130 
A P P 
was supposed to convey the soul of the de- 
ceased to heaven, and thenccfo. ward he was 
ranked among the gods. 
APOTOME, in geometry, the difference 
between two incommensurable lines : such 
is the difference between 2 and 1, and such 
is the excess of the diagonal of a square 
above its side. 
APOTOME, in music, the difference be- 
tween a greater and lesser semi-tone, expres- 
sed by the ratio 128 : 125. 
Apparent, among mathematicians and 
astronomers, denotes things as they appear 
to us, in contradistinction from real or true; 
thus we say, the apparent diameter, distance, 
magnitude, place, figure, &c. of bodies. 
APPARITION, in astronomy, signifies a 
star or other luminary’s becoming visible, 
which before was hid. " It stands opposed to 
occultation. 
APPARITOR, among the Romans, a ge- 
neral term to comprehend all attendants of 
judges and magistrates appointed to receive 
and execute their orders. Apparitor, with 
us, is a messenger, tliat serves the process 
of a spiritual court, or a beadle in an univer- 
sity, who carries the mace. 
APPEAL, in law, the removal of a cause 
from an inferior to a superior court or judge, 
when a person thinks himself aggrieved by 
the sentence of the inferior judge. Appeals 
lie from all the ordinary courts of justice to 
the house of lords. In ecclesiastical causes, 
if an appeal is brought before a bishop, it 
may be removed to the archbishop ; if before 
an archdeacon to the court of arches, and 
thence to the archbishop ; and from the 
archbishop’s court to the king in chancery. 
Appeal, in our old common law, is taken 
for the accusation of a murderer by a person 
who had interest in the party killed ; of a 
felon by an accomplice ; or for rape or may- 
hem by the party injured. It was prosecut- 
ed either by writ or by bill : by writ, when 
a writ was purchased out ot the chancery by 
one person against another, commanding 
him to appeal some third person of felony, 
and to find pledges for doing it effectually : 
by bill, when the person himself gave in his 
accusation in writing, offering to undergo the 
burden of appealing the person therein 
named. The extreme nicety of conducting 
appeals has caused them to be wholly dis- 
used, and the proceeding is now always by 
indictment. 4 Black. 313. 
APPEARANCE, in law, signifies a de- 
fendant’s filing common or special bail, on 
any process issued out of a court of judica- 
ture. In actions by original, appearances 
are entered with the phiiazer of the county ; 
and by bill, with the prothonotary. 
In perspective, appearance is the projec- 
tion of a figure or bodyon the perspective plane. 
In astronomy it signifies the same as phe- 
nomena or phases ; and in physiology, the 
same as phasmata. 
APPELLANTS, in church-history,.an ap- 
pellation given to such of the Roman catho- 
lic clergy, as appealed from the constitution 
unigomtus, to a general council. 
APPELLATIVE, in grammar, a noun 
which is applicable to a. whole species or kind, 
as man, horse ; in. contradistinction to a pro- 
per noun. 
APPENDANT, in law, any thing that is 
inheritable, belonging to some more worthy 
inheritance ; as an advowson, common, or 
court, may be appendant to a manor, land 
A P P 
to an office, &c. but land cannot be append- 
ant to land, for both are corporeal inherit- 
ances, and one thing corporeal cannot be 
appendant to another. 
APPLICATION, in geometry, is used 
for applying one quantity to another, whose 
areas, but not figures, shall be the same ; or 
for transferring a given line into a circle, or 
other figure, so that its ends shall be in the 
perimeter of the figure. 
By application it is proved in Euclid’s ele- 
ments that two triangles having two sides of 
one equal to two sides in the other, and the 
included angles equal, are equal in all respects. 
Application is used in arithmetic for di- 
vision ; thus 16 applied to, or divided by 4, 
gives 4. 
Application, of one science to another, 
signifies the use that is made of the princi- 
ples of the one for augmenting and perfect- 
ing the other. Thus algebra has been ap- 
plied to geometry, and vice versa, and both 
are made use of in illustrating and demon- 
strating the principles of mechanics, astro- 
nomy, navigation, &c. See Geometrv. 
APPOINTEE, in heraldry, the same as 
aguisee: thus we say, a cross appointee, to 
signify that which has two angles at the end 
cut off, so as to terminate in points. 
APPORTIONMENT, in law, the divi- 
sion of a rent into parts, in the same manner 
as the land out of which it issues is divided : 
for example, if a person leases three acres of 
land for a certain rent, and afterwards grants 
away one acre thereof to another, the rent 
shall be apportioned between them. 
APPOSAL of sheriffs, the charging them 
with money received on their accounts in 
the exchequer. 
APPOSITION, in grammar, the placing 
two or more substantives together, in the 
same case, without any copulative conjunc- 
tion between them ; as Ardebat Alexim deli- 
cias domini. 
APPRAISING, the valuing or setting a 
price on goods. This is usually done by a 
sworn appraiser, who, it he values (lie goods 
too high, is obliged to take them at the price 
appraised. 
APPREHENSION, in logic, denotes the 
simple attention of the mind to an object pre- 
sented either to our senses or our imagina- 
tion, without passing a judgment, or making 
any inference. The word is also used to 
express an inadequate and imperfect idea. 
APPRENTICE, a young person bound 
by indenture to some tradesman, in order to 
be instructed in the mystery or trade. By 
the laws of England, a master may be in- 
dicted for not providing for, or for turning 
away his apprentice : and upon complaint 
from a master, that he neglects his duty, an 
apprentice may be committed to Bridewell, 
or be bound over to the sessions. By 5 
Eliz. no person can exercise any trade in 
any part of England, without having served 
a regular agprenticeship of at least seven 
years. No trades, however, are held 
to be within the statute but such as were 
in being at the making of it in the reign 
of Elizabeth. Apprenticeships are not ne- 
cessary to carry on a trade in a country vil- 
lage. "And following a trade seven years, 
either as master or servant, without effectual 
prosecution, is sufficient without an appren- 
ticeship. 
A duty of fid. in the pound is grantee? for 
every sum of 50/. or under, and 12d. An the- 
A P P 
pound for sums not exceeding 50/. given I 
with all apprentices, except such as are I 
placed out by church- wardens, &c. 1 
APPRISING, in Scots law, the name of I 
an action by which a creditor formerly be- I 
came invested with the estate of his debtor I 
for payment. . ] 
APPROACH, curve of equable, is of such j 
a nature, that a body descending in it by the j 
sole power of gravity, approaches the hori- j 
zon equally in equal times. See Cur ve. 
APPROACHES, method of, in mathe- j 
matics, a name given to a mode of resolving j ; 
certain problems relating to square numbers, j 
by first assigning certain limits to the quanti- 1 
ties required, and then approaching nearer 
and nearer till a coincidence is obtained. I he J 
double rule of false position may be considered J 
as a method of approaches.^ 
Approaches, in fortification, the works | 
thrown up by the besiegers, in order to get I 
nearer a fortress, without being exposed to | 
the enemy’s cannon : such, in a more parti- 1 
cular manner, are the trenches, which, I 
should be connected by parallels, or lines ol V 
communication. j 
Approaching, in fowling, a method of j 
getting near the birds by means of a ma-i 
chine, made of hoops and boughs of, trees I 
within which the sportsman conceals himself. | 
APPROPRIARE com muni am, in law, j 
is to discommon, or inclose any parcel ofjl 
land that before was open and common. 
APPROPRIATION, the annexing a be- 1 
nefice to the proper and perpetual use of a j 
religious house, bishopric, college, &c. | 
Where the king is patron, he may make ap- j 
propriations himselt ; but in other cases, 1 
after obtaining his licence in chancery, the I 
consent of the ordinary, patron, and incumb-| 
ent, is requisite. Appropriations cannot be I 
assigned over, but those to whom they 7 are I 
granted may make leases of the profits, j 
There are in England 2345 impropriations. 8 
APPROVEMENT, in law, is the inclosl 
ing'part of a common by the lord of the manor. 
APPROVER, in law, one who before im- 
prisonment, confessing that lie has committed 
a felony, accuses one or more of his accom- 
plices. ' Approvers, also, signify bailiffs off 
lords in their franchises, sheriffs, and likewise j 
such persons as have the letting the king’s! 
demesnes in small manors. 
APPROXIMATION, in arithmetic and I 
algebra, the coming nearer and nearer to ar 
root or other quantity sought, without expect-j 
ing to be ever able to find it exactly. r l here! 
are several methods fordoing this, to be found 
in mathematical books, being nothing but in- j 
finitely coverging series, some approaching! 
quicker, others slower towards the truth. 
By such an approximation the value of aj 
quantity may be found, though not to the ut-l 
most degree of exactness, yet sufficiently so for! 
practice. Thus 2 = 1.41421356, See. — the! 
4 1 4 j 
approximating series 1 + ^ ^ 
+ Y5555 +> &c - or supposing * = jQ , equal 
4 1 4 2 J 
to the series 1 x — + -jr + + ijr'T’ &e ! 
= x+ 4 x - 1 +*- 2 -f 4*~ 3 + 2*-<-M 
&c. 
The most easy and general method of ap 4 
proximation, is perhaps by the rule of Double 
Position, or, what is sometimes called, the Me| 
thod of Trial-and-error ; which method see unj 
der its own name. And among all the method^ 
