APP 
mechanics is founded on the same principles 
as the application of algebra to geometry. 
It consists principally in representing by 
equations the curves described by bodies in 
motion, by determining the equation be- 
tween the spaces which the bodies describe 
when actuated by any forces, and the times 
employed in describing them. Asa familiar 
instance, we may refer to the article Acce- 
leration, where the perpendiculars of tri- 
angles represent the times, the bases the 
velocities, and the areas the spaces described 
by bodies in motion, a method first invented 
by Galileo. As lines and figures may be 
treated of algebraically, it is evident in 
what way the principles of geometry and 
algebra may be applied to mechanics, and 
indeed to every branch ofmixt mathematics. 
Application of mechanics to geometry 
consists in the use that is made of the centre 
of gravity of figures for determining the con- 
tents of solid bodies described by those 
figures. 
Application of geometry and astronomy 
to geography consists in determining the 
figure and magnitude of the earth ; in de- 
termining the positions of places by obser- 
vations of latitudes and longitudes ; and in 
determining by geometrical operations the 
positions of such places as are not far distant 
from one another. 
Application of geometry and algebra to 
natural philosophy was invented chiefly by 
Sir Isaac Newton, and upon this application 
are founded all the mixed sciences of ma- 
thematical and natural philosophy. Here 
a single observation or experiment will fre- 
quently produce a whole science, or branch 
of science. Thus, when it is proved by ex- 
periment that the rays of light, in reflecting, • 
make the angle of incidence equal to the 
pngie of reflection, we deduce the whole 
science of catoptrics ; for this fact being es- 
tablished, catoptrics becomes a science 
purely geometrical, since it is reduced to 
the comparison of angles and lines given in 
position. 
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 man- 
ner 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 be- 
tween them. 
APP 
APPOSITION, in grammar, the placing 
two or more substantives together, in the 
same case, without any copulative conjunc- 
tion between them ; as, ardehat Alexim de- 
Udas domini. 
APPRAISING, the valuing or setting a 
price on goods. This is usually done by a 
sworn appraiser, who, if be values the goods 
too high, is obliged to take them at the price 
appraised. 
APPREHENSION, in logic, the first or 
most simple act of the mind, whereby it 
perceives, or is conscious of some, idea : it 
is more usually called perception. 
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. Appren- 
tices may be bound to husbandmen, or even 
to gentlemen of fortune and clergymen, w ho, 
as well as tradesmen, are compellable to 
take the children of the poor, under a penalty 
of 101. And the church-wardens and over- 
seers, with the consent of two justices, may 
bind them till the age of 21 years. Justices 
may compel certain persons under age to be 
bound apprentices, and on refusal may com- 
mit them. Apprentices may be discharged 
on reasonable cause, either at their own re- 
quest or that of their masters. If any, whose 
premium has been less than ten pounds, run 
away from their masters, they are compel- 
lable to serve out the time of absence, or 
give satisfaction for it, any period within 
seven years after the expiration of the origi- 
nal contract. Indentures are to be stamped, 
and are chargeable with several duties by 
act of parliament. 
APPRENTICESHIP, denotes the ser- 
vitude of an apprentice, or the duration of 
bis indenture. The competition in several 
employments is restrained to a smaller 
number, than would otherwise be disposed 
to enter into them, partly by the limita- 
tion of the number of apprentices, which 
attends the exclusive privilege of incorpo- 
rated trades ; and partly by the long term 
of apprenticeship, which increases the ex- 
pense of education. Seven years seem 
formerly to have been, all over Europe, 
the usual term established for the duration 
of apprenticeships in the greater number 
of incorporated trades. Such incorpora- 
tions were anciently called universities, 
