APP 
APT 
This is the most difficult part of a siege, 
and where most lives are lost. The ground 
is disputed inch by inch, and it is of the ut- 
most importance to make the approaches 
with great caution, and to secure them as 
much as possible. 
The besieged frequently make counter- 
approaches, to interrupt and defeat the ene- 
my’s approaches. 
APPROPRIATION, the annexing a be- 
nefice to the proper and perpetual use of a 
religious house, bishopric, college, &c. 
Where the king is patron, he may make ap- 
propriations himself; but in other cases, af- 
ter obtaining his licence in chancery, the 
consent of the ordinary, patron, and incum- 
bent is requisite. Appropriations cannot 
be assigned over, but those to whom they 
are granted may make leases of the profits. 
There are in England 2845 impropriations. 
APPROVER, in law, a person, who be- 
ing indicted of treason or felony, for which 
he is not in prison, confesses the indictment; 
and being sworn to reveal all the treasons 
and felonies he knows, enters before the co- 
roner his appeal against all his partners in 
the crime. All persons may be approvers, 
except peers of the rehhn, persons attainted 
of treason or felony, or out-lawed, infants, 
women, persons non compos, or in holy or- 
ders. 
APPROXIMATION, in arithmetic and 
algebra, the coming nearer and nearer to a 
root, or other quantity sought, without ex- 
pecting to be ever able to find it exactly. 
There are several methods for doing this, to 
be found in mathematical books, being no- 
thing but infinitely converging series, some 
approaching quicker, others slower towards 
the truth. 
By such an approximation the value of a 
quantity may be found, though not to the 
utmost degree of exactness, yet sufficiently 
so for practice. Thus \/ 2 = 1.41421356, 
&c. = the approximating series 1 -f- A 
+ foo+n 4 5o + ro?oo+, or supposing 
4 14 
x — Vo, equal to the series 1 x--(- ~-f- — 
— -j-, &c. = 1 -j- 4 tf— 1 -|~ x~' 2 4* 4 x~ 3 -J- 
2 -f-, &c. 
Again, supposing a 2 -j- b to be a non-qua- 
drate number, and a 3 -J- b to be a non-en- 
bic one ; then will \/ a 2 -f- b — a -f- 
ub , s/ — ~ . — r . ab 
2 a 2 -j- 1 b 
, and \/ a? a 
3 a 3 4- b 
= \/ i 4* — neatly. 
5 (i 
There is a general method ofinvestigating 
the value of such series, for which see Se- 
ries. 
APPULSE, in astronomy, the approach 
of a planet towards a conjunction with the 
sun, or any of the fixed stars. The appulses 
of the planets to the fixed stars have always 
been of great use to astronomers in order to 
fix the places of the former. The ancients 
wanting an easy method of comparing the 
planets with the ecliptic, which is not 
visible, had scarce any other way of fixing 
their situations, but by observing their tract 
among the fixed stars, and remarking their 
appulses to some of those visible points. 
Dr. Halley has published a method of de- 
termining the places of the planets, by ob- 
serving their near appulses to the fixed 
stars. 
APPURTENANCES, in common law, 
signify things corporeal and incorporeal, 
that appertain to another thing as principal ; 
as hamlets to a manor, and common of pas- 
ture and fishery. Things must agree in na- 
ture and quality to be appurtenant, as a tur- 
bary, or a seat in a church, to a house. 
APRICOT, in botany, a species of prunus, 
with rosaceous flowers, and a delicious fleshy 
fruit, of a roundish figure. See Prunus. 
APRON, in gunnery, the piece of lead 
which covers the touch hole of a cannon. 
The dimensions of aprons are as follow ; 
viz. for 42, 32, and 24 pounders, 15 inches 
by 13; for 18, 12, and 9 pounders, 12 in- 
ches by 10 ; and for cannon of less calibre, 
10 inches by 8. They are tied by two 
strings of white marline. 
APSIS, in astronomy, a term used indif- 
ferently for either of the two points of a 
planet’s orbit, where it is at the greatest or 
least distance from tire sun or earth. Hence 
the line connecting these points, is called 
the line of the apsides. 
APTENODYTES, in ornithology pen- 
guin, a genus of the order Anseres. The 
bill is straight, rather compressed, and 
sharp along the edges; the upper mandible 
is obliquely sulcated, lengthwise ; feet pal- 
mated, shackled ; wings fin-shaped, and 
without quill-feathers ; feet fettered, four- 
toed. This genus resembles the alca in 
colour, food, stupidity, eggs, nest, position of 
legs behind the equilibrium, and consequent 
erect posture. They are totally unfit for 
flight, but swim dextrously ; nostrils linear, 
hid in the groove of the bill, palate as well 
as the tongue beset with a few rows of 
conic, retroflected, stiff papilla; ; wings co- 
vered with a strong broad membrane ; tail 
