OT* THE GRAVE HARMONICS. 73 



place where two founds meet, receives an agitation different 

 from that whieh is produced by each found ; if therefore the 

 founds are of fuch a nature that their vibrations coincide al- 

 ways after a certain given time, the continued and regular 

 impreflion of thefe compound agitations may be diftinguifhed 

 from the fimple agitations, and an ear fufficiently exercifed 

 will hear a third found, of which the relation to the others 

 may be found by comparing the number of feparate vibrations 

 that each of them completes between two fucceffive coinci- 

 dences, " p. 103. " And the compound agitation may be 



conveyed to the ear in an infinite number of fituations." 



p. 104. " We have already fpoken of the beats of Mr. 

 Sauveur, and we have ken that they correfpond exactly with 

 the coincidences of the vibrations ; there is therefore every 

 reafon to believe that they are formed in the fame manner by 

 the meeting of two founds. And it is probable that the third - 

 found of Tartini is only produced by a feries of thefe beats." 

 P. 105. 



Were the contelr. to be decided by authority, it is probable If the grave har- 

 that your readers would prefer that of Lagrange to Mr. JS^Vm! 

 Gough's and mine united : but we have no occafion for any parifon; unions, 

 thing more than reafon and experiment. If the mind were°f, wh ! ch tl )^, « 



i i r i • /• i • , , ^ vibrations bifeft 



capable ot making up a iound in the way that Mr. Gough each other, 

 fuppofed, we ought to hear, whenever the impulfes of one 0,, S htto g' ve . 

 found bifect either accurately or very nearly, the intervals be- butif theyrefult 

 tween the impulfes of another found, an imaginary note, an from coalefcence 

 octave above the feparate founds: if, on the contrary, my the^undsmuft 

 opinion is true, we muft conclude that the retrograde motions here defrroy 

 of the one will counteract, the direft motions of the other, and each other# 

 that both the founds will be deftroyed. 



Happily the point thus at iffue may be determined by a Experiment to 

 very fimple experiment : we have two founds ftandine: in this f hew J « t] } s 



i • • i • ii ii r ^ latter fa£ ob- 



relation, in the intervals between the beats or two mulical tains in nature, 



chords tuned very nearly in unifon. And if we liflen to a 



grave found which beats very flowly, while it is dying away, 



we (hall obferve, that in the interval of the laft and fainteft 



beats, when the found is leaft mixed by reflections and irre-r 



gular propagations, the note, inftead of riling to the octave, 



is wholly loft. 



I confefs with pleafure, that Mr. Gough 's explanation of The perception 



the refemblance which I have pointed out between the per-? fa faint f ? und 



V r rrom a tuning 



ception fork held be- 



