S94 INC 
Con, in the year 1763. The method is nearly allied to 
Newton’s Doftuine of Fluxions, and arifes out of it. Alfo 
the Differential Method of Mr. Stirling, which he applies 
to the fummation and interpolation of feries, is of the 
fame nature as the Method of Increments, but not fo ge¬ 
neral and extenfive. 
From the method of increments, Mr. Emerfon obferves, 
“ the principal foundation of the method of fluxions 
may eafily be derived. For as, in the method of incre¬ 
ments, the increment may be of any magnitude, fo, in the 
method of fluxions, it muft be fuppofed infinitely final! ; 
whence all preceding and fucceftive values of the variable 
quantity will be equal ; from which equality the rules for 
performing the principal operations of fluxions are imme¬ 
diately deduced. That I may give theVeader,” continues 
he, “a more perfeft idea of the nature of this method ; 
fuppofe the abfciffa of a curve be divided into any number 
of equal parts, each part of which is called the increment 
of the abfciffa; and imagine fo many parallelograms to 
be erefted thereon, either circumfcribing the curvilineal 
figure, or iofcribed in it ; then the finding the fum of all 
thefe parallelograms is the bufinefs of the method of incre¬ 
ments. But, if the parts of the abfciffa be taken infinitely 
final], then thefe parallelograms degenerate into the curve; 
and then it is the bufinefs of the method oj fluxions to find 
the fum of allj or the area of the curve. So that the me¬ 
thod of increments finds the fum of any number of finite 
quantities ; and the method of fluxions the fum of any 
infinite number of infinitely fmall ones ; and this is the 
effential difference between thefe two methods.” Again, 
“ There is fuch a near relation between the method of 
fluxions and that of increments, that many of the rules 
for the one with little variation ferve alfo for the other. 
And here, as in the method of fluxions, fome queitions 
may be folved, and the integrals found, in finite terms ; 
whilff in others we are forced to have recourfe to infinite 
feries for a folution. And the like difficulties will occur 
in the method of increments as ufualiy happen in fluxi¬ 
ons. For whilll fome fluxionary quantities have no flu¬ 
ents, but what are exprefled by feries; fo fome increments 
have no integrals, but what infinite feries afford; which 
will often, as in fluxions, diverge and become ufelels.” 
By means of the method of increments, many curious 
and ufeful problems are eafily refolved, which fcarcely 
admit of a folution in any other way. As, fuppofe feveral 
’ feries of quantities be given, whofe terms are all formed 
according to fome certain law, which is given ; the me¬ 
thod of increments will find out a general feries, which 
comprehends all particular cafes, and from which all of 
that kind may be found. The method of increments is 
alfo of great ufe in finding any term of a feries propofed ; 
for, the law being given by which the terms are formed, 
by means of this general law the method of increments 
will help us to this term, either exprefled in finite quan¬ 
tities, or by an infinite feries. Another ufe of the me¬ 
thod of increments, is to find the fums of feries; w’hich 
it will often do in finite terms. And when the fum of a 
feries cannot be had in finite terms, we muft have recourfe 
to infinite feries ; for, the integral being exprefled by fuch 
a feries, the fum of a competent number of its terms will 
give the fum of the feries required. This is equivalent 
to transforming one feries into another, converging quick¬ 
er : and fometimes a very few terms of this feries will 
give the fum of the feries fought. For the procefs, fee 
the article Algebra, vol. i. p. 314. 
INCREMEN'TUM, f. [Latin.] A figure in rhetoric 
in which the fenfe riles in every member of a fentence. 
INCREMEN'TUM, f. In old records, an improve¬ 
ment of land ; an advanced rent; a piece of land taken in 
from the common. 
To IN'CREPATE, v. a. [increpo, Lat.] To chide; to 
reprehend. 
INCREPA'TION, f. \_increpatio, Lat.] Reprelienfion ; 
chiding.—Tire admonitions, fraternal or paternal, of his 
INC 
feliow-chriftians, or of the governors of the church, than 
more public reprehenfions and increpations. Hammond. 
INCRES'CENT, adj. [from increfco, Lat. to increafe.J 
In heraldry, increafing as the moon before the full. 
INCRES'SANT, adj. Increafing as the moon before 
the full. 
INCRIM'INATE, v. a. [from in, Lat. and criminor, to 
accufe.] To recriminate. Scott. 
To INCROACH, v. n. To encroach. 
INCRO'ACHINGNESS, f. The act of encroaching ; a 
difpolition to encroach. Scott. 
INCRO'ACHMENT, f. An encroachment. Scott. 
INCRUEN'TOUS, adj. [from in, Lat. contrary to, and 
cruentus, bloody.] Void of blood ; untainted with blood. 
Scott. 
To INCRUST', or Incrust'ate, v. a. [incruflo , Lat. 
incrufler, Fr. ] To cover with an additional coat adhering 
to the internal matter.—The finer part gf the wood will 
be turned into air, and the grofler Itick baked and incruf- 
tate upon the fides of the veffel. Bacon. 
Save but our army; and let Jove inernfl 
Swords, pikes, and guns, with everlafting raft. Pope. 
INCRUS'TATING, f. The aft of covering with a kind 
of cruft. 
INCRUSTA'TION,/. [Fr. from incruflo, Lat.] An 
adherent covering ; fomething fuperinduced.—Having 
fych a prodigious Itock of marble, their chapels are laid 
over with fuch a rich variety of incruflations as cannot be 
found in any other part. Add Jon. 
To IN'CUBATE,. v. n. \incubo, Lat.] To fit upon 
eggs. 
INCUBA'TING, f. The aft" of fitting on eggs. 
INCUBA'TION, f. The aft of fitting upon eggs to 
hatch them.—When the whole tribe of birds by incubation 
produce their young, it is a wonderful deviation, that 
fome few families fhould do it in a more novercal way. 
Dcrham. 
INCU'BITURE, /. Incubation. 
IN'CUBUS, f. [from incubo, Lat. to lie on; called alfo 
ephialtes , front z(paWoucci, Gr. to leap upon; epibole, from 
zriQxX/'.u.’, to prels on; becaufe the patient imagines that 
fomething leaps or preffes- upon him ; and babuzicarius, 
from (IccQuta, to fpeak inarticulately, becaufe, in his dif- 
trefs, he mutters indiftinftly.] The Night-mare. —The 
incubus is an inflation of the membranes of the ftomach, 
which hinders the motion of the diaphragma, lungs, and 
puife, with a fenfe of a weight oppreffmg the breaft. 
Fioyer. 
Incubus is fynonymous with oneirodynia in Cullen’s fyf- 
tem. It always happens during• lleep ; the patient fud- 
denly feels a fenfe of weight, a dread of fuffocation, an 
oppreifion as from fomebody falling upon him, with an 
intent to deprive him of life, not fullering him to cry out; 
hence it is ufual with thefe patients to mourn with a con- 
fufed inarticulate voice; they move with difficulty; but, 
on the firft motion, the diftreflmg feelings vanifh. 
This diforder hath been fuppofed to proceed from a 
ftagnation of blood in the brain and lungs : but it is a 
nervous affection, chiefly from indigefiion ; and thole 
whofe nerves are weak, who lead fedentary lives, feed 
heartily, and fop late, are the mofo fubjeft to it. Wind 
is a frequent cauie; deep thought, anxiety, or any op- • 
preflion of mind, equally produce it. It is laid that none 
are attacked with the ephialtes but when laid on their 
backs. If the pati'ent hath a fanguine plethora, bleeding, 
a [pare diet, and aloetic purges, relieve the complaint. A 
flight (upper, cheerfulnels before bed-time, and due exer- 
cife during the day, are the beft remedies ; but, if thefe 
fail, the fetid gums, with camphor joined to opium, at 
bed-time, will lucceed. 
To INCUL'CATE, v. a. [ inculco , Lat. inculquer, Fr.] 
To imprefs by frequent admonitions ; to enforce by con- 
ftant repetition.—Manifeft truth may deferve fometimes 
to 
