VIBRATION. 



tion of a bodyi e. g. a pendulum ; wliich, being fufpended 

 at freedom, fvving.s, or vibrates, firft this way, then that. 

 For the bob being raifed, falls again by its gravity ; and 

 with the velocity thus acquired, rifes to the fame height on 

 the other lide ; whence its gravity makes it fall again : and 

 thus its vibrations are co"tinued. 



Mechanical authors, i.. lieu of vibration, frequently ufe 

 the term ofctllalion ; which fee. 



The vibrations of the fame pendulum are all ifochronal ; 

 that is, they are performed in equal time, at lead in the 

 fame climate : for, towards the equator, they are found 

 fomewhat flower. See Pen'dulum. 



A pendulum 3 feet 3,-5 inches, according to Huygens, or 

 39.25 inches, according to lir J. Moor and lord Brouncker, 

 vibrates feconds, or makes 3600 vibrations in an hour. 



The vibrations of a longer pendulum take up more time 

 than thofe of a fhorter one, in a fubduple ratio of the 

 lengths. Thus, a pendulum three feet long will make ten 

 vibrations, while another nine inches long makes twenty. 

 For 10 is the half of 20, and 3 feet, or 36 inches, are the 

 fquare of 6 inches; which is double of 3, whofe fquare is 9 ; 

 fo that 10 is to 20 in a fubduple ratio of 36 to 9. 



The fame thing is meant when we fay, that the number 

 of vibrations of pendulums, in a given time, is in a reci- 

 procal fubduple ratio of their lengths. 



The following table (hews the number of vibrations in a 

 minute, correfponding to pendulums of different lengths, 

 exprefled in inches. 



M. Mouton, a pried of Lyons, wrote an exprefs treatife 

 to fhew, that, by means of the number of vibrations of a 

 given pendulum, in a certain time, one miglu eftablifli an 

 univerfal mcafure throughout the whole world ; and fix the 

 fevcral meafures in ufe among us, in fuch manner, as that 

 they might be recovered again, if at any time they fhould 

 chance to be loil, as is the cafe of mod of the ancient mea- 

 fures ; which we now only know by conjefture. See 

 Univerfal Measurf and Standard. 



The vibrations of wjlnlched chord, or firing, arife from its 

 elafticity ; which power being of the fame kind with that 

 of gravity, the vibrations of a chord follow the fame laws 

 as thofe of pendulums : confequently, the vibrations of the 

 fame chord equally ftretched, though they be unequal in 

 length, are equidiurnal, or arc performed in equal times : 

 and the fquares o£ the times of the vibrations are among 

 themfelves, inverfely, as the powers by which they are 

 equally bent and infleftcd. (See Chord and String.) 

 On this fubjeft, fee Young's Philof. vol.ii. p. 546. 



The fouiuliiig body in aftion quits its tranquil date by 

 flight, but fenfiblc and frequent undulations, each of which 

 is called a vibration. Thefe vibrations, communicated to 

 the air, convey to the ear, by that vehicle, the fenfation of 

 found ; and this found is grave or acute, in proportion as 

 the vibrations are more or lefs frequent in the fame time. 

 Sec Sound. 



The vibrations of 1. Jlrivg (which fee), too, arc propor- 

 tionable to the powers by which it is bent : thcfe follow the 

 fame laws as thofe of the chord, or pendulum ; and, confe- 



7 



quently, are equidiurnal ; which is the foundation of fpring 

 watches. 



For Pythagoras's account of the doftrine of vibrations, 

 fee Pythagoras^. 



Vibrations are alfo ufed in Phyfcs, &c. for divers 

 other regular alternate motions.- Senlation is fuppofed to 

 be performed by means of the vibratory motion of the con- 

 tents of the nerves, begun by external objcdls, and pro- 

 pagated to the brain. 



This doftrine has been particularly illuftrated by Dr. 

 Hartley, and extended farther by him than by any other 

 writer, in edablifliing a new theory of our mental opera- 

 tions. The dotlrine of vibrations, and its ufe in explaining 

 our fenfations, are comprifed by this writer in the following 

 propoCtions : that the whole medullary fubdance ot the 

 brain, fpinal marrow, and the nerves proceeding from tiiem, 

 is the immediate inllrument of fenfation and motion : that 

 this white medullary fubdance of the brain is alfo the imme- 

 diate indrument by which ideas are prefented to the mind ; 

 or, in other words, whatever changes are made in this fub- 

 dance, correfponding changes are made in our ideas, and 

 •vice verfa : that the ienfations remain in the mind for a Ihort 

 time aftej- the fenfible objects are removed : that external 

 objefts impreffed upon the fenfes occaiion, fird in the nerves 

 on which they are iniprefied, and then in the brain, vibra- 

 tions of the fmall, and, as one may fav. inlinitefimal, me- 

 dullary particles : that thefe vibrations are excited, propa- 

 gated, and kept up, partly by the ether, »'. e. by a very 

 fubtile and eladic fluid, and partly by ihe uniformity, conti- 

 nuity, foftnefs, and aclive powers of the medullary fubdance 

 of the brain, fpinal marrow, and nerves ; which Dr. Hart- 

 ley fuppofcs are rather folid capillaments, according to fir 

 liaac Newton, than fmall tubuli, according to Boerhaave : 

 and that the phenomena of fenfible pleafurc and pain, and alfo 

 thofe of flecp, appear to be very fuitable to the doftrine of 

 vibrations. Hence he proceeds to cdabiifli the agreement of 

 the doftrine of vibrations with the phenomena of ideas. Sen- 

 fations, he fays, by being often repeated, leave certain vediges, 

 types, or images of themfelves, which may be called fimple 

 ideas of fenfation ; becaufe the mod vivid of thefe ideas are 

 thofe where the correfponding fenfations are mod vigoroufly 

 imprefled, or mod frequently renewed ; whereaSj it the fen- 

 iation be faint or uncommon, the generated idea is alio faint 

 in proportion, and, in extreme cales, evanefccnt and imper- 

 ceptible. The ex aft obfervance of the order of place in 

 vifible ideas, and pf the order of time in audible ones, may 

 likewife fervo to ihew, that thcfe ideas are copies and ofT- 

 fprings of the imprclfions made on the eye and ear, in which 

 the fame orders were obferved refpeftively : and though it 

 happens that trains of vifible and audible ideas are prefented 

 in fallies of the fancy, and in dreams, in which the order ot 

 time and place is dilFercnt from that of any former impref- 

 fions ; yet the fmall component parts of thcfe trams are 

 copies of former impreflions j and reafons may be given of 

 the varieties of their compofitions. Seufory vibrations, by 

 being often repeated, beget, in tlie medullary fubdance of 

 the brani, a difpofition to diminutive vibrations, which may 

 be alfo called vibraliundes and miniatures correfponding to 

 themfelves refpeftively : fo that if it be allowed tiiat ori- 

 ginal imprefled vibratory motions leave a tendency to minia- 

 ture ones of the fame kind, pLice, and line of direftion, 

 this author infers, that fenfations mud beget ideas, not only 

 in the fenfes of fight and hearing, where the ideas are (uffi- 

 ciently vivid and didinft, but in the tliree others, fince (heir 

 fenfations are alfo conveyed to the mind by means of vibra- 

 tory motions. 



Any fenfations, fays Dr. Hartley; by being affociated with 



