ICC
They declaimed much .aga'nft the Senfes ; and charg'd them with a principal Hand in /educing and leading us into Error, Sec Sense, Error, Truth, Falshood, Doubt- ing, &c.
The Word is a Compound of the Privative et, and xaV-
- ay.gM>a l deprchendo, I find cut ; of x&T<i, and Aa^&tM, Ca-
fio, I take. See Catalepsis.
ACCAPITCJM, in our antient Law-Books, fignifics Re- lief to the Chief Lord. — Hence alfo,
Accapitare, to pay Relief to the Chief Lord. See Relief.
ACCEDAS ad Curiam, is a Writ which lies for him who has received falfe Judgment, or fears Partiality, in a Court- Baron, or Hundred Court ; being directed to the Sheriff.— The like Writ lies alfo for him that has received fuch Judg- ment in the County-Court , and is called de Falfo Judicio.
The Accedas ad Curiam lies alfo for Juflice delayed, as well as falfly given ; and is a Species of the Writ Rccor- dari. See Recordari.
Accedas ad Vice-ccmitem, is a Writ directed to the Co- foner, commanding him to deliver a Writ to the Sheriff 5 who having a Pone deliver'd to him, fupprefles it. See Pone.
ACCELERATED Motion, in Mechanicks, is a Motion which receives continual Increments, or Accefllons of Velo- city. See Motion.
If the Acceffions of Velocity be equal in equal Times ; the Motion is faid to be uniformly accelerated. See Acce-
f.ER ATION.
The Motion of falling Bodies is an accelerated Motion : And fuppofing the Medium they fall thro', i. e. the Air, void of Refinance ; the fame Motion may be alfo confider'd as uniformly accelerated. See Descent, i$c.
For the Laws of Accelerated Motion, fee Motion.
ACCELERATION, in Mechanicks, the Increafe of Ve- locity in a moving Body. See Velocity, and Accelera- ted Motion.
deceleration ftands directly oppofed to Retardation, which denotes a Diminution of Velocity. See Retardation.
Acceleration is chiefly ufed in Phyficks, in refpect, of falling Bodies, i.e. of heavy Bodies tending towards the Centre of the Earth by the Force of Gravity. Sec Gravi- ty, and Centre.
That Natural Bodies are accelerated in their Defcent, is evident from various Considerations, both d priori and pofte- riori. — Thus, we actually find, that the greater Height a Body falls from, the greater Impreffion it makes, and the more vehemently does it ftrike the fubject Plane, or other Obftacle.
Caufe of the Acceleration of Falling "Bodies.
Various are the Syflems and Opinions which Philofophers have produced to account for this Acceleration. — Some attri- bute it to the Preflure of the Air : The farther, fay they, a Body falls, the greater Load of Atmofphere is of confequence incumbent on it : and the Preflure of a Fluid, is in propor- tion to the perpendicular Altitude of the Column thereof — Add, that the whole Body of the Fluid preffing in innume- rable right Lines, which all meet in a Point, viz. the Cen- tre 5 that Point, by the meeting of thofe Lines, fuftains, as it were, the Preffion of the whole Mafs : Confequently, the nearer a Body approaches theteto, the Effect or Preflure of more united Lines muit it fuftain. See Air, and Atmo- sphere.
But what overturns this Account, is, that as the Preflure of the Air downwards increafes ; fo, by the known Laws of Staticks, does the Refiftance, or the Force wherewith the fame Fluid tends to repel, or drive the Body upwards again. See Fluid.
Others infift, that the incumbent Air is the grofler and more vaporous, the nearer the Earth ; and fill'd with more heterogeneous Particles, which are not true elaflick Air : and hence, fay they, a defcending Body, meeting continually with lefs Refiftance from the Elafticity of the Air, and hav- ing the fame Force of Gravity Hill acting on it, nil necef- farily be accelerated. See Elasticity.
But what overturns all Accounts where the Air or Atmo- fphere are concern'd, is, that the Acceleration holds in Va- cuo, and even more regularly than in Air. See Vacuum.
The 'Peripatetic Account is worfe than this : The Mo- tion of heavy Bodies downwards, fay they, arifes from an intriniick Principle, which makes 'em tend to the Centre, as their proper Sear, or Element, where they would be at reft : Hence, add they, the nearer Bodies approach thereto, the more is their Motion intended. See Element, Qua- lity, &c.
The Gajfindifls, on the other hand, hold that the Earth emits a fort of attractive Effluvia, innumerable Threads whereof continually afcend and defcend ; which Threads, proceeding like Radii from a common Centre, divaricate the more, the further they go : So that the nearer a heavy Body is to the Centre, the more of thefe magnetic Threads
XM)
A C C
it receives; and hence the more is its Motion accelerated See Effluvia, and Magnetism.
But this is rcfell'd by an cafy Experiment : for if a Ball be let fall out or the loweft Window of a high Tower and alfo out of the higheft ; the Accclentiai- will be the feme in both Cafes, notwithstanding the greater Vicinity to the Centre m rhe one, than in the other Cafe.
The Cartcfians account for the Acceleration, from the repeated Pulfcs of a fubtil ethcrial Matter, which is conti- nually acting on the failing Body, and impelling it downwards. SeeCARTEsiANisM, jEther, Element, Matter, Sub- tile, £s?c.
Alter all, the Caufe of Acceleration is nothing myftcrious ; the Principle of Gravitation, which determines the Body to defcend, determining it to he accelerated by a neceflary Con- fequence. See Gravitation.
For, fuppofo a Body let fall from on high : the primary Caule of its beginning to defcend, is, doubtlefs, the Power of Gravity ; but when once the Defcent is commenced, that State becomes in fome meafure natural to the Body ; fo that if left to it feif, it would pcrfevere in it for ever, even tho the firft Caufe fhould ceafe ; as we fee in a Stone caft with the Hand, which continues to move, after it is left by the Caufe that gave it Motion. See Law of Nature.
But, befidc the Propensity to defcend imprefs'd by the firft Caufe, and which of it felf were fufficient to continue the fame degree of Motion once begun, in infinitum ; there is a conftant Acceflion of fubfequent Efforts of the fame Principle, Gravity, which continues to aft on the Body al- ready in Motion, in the fame manner as if it were at reft.
Here, then, being a double Caufe of Motion, and both acting in the fame Direction, viz. directly towards the Cen- tre of the Earth ; the Motion they jointly produce muft ne- ceflarily be greater than that of one of 'em.— Ani the Velocity thus increas'd, having the fame Caufe of Increafe flill perfifting, the Defcent muft neceflarily be continually accelerated.
For, fuppofing Gravity, whatever it be, to aft uniformly on all Bodies, at equal Diftances from the Earth's Centre ; and that the Time in which a heavy Body falls to the Earth, be divided into equal Parts infinitely fmall : let this Gra- vity incline the Body towatds the Earth's Centre, while it moves, in the firft infinitely fmall Part of the Time of its Defcent ; if after this, the Action of Gravity be fuppos'd to ceafe, the Body would proceed uniformly on towards the Earth's Centre, with a Velocity equal to the Force of the firft Impreflion.
But, now, fince the Action of Gravity is here fuppofed ftill to continue ; in the fecond Moment of Time, the Body will receive a new Impulfe downwards, equal to what it re- ceived at firft 5 and thus its Velocity will be double of what it was in the firft Moment : in the third Moment it will be ttiple ; in the fourth quadruple, and fo on continually : For the Impreflion made in one Moment, is not at all alter'd by what is made in another; but the two are, as it wete, ag- gregated, or brought into one Sum.
Wherefore, fince the Particles of Time are fuppofed infi- nitely fmall, and all equal to one another ; the Impetus ac- quir'd by the falling Body, will be every where as the Times from the Beginning of the Defcent. — And hence, fince the Quantity of Matter in the Body given, continues the fame 5 the Velocity will be as the Time in which it is acquir'd.
Further, the Space pafs'd over by a moving Body in a given Time, and with a given Velocity, may be confider'd
as a Rectangle made by the Time and the Velocity. .
Suppofe A, (Tab. Mechanicks, Fig. 61.) a heavy Body de- fcending, and let A B reprefent the Time of its Defcent 5 which Line fuppofe divided intoany Number of equal Parts, AC, CE, EG, ($c. reprefentative of the Intervals, or Mo- ments of the given Time.— Let the Body defcend thro' the firft of thofe Divifions, AC, with a certain equable Velocity arifing from the propofed Degree of Gravity : this Velocity will be reprefented by AD ; and the Space pafs'd over, by the ReaangleCAD.
Now, as the Action of Gravity in the firft Moment pro- duced the Velocity A D, in the Body before at reft ; in the fecond Moment, the fame will produce in the Body fo moving, a double Velocity, C F ; in the third Moment, to the Velocity C F wii! be added a further degree, which together therewith, will make the Velocity E H, which is triple of the* firft, and fo of the reft. So that in the whole Time A B, the Body will have acquir'd a Velocity B K. — Again, taking the Divifions of the Line, e.g. AC, CE, &c. for the Times, the Spaces gone thro' will be the Areas or Rectan- gles, CD, E F, S?c. So that in the whole Time A B, the Space defcribed by the Moveable, will be equal to all the Rectangles, i. e. to the dented Figure ABK.
Such would be the Cafe, if the Accefllons of Velocity on- ly happen'd in certain given Points of Time, e.g. in C, in E, c5c So that the Degree o^ Motion fliouid continue the
fame till the next Period of Acceleration come up.
If the Divifions or Intervals of Tims were fuppofed lefs,
e.g.
