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third book of tiie Frincipia; and mors particularly explained byhim in his Optics, where he exhibits the method of proceed-ing in philosophy, tiie first part of which is as follows : As in ma-thematics, so in natural history, the investigation of difficult things,by way of analysis, ought always to precede the method of com-,position. This analysis consists in making experiments and obser-vations, and in drawing general conclusions from them by induc-tion (f. e. reasoning from the analogy of things by natural conse-quence,) and admiling no objections against the conclusion', butwhat are taken from experiments or ceit’.in truths. And althoughthe arguing from experiments and observation, by induction, beno demonstration of general conclusions, yet it is the best way ofarguing which the nature of things admits of, and may be lookedon as so much the stronger, by how much the induction is moregeneral; and if no exception occur from phxnomena, the conclu-sion may be pronounced generally; but if at any time after-wards any exception shall occur from experiments, it maythen be pronounced with such exceptions: by this way ofanalysis we msv proceed from compounds to ingredients, andfrom motions to the cause producing them ; and, in general, fromeffects to their causes; and from particular causes to more generalones, till the argument ends in the most general: this is the me-thod of analysis. And that of synthesis, or composition, consists iin assuming causes, discovered and established as principles, and 'by them explaining the phenomena, proceeding from them, and-proving the explanations. See Philosophy, and Physics .
EXPERIMENTUM GRUC1S, a capital or decisive experi-ment; thus termed, either on account of its being like a cross, ordirection post, placed in the meeting of several roads, as guidingnun to the true knowledge of the nature of that thing they are in-quiring after; or on account of its being a kind of torture, wherebythe nature of tiie thing is as it were extorted by force.
EXPIATION, in a figurative sense, is applied to tiie pardonprocured to tiie sins of tiie penitent by the merit of Christ’s death.
Expiation, among tiie Heathens, was of several kinds; by sa-crifices and religious washing. They were used for effacing acrime, averting any calamity, and on numberless other occasions,as purifying towns, temples, ike. and armies before and after bat-tle. And they were peiformed for whole cities, as well as parti-cular persons.
Expiation, among the Jews , was chiefly by sacrifice, whe-ther for sins of ignorance, or to purify themselves from certainpollutions.
Expiation, tub Feast of, among the Jews , called by ourtranslators the day of atonement, was held on the 10th day ofTisri, the seventh month of the Jewish year, answering to part ofSeptember and October. See Levit. xvi. xxiii. 27, &v.
EXPIRATION, in physic, that part of respiration wherebytile air is expelled, or driven out of the lungs.
Expiration, in chemi try, is applied to all sorts of evaporation,and suhtde effluvia, tl at go off into tiie air.
Expiration is also used ior the end of any term agreed upon.It likewise signifies death.
EXPLOSION , in natural philosophy, a sudden and violentexpansion of an aerial or other elastic fluid, by which it instantlythrows off any obstacle, sometimes with incredible force, and insuch a manner as to produce the most astonishing effects upon theneighbouring objects. Explosion differs from expansion, in thatthe latter is a gradual and continued power, acting uniformly for*ome time ; whereas the former is always sudden, and only of mo-mentary duration. The expansions of solid substances do not ter-minate in violent explosions, on account of their slowness, and thesmall space through which the metal, or other expanding sub-stance, moves ; though their strength may be equally greatwith that of the most active aerial fluids. Thus we find, thatthough wedges of wood, when wetted, will cleave solid blocks ofstone, they never throw them to any distance, as is the ease withgunpowder. On tiie other hand, it is seldom that the expansionofanv elastic fluid bursts a solid substance, without throwing tiiefragments of it to a considerable distance, the effects of which areoften very ter; ible. The reasons ol the above phanomcna are,1. The immense velocity with which the aerial fluids expand, wheneffected by considerable degrees of beat ; and, 2/I'hcir celerity inacquiring he. t, and being affected by it, which is much superior tothat of solid substances. Thus air, heated as much as iron, whenbrought to a white heat, is expanded to four times its bulk ; but
the metal will not be expanded the 600th part of the space. lr»tiie case of gun-powder, tiie velocity with which the flame movesis calculated by Mr. Robins, in his Treatise upon Gunnery, to beno less titan seven thousand feet in a second, or nearly seventy-nine miles per minute. Hence the impulse of the fluid is incon-ceivably great, and the obstacles on which it strikes are hurriedoff with vast velocity, though much less than that just mentioned ;lbr a cannon bullet, with the greatest charge of powder that cun liecon leniently given, dees not move at a greater rate than two thou-sand four hundred feet per second, or little more than tw enty-seven miles per minute. The velocity of the bullet again is pro-moted by tiie sudden propagation of tiie heat through the wholebody of air, as soon as it is extricated from the materials of whichtiie gun-powder is made ; so that it. is enabled to strike all at once,and thus greatly to augment the momentum of the ball. It isevident that this contributes very much to the force of the explo-sion, by what happens when powder is wetted or mixed with anysubstance,which prevents it from taking fire all at once. In this casethe force of the explosion, even when the same quantity of powderis made use of, is vastly inferior to that of dry powder. Uponthese principles we may conclude, that the force of an explosiondepends, 1. On the quantity of elastic, fluid to be expanded. 2.On the velocity it acquires by a certain degree of heat; and, 3.Oil the celerity with which the degree of heat affects the v, hole ofthe expansible fluid. These three take place in the greatest per-fect foil where the electric fluid is concerned; as in.cases.of light-
ning, earthquakes, and volcanoes.
EXPON ENT,, [from expono, to shew,] in algebra, is a uum-' cr placed over any power or involved quantity, to shew to whateight the root is raised: thus 2.is the exponent of a 3 , and 4 the
b
he
exponent of art, u j.r.r. See Algebra .
EXPON KNTJAL CALCULUS. See Calculus.Exponential Curve is that whose nature is defined or ex-pressed by an exponential equation; as the curve denoted by=; y, or by X s - = y. The area of any exponential curvu,whose nature is expressed by this exponential equation a‘ — y
1 1 . 1
finaking 1. v = x) will be-c 3 -j-o 3 -vrt
0 . 1.2 0 . 1 . 2 , 3 . 0 . 1 . 2 . 3.4
1 1
-j-t*-- E C ,.&C.
0.1.2.3.4.5 0.1.2.3.4.i.'i
Exponential Equation is one in which is contained an ex-ponential quantity : as the equation = l>, or .i* =: aO, Ac.
Exponential Quantity is a quantity whose power is a variablequantity, as Exponential quantities are of several degrees
and orders, according as the exponents themselves are more orless involved. If the expound be a simple quantity, as z y , it iscalled an exponential of the first.or lowest degree; but when flic
X
exponent i'self is an exponential of the first degree as z y it iscalled an exponential ot the second degree. In like manner, if the
U
exponent itself be an exponential of tiie second degree, asiR, itis called an exponential of the third degree, &c.
EXPOSING, in the Latin church, tiie sacrament is said (obe exposed when it is shewn in public uncovered on festival days*and during tiie time of plenary indulgences.
Exposing of Children, a barbarous custom practised bymost ancient nations, excepting the '1 Indians, who had an expresslaw, whereby it was made capital to expose children, and ordain-ed that such as were not in a condition to educate them shouldbring them to the magistrates, to he brought up at the public ex-pence. Among the other Greeks, when a child was born, it waslaid on the ground: and if the father ciesigi ed to educate hischild, lie immediately took it up: but if lie forbore to do this, thechild was carried awav and exposed.
EXPRESSED OILS, in chemistry, such oils as arc obtainedfrom bodies only by pressing. See On..
EXPRESSION, in algebra, any algebraical quantity’, simpleor compound; as 3 a, '2nb, or 4«x -f- d, &c.
Expression, in chemistry, or pharmacy, denotes the. act ofpressing out the juices of vegetables, which is one of the threeways ot obtaining them ; the oilier two being by infusion and de-coction. Sec Pharmacy.
-*
Expression,