THEORY OP COMPOUND SOUNDS. 153 



a (ingle found. Thirdly, I have found by making the expe- A number of 



riment, that any number of mufjcal firings may be made to jnto^ Nation by 



vibrate by a compound found acting upon them, provided this the compound 



compound be oceafioned by an equal number of firings with ™." ° . ot . * r 



the former, having one in the latter fet in unifon with each one unifon to each 



in the preceding i'et. This is an experimental proof that there refpeftively. 



are as many fets of pulfes in an aggregate of founds as that 



aggregate contains elements, becaufe no firing whatever is in 



unifon with a concord or difcord. Laflly, if it were poffible If founds coalefce 



for founds to coalefce, men would never hear any thing more™ e . ou , con " 



than one noife at one time : The general hum would have va- varying noife, 



ried perpetually from the extinction of exifling founds, and 



the intrufion of frefh ones ; but the human mind would have 



had no conception of two cotemporary founds ; becaufe the 



ear being in that cafe incapable of conveying the complex fen- 



fation, the idea of fuch an exiflence would have tranfgreffed 



the fphere of human knowledge. The preceding arguments 



are drawn, for the mofl part, from common experience ; and 



they (hew, that the free paffage of cotemporary founds through 



the air may be fafely admitted as an axiom in harmonies. I 



fhall therefore proceed to prove the fame propofition to be 



confiflent with the doctrine of forces. 



The propagation of found through the atmofphere, and the Mechanical 

 nature of aereal pulfes are commonly explained in elementary ar S ume,its « 

 books of natural philofophy ; I fhall, for this reafon, enume- 

 rate only a few particulars; the recollection of which will be 

 found ufeful. 



Propofition I. Two contiguous particles of air which are Prop. i. Vibra- 

 agitated by a vibrating body, either directly or by the inter- 11 . 011 °f the P am - 

 vention of an elaflic medium, receive two motions from each found, 

 impulfe ; firft, an abfolute motion carries them to a greater 

 diflance from the founding body, and afterwards brings them 

 towards it again, both the progrefs and regrefs being per- 

 formed in the time of a fingle vibration : fecond, a relative 

 motion refulting from the former, compels the two particles 

 to approach and recede alternately, which double motion is 

 alfo accomplifhed in the time of a fingle vibration. 



Propofition II. Both the abfolute and relative motions are Prop. 2. The 

 greatefl amongfl thofe particles which are nearefl the founding P articles are not 

 body, and they diminifh as the diflance from that body in- ni yremove 

 f reafes j but, in all cafes, the change of its place too fmall to be 



perceived 



