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nicnts of great mafters dilp^rncc the compofitions wliicli tliey 

 mean to embellll"h, and diitjiill their hearers. Darliii^ imi- 

 tators of the bold rr.oduUitioii of Hnydii, and of the rapid 

 running up and down the keys in half notes, as Mozart did 

 in his juvenile days, have deformed melody, and corrupted 

 harmony. Theic great mailers knew when to ftop ; but 

 their apes think they never can feafon their prodiielions 

 too highly ; and, it is to be feared, that the lovers of lim- 

 plicity will never be indvdged again with plain food, 

 even by thofe who have no means of gratifying them with 

 hixuries. 



ACCELERATING Force, in Mechanics. Sec Force. 



ACCELERATION, in 7Wrf/ja«;rx, the increafe of ve- 

 locity in n movmg body. 



Accelerated mohon is that which continually receives frcfli 

 accelTions ol velocity, and is eithcj- equably or unequably ac- 

 celerated. If the accefTions of velocity be always equal in 

 equal times, the motion is laid to be equably or uniformly 

 accelerated; but if the accefiions in equal times either in- 

 creafe or decreafe, the motion is uneq.iably or variably ac- 

 celerated, ylcce/eratioii (iands directly oppoied to retardation, 

 which denotes a diminution of velocity. 



AcCELKRATiON is chiefly ufed in Phvfia, in refpeft of 

 falling bodies, i. e. of heavy bodies tending towards the 

 centre of the earth by the force of gravity. 



That natural bodies are accelerated in their defcent, is evi- 

 dent from various confiderations, both ci priori and pojleriori. 

 —Thus, we aftually find that the greater height a body 

 defcends from, the greater imprefiion it makes, and the more 

 vehemently does it ftrike the plane or other obftacle on 

 which it falls. 



Various are the fyftems and opinions which philofophers 

 have produced to account for this acceleration. Some at- 

 tribute to it the prclfure of the air : the farther, fay they, a 

 body falls, the greater load of atmofphere is confequently 

 incumbent on it : and the prclTure of a fluid is in propor- 

 tion to the perpendicular altitude of the column thereof. — 

 Add, that the whole body of the fluid prcffing in innume- 

 rable right lines, which all meet in a point, viz. the centre of 

 the earth ; that point, by the meeting of thole lines, fuf- 

 tains, as it were, the preflure of the whole mafs : confe- 

 quently, the nearer a body approaches to it, the effeft or 

 prefTure of more united lines muft it fuihiin. 



But what overturns this account is, that as the preflure 

 of the air downwards increafes ; fo, by the known laws of 

 ftatics, does the refiftance, or the force wherewith the fame 

 fluid tends to repel, or drive the body upwards again. 

 Others infill, that the incumbent air is the grofler and more 

 vaporous, the nearer the earth ; and filled with more he- 

 terogeneous particles, which are not true clailic air : and 

 hence, fay they, a defcending body, meeting continually 

 .with Icfs refiftance from the elailicity of the air, and having 

 the fame force of gravity ftill afting on it, muft neceflarily 

 be accelerated. Hobbes (Philof. Probl. cap. i. p. 3.) at- 

 tributes acceleration to a new impreflion of the caufe which 

 makes bodies fall ; which, on his principles, is alfo the air. 

 As part of this mounts, part alfo muft defcend ; for reafons 

 drawn from the motion of the earth, which is compounded 

 of two motions, one circular, the other progrefTive ; confe- 

 quently, the air defcends, and circulates at once. As the 

 body, in its fall, receives a new preflure in every point 

 in its defcent, its motion, he fays, mull needs be accele- 

 rated. 



But what overturns all accounts where the air or atmo- 

 fphere is concerned, is, that the acceleration holds in vacuo, 

 and even more regularly than in air. See Vacuum. 



The Peripatetic account is worfc than this : the motion 

 of heavy bodies downwards, fay they, ariles Irom an intrin- 



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flc principle, wlu'ch makes thtm fend to the ccntrf, as th. ir 

 proper feat, or clement, where they uould be at nil : liciicff 

 add thiy, the nearer bodies approach to it^ the more in thtir 



motion accclenited. 



The Gafl'cndiib, on the other hand, ho'd that ihe earth 

 enuts a fort of attraclivc elUiivia, innnnKrahIc threads where- 

 of continually afccnd and dtfccnd ; which thre.-.ds, proceed- 

 ing lik^ radii from a common centre, diverge the more the 

 farther they go : fo that the nearer a heav)- bidy is to the 

 Centre, the more of thefe magnetic threads it receives; and 

 hence the more is its motion accelerated. But this is re- 

 futed by an eafy experiment : for if a hall he kt fall out of 

 the lowcft window of a high tower, and alfo out of the 

 higheft, the acceleration will be very nearly the fame in K.th 

 cafes, notwithllanding the greater vicinity to the centre in 

 the one, than in the other cafe. 



Tiie Cartelians accoimt for acceleration, from the repeated 

 pulfcs of a fubtile ethtrial matter, which is continually a(fling 

 on the falling body, and impelling it downward-;. 



After all, the immediate catife of acceleration is rot 

 myilerlous ; the principle of gravitation being once ad- 

 mitted, will determine the b< dy to defcend, and its motion 

 will be accelerated by neceflary confequencc. 



Suppofe a body kt fall from on high : the primary- caufe 

 of its beginning to defcend, is dcnibtlcfs the power of gra- 

 vity ; but when once the defcent is commenced, that ftatc 

 becomes in feme mcafure natural to the bcdy ; fo that if 

 left to itfelf, it would perfevere in it for ever, even though 

 the aftion of the firil caufe fliould ceafe : as we fee in a 

 ftone caft with the hand, which continues to move after it is 

 left by the caufe that gave it motion. 



Bnt, beiide the propenfity to defcerd, imprcffed by the 

 firft caufe, and which of itfelf were fuflicicnt to continue 

 the fame degree of motion once begun, in iiifnitum ; there 

 is a conftant acccffion of fuhfequent eflorts 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 two caufes of motion ; and both afting 

 in the fame direftion, the motion they jointly produce muft 

 neceff;\rily be greater than that of any one of them. — And 

 the velocity thus increafed having the fame caufe of in- 

 creafe ftill periifting, the defcent muft of coutfc be con- 

 tinually accelerated. 



For, fuppofing gravity, whatever it be, to aft uniformly 

 on all bodice, 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 indefinitely fniall : let this gravity 

 incline the body towards the earth's centre, while it moves 

 in the firft indefinitely fmall part of the time of its defcent ; 

 if after this, the aftion of gravity be fuppofed to ceafe, the 

 body would proceed unifonnly towards the earth's centre, 

 with a velocity equal to that which refults from the force of 

 the firll impreflion. 



But now, fince the aftion of gravity is here fuppofed 

 ftill to continue ; in the fecond moment of time, the 

 body will receive a new inipulfc downwards, equal to 

 what it received at firft ; ar.d thus its velocity will be 

 double of what it was in the firft moment ; in the third mo- 

 ment it will be triple ; in the fourth quadruple, and fo on 

 continually : for the impreflion made in one moment, is not 

 at all altered by what is made in another : but the two are, 

 as it were, aggregated or brought into one fum. 



Wherefore, fincc the particles of time are fuppofed inde- 

 finitely fmall, and all equal to one another ; the velocity 

 acquired by the falling body will be evei7 where propor- 

 tioned to the times from the beginning of the defcent j and 

 the velocity will be confequently proportional to the time ia 



which it is acquired. ^, 



Thus 



