities multi- 
plied by one and the same number or quan- 
tity. llehce, equimultiples are always in the 
same ratio to each other, as the simple quan- 
tities before multiplication: thus if 6 and 8 
are multiplied by 4, the equimultiples 24 and 
33 will be to each other as 6 to S. 
EQUINOCTIAL, a great circle in the 
heavens under which the equator moves in its 
diurnal motion. The poles of this circle are 
the poles of the world. It divides the sphere 
into two equal parts, the northern and south- 
ern. It cuts the horizon of any place, in 
the east and west points ; and at the meridian 
its elevation above the horizon is equal to the 
co-latitude of the place. The equinoctial has 
also various other properties ; as, 
1. Whenever the sun comes to this circle, 
lie makes equal days and nights all round the 
globe; because he then rises due east, and 
sets due west. Hence it has the name equi- 
noctial. All stars which are under this circle, 
or have no declination, also rise due east, 
and set due west. 
2. All people living under this circle, or 
upon the equator or line, have their days 
and nights at all times equal to each other. 
3. From this circle, on the globe, are count- 
ed, upon the meridian, the declination in the 
heavens, and the latitude on the earth. 
4. Upon the equinoctial, or equator, is 
counted the longitude, making in all 360° 
quite round, or else 180° east and 180° west. 
5. And as the time of one whole revolu- 
tion is divided into 24 hours, therefore 1 
hour answers to 15°, or the 24th part of 360 9 . 
FI ence, 
1° of longitude answers to 4 min. of time, 
lb' - - - - - - - to 1 min. of time, 
l f ----- - to 4 sec. of time, &c. 
6. The shadows of those people who live 
under this circle are cast to the southward of 
them for one half of the year, and to the 
northward of them during the other halt; and 
twice a year, viz. at the time of the equi- 
noxes, the sun at noon casts no shadow, being 
exactly in their zenith. 
EQUINOX, the time when the sun enters 
either of the equinoctial points, where the 
ecliptic intersects the equinoctial. 
It is so called, because when the sun is in 
these points, the days and nights are of an 
equal length all the world over. As the sun 
is in one of them in the spring, viz. about the 
20th of March, it is called the vernal equi- 
nox; and in the other in autumn, viz. about 
Sept. 23d, it is called the autumnal equinox. 
4 M2 
As the sun's motion is unequal, being some- 
times quicker and sometimes slower, it hap- 
pens that there are about 8 days more from 
the vernal to the autumnal equinox, or while 
the sun is on the northern side of the equa- 
tor, than while he is moving through the 
southern signs from the autumnal to the ver- 
nal equinox. According to Cassini the sun is 
186 d. I4h. 53 m. in the N . signs 
178 14 56 in the S. signs. 
So that 7 23 57 is the difference 
of them, or nearly 8 days. 
Equinoxes, precession of. Astronomers 
consider the year under two distinctions ; viz. 
the solar and the astral. The tropical or 
solar year, upon which the seasons depend, 
is the exact time in which the sun moves 
all round from one equinox to the same 
again, and which period has been found to be 
equal to 365 days, 5 hours, 48', 49". The 
astral year is the time that the sun employs 
in going from one fixed part of the heavens, 
viz. from a given fixed star, all round, and 
again to the same precise point of the heavens: 
and this period, or astral year, is a little longer 
than that of the solar year, viz. it is equal to 
365 days, 6 hours, </, 12", which is longer 
than the solar year by 20', 23", of time, or to 
ail arch of 50". 25 (for in 20' 23" of time, the 
sun runs through an arch of 50". 25 ;) so that 
the sun, as seen from the earth, arrives at the 
equinoctial point, viz. at the equator, a little 
before it arrives at that same precise point of 
the heavens, with which it coincided when it 
crossed the equator in the preceding year. 
This difference between the period of the 
sun’s going from one equinox to the same, 
and. the period of its going from a given star, 
or part of the heavens, to the same again, is 
called the precession of the equinoxes. This 
precession in one ye3r is very trilling ; but the 
accumulation of it, after a number of years, 
produces a considerable difference, which 
can by no means be passed unnoticed ; thus, 
in a hundred years (which is called the secu- 
lar precession) it amounts to 1°, 23' 45"; and 
the difference which it has produced since the 
stars were first observed, and their positions 
were delineated, is very striking. 
How can the sun return to the same equi- 
nox at the end of every year, without relum- 
ing to the same spot in the heavens, or to the 
same fixed star? is the usual difficulty. In 
order to clear this difficulty, the reader must 
recollect that the equator is a circle which, 
being equidistant from the poles, divides the 
celestial sphere into two equal portions. 
Now, if the poles were stationary, viz. coin- 
cided constantly with the same spots in the 
heavens, then the equator would likewise pass 
constantly over the same fixed stars, and 
would cut the ecliptic constantly at the same 
points ; for the ecliptic is an invariable circle, 
viz. it passes always over the same stars! But it 
has been observed, that the poles are subject to 
a constant, though very small, movement: 
so that if at one time any of the two points in 
the heavens, which do not revolve with the 
daily revolution of the rest of the sphere, and 
which we for that reason call the poles, be 
near a certain star, some years after it will be 
found near some other star; or, in other 
words, the .polar star is not always the same. 
It appears, from the result' of calculations es- 
tablished upon the observations • "made during 
several' centuries, 'that the path of either of 
