B E A 



wtnl, is equal to one vibration or ofciUation, but is not 

 exactly contemporary' villi it, becaufe the latter is counted 

 as commencing at one of tlic extremities of its arc ; where- 

 as the former begins at fnch other degree of it, as the 

 nature of the elcapement determines : u vibration here im- 

 plies either one direit or one retrograde paiTage through the 

 whole arc of a pendulum, and an ofciUation one dire£l or 

 Ol^e retrograde motion of a balance through its whole arc. 

 Hence, in a common clock or watch, the words beat, vi- 

 bration, and ofciUation, are fynonimous terms, when ap. 

 plied as the meafure of the fmallcft fubdivifion of time ; 

 there being a llroke of the lall wheel at fonic part of every 

 nbration or olcillation : but in thofe aftronomical and marine 

 Imic-pieces which have detached efcapements, there is but 

 one beat in two vibrations or ofcillations, the alternate ftroke 

 of the piece which unlocks the detent being ufually filent ; 

 in thcfe machines, therefore, the beato an. Ilower by one 

 luih than in ordinary oneb, notwithllanding the movements, 

 or mtciianilm ot wheels and pinions, may be the fame in 

 both, and the vibrations or ofcillations fimilar. In any horo- 

 logical machine, the number of vibrations or ofcillations 

 which it makes in an hour, is the value of its train, which 

 may be thus determined, viz. " Divide double the produA 

 of all the wheels, by the exaCl produd of all the pinions, 

 and the quotient will be the train univerfally ;" the great 

 wheel and its pinion, however, being ufcd only to regulate 

 tlie period of going after winding up, and to communicate 

 motion, are left out of the calculation. The reafon why 

 the produdl of all the wheels is required to be doubled, is, 

 that one tooth of the lall wheel docs not completely efcape 

 Its pallet in lets than two fucccflive vibrations or ofcillations 

 iu any efcapement. The beats of a pocket watch arc a very 

 convenient meafure of fmall portions of time, and might be 

 applied to many uftful purpofts with advantage, particu- 

 laijy if they were each an exaft fradlion, fuch as J or 

 -J- of the fecond, which they might as cafily be as other- 

 wife. (Vid. Nicholfon's Journal, vol. iii. p. 49 — and 189. 

 and vol. v. p. 46, 4to. Series.) In the bed time pieces or 

 chronometers for determining the longitude, this circnm- 

 ftancc is attended to, and the trains are ufually either 14,400 

 or 18,000, namely, either four or five ofcillations; i.e. 

 either two, or two and a half beats per fecond, by reafon of 

 their efcapements being detached. If the fame attention 

 were paid to the trains of common pocket watches, the 

 frequency of their bents would fit them for nice obfervations 

 in fome of the departments of philofophy, and give them, 

 m this refptft, a preference even over more accurate inftru- 

 nients with Icfs frequent beats : but at prefent, the only at- 

 tention that is paid by the makers to the value of the train 

 of a common watch is, that, for a fmall balance, it nlay be a 

 quick one, and tor a large balance a flow one ; or, in other 

 word;, that tlie momentum of the balance fhall not be too 

 Jmich controlled by the maintaining power, which necef- 

 lai y provifion might be equally attended to, if the beat were 

 made an exaft fraftional portion of a fecond. In any watch 

 the whole train or vibrations in an hour divided by 3600, 

 the feconds in an lu)nr, will give the vibrations per fecond 

 of that watch. See Clock-Movement, Dfad-Beat, 

 EscAPKMrsT, See. 



BrATs, in Mufic, are certain pulfations of two conti- 

 nued founds, as in an organ, that arc out of time, oc- 

 calioned by wairing vibrations that prevent coincidence 

 in any two concords. Tliis phenomenon, which was firil 

 difcovered by M. Sauveur, has not only been defcribed by 

 Dr. Smith in his "Harmonics" but made the foundation of a 

 l5-ftem of temperament. " In tuning mufical inllruments, 

 (fays he, Sed.IV. Prop. X.) efpecialty organs, it is a 

 known thing, that while a confonancc is imperfect, it i: not 



B E A 



fmooth and uniform as when perfect, but interrupted with 

 very fenfible undulations or kills ; which, while the two 

 founda continue at the fame pitch, fuccced one another in 

 equal times, and in longer-and longer times, while either of 

 the founds approaches gradually to a perfect confonancc with 

 the other ; till at lafl the undulations vaniih, and have a 

 fmouth, uniform, confonancc." 



Thcfe beats, the fame author obfcrvcs, are of ufe in 

 tuning an organ to any defired degree of exaitnefs. 



The work of Dr. Smith, though excellent, is far too 

 profound for the perfons moil in want of it : the organ and 

 harpfichord tuners are feldom mathematicians, and to com- 

 prehend tlie doclrines laid down in this book, would re- 

 quire as much fcience as Newton's " Principia". 



Tl'.e beats of two dilTonant organ pipes, rcfenille the 

 beating of the pulfe to the touch : and, like the human 

 pulfe in a fever, the more dilfonant are the founds, the 

 quicker they beat, and the flower as they become better in 

 tune ; till at length they are loft in the coincident vibrations 

 of the two founds. See Viiiration, Temperamtnt, and 

 Tun IN o. 



BEATTIE, James, L. L.D., \i\ Biography, a celebrated 

 moral pliilofopher and poet, was born about 1735, in 

 the county of Kincardine, in North-Britain. His father 

 was in a llation of life no higher than that of a little farmer, 

 a clafs of men fubjcft to much hardfhip and indigence in 

 Scotland. He was, however, poflcfl^td with that laudable 

 fpirit which fo frequently in that country raifts native 

 genius from obfcurity ; and he befl;owed upon his fon a lite- 

 rary education, firft in the parochial fchool of his neighbour- 

 hood, and then in the college of New Aberdeen. The 

 youth was aflifted in his progrefs through the lludies of the 

 latter, by one of thofe fmall exhibitions which have been 

 annexed to it fsr the encouragement of learning ; and it 

 is fuppofed that he fupported himfelf in the intei-vals of the 

 fefiions by teaching at a countiy fchool. For fome con- 

 fiderable portion of his early life, it is known that he afted 

 as a fchoolmafter at Alloa and in Kincardinefliire. At length 

 he removed to Aberdeen, and engaged as afllftant to the 

 mafter of the principal grammar fchool, whofe daughter he 

 married. 



The talent which firft made him known to the world 

 was that of poetry, which he had cultivated from his youth. 

 In 1760, he publiflied a volume of " Original Poems and 

 Tranflations," which in 1765 was followed by " The 

 Judgment of Paris." Thcfe performances were charaflerifed 

 by richnefs and elegance of language and melody of verfifi- 

 cation ; but rather denoted a refined tafte in povtry, than 

 a powerful and inventive genius. They probably brought 

 the author into notice at the place of his refidtnce, but 

 feem to have excited little attention among readers in gene- 

 ra!. 



One of the fi-uits of his rifing reputation was to obtain for 

 himthepatronageof theearlof Errol,whorcfidedin the neigh- 

 bourhood of Aberdeen. Befides other benefits, the influence 

 of this nobleman acquired for Mr. Beattie the honourable 

 fituation of profcflor of moral philofophy and logic in the 

 marifchal college of Aberdeen. In this capacity he next 

 appeared before the public as the author of a pliilofophical 

 work, entitled " An Efliiy on the Nature and Immutability 

 of Truth, in Oppofition to Sophiftry and Scepticifm," 8vo. 

 1760. The progrefs made about this time by Mr. Hume's 

 principles, efpecially ainong his countrymen, could not fail 

 of exciting alarm among the friends of revealed religion. 

 How long Beattie had ranked among thcfe, does not clearly 

 appear. An admired poem of his, " The Hermit," in its 

 firll form ftrongly exprefles that doubt of a future exif. 

 tence which could not be baniflied from heathen philofo. 

 I phy. 



