IND 
merits perpendicularly, the number of 
points in that line will be the same as the 
number of the elements ; whence we may 
see that a parallelogram, prism, or cylinder, 
is resolvable into elements or indivisibles, 
all equal to each other, parallel and like to 
the base ; a triangle into lines parallel to 
the base, but decreasing in arithmetical- 
proportion, and so are the circles which 
constitute the parabolic conoid, and those 
which constitute, the plane of a circle, 
or surface of an isosceles-cone. See Infi- 
nitesimals. 
A cylinder may be resolved into cylin- 
drical curve surfaces, having all the same 
height, and continually decreasing inwards, 
as the circles of the base do on which they 
insist. , 
The method of indivisibles is only the 
ancient method of exhaustions, a little dis- 
guised and contracted. It is found of great 
use in shortening mathematical demonstra- 
tions, of which take the following instance 
in the famous proposition of Archimedes, 
viz. that a sphere is two thirds of a cylinder 
circumscribing it. 
Suppose a cylinder, an hemisphere, and 
anin verted cone (Plate Miscel. VI. fig. 13.), 
to have the same base and altitude, and to 
be cut by infinite planes all parallel to the 
base, of which dg is one. It is plain the 
square of dh will be every where equal to 
the, square of fee (the radius/of the sphere) 
the square he — eh square ; and consequent- 
ly, since circles are to one another as the 
squares of the radii, all the circles of the 
hemisphere will be equal to ail those of the 
-cylinder, deducting thence ail those of the 
cone : wherefore the cylinder, deducting 
the cone, is equal to the hemisphere ; but it 
is known that the cone is one-third of the 
cylinder, and consequently the sphere must 
be two-thirds of it, Q. E. D. 
INDORSEMENT, in law, signifies any 
thing written upon the back of a deed or 
other instrument. On sealing of a bond 
the condition of the bond may be indorsed, 
and then the bond and indorsement shall 
both stand together. In order to the exe- 
cuting a justice of the peace’s warrant in 
another county, it must be indorsed by 
some justice in such other county, which is 
commonly called backing the warrant. It 
it customary also to indorse the receipt of 
the consideration-money upon a deed ; or 
an assignment of a lease may sometimes be 
made by indorsement. Indorsement, is 
also that act by which the holder of a bill 
of exchange, or promissory note, payable 
INE 
to order, transfers such instrument, and his 
interest, therein, to some other person, who 
is then termed the indorsee, and who, by 
such transfer and assignment renders him- 
self responsible for presenting such instru- 
ment, and using all due diligence to obtain 
payment of the acceptor or maker. 
INDUCTION is the giving a clerk insti- 
tuted to a benefice, the actual possession 
of the temporalities belonging to it, in the 
nature of livery of seisin. It is performed 
by a mandate from the bishop to the arch- 
deacon, who commonly issues out a pre- 
cept to some other clergyman to perform it 
for him ; which being done, the clergyman 
who inducts him indorses a certificate ofhis 
induction on the archdeacon’s mandate, and 
they who were present testify the fact un- 
der their hands. And by this the person 
inducted is in full and complete possession 
of all the temporalities of his church. 
INEBRIANTS, a term derived from the 
Latin, and applied to that class of substances 
that affect the nerves in a particular and 
agreeable manner, and through them alter 
and disturb the functions of the mind. They 
are divided into natural and artificial : the 
former are chiefly in use among oriental 
nations; to the latter Europeans have re- 
course. Natural inebriants are opium, in 
use in Turkey and the East ; peganum har- 
mala, Sirian rue ; of this the seeds are 
chiefly used : maslac of the Turks, or ban- 
gue of the Persians, prepared from the dust 
of the male flower of hemp ; bangue of the 
Indians, from the leaves of the hibiscus 
abelmoschus; seeds of various species of 
the datura, or thorny apple ; penang, or be- 
tel, of the Indians ; roots of black henbane ; 
hyoscyamus physaloides ; berries of the 
night shade ; leaves of millefoil ; tobacco. 
Artificial inebriants are fermented liquors 
from farinaceous seeds; wines and spirits 
drawn by distillation. See Drunkenness. 
INERTIA of matter, in philosophy, is 
defined by Sir Tsaac Newton to be a passive 
principle by which bodies persist in a state of 
motion or rest, receive motion in propor- 
tion to the force impressing it, and resist as 
much as they are resisted. It is also de- 
fined by the same author to be a power im- 
planted in all matter, whereby it resists any 
change endeavoured to be made in its state. 
See Mechanics. 
All bodies persevere or continue, as of 
themselves, in their state of rest or of uni- 
form motion in a right line, in such manner, 
that a body at rest cannot move without 
being solicited or urged by some force; 
