THEORY OF COMPOUND SOUNDS. 157 



to be combined with time, which combination is wanting in 

 the prefent inftance ; wherefore the coalefcence of founds is 

 impoffible. 



Proportion V*. It may be demonftrated from mechanical Pr0 P» 5* DJf - 



• i i i r- !•/-!• ^ c i ,tin« cotempo- 



principies, that a number of diltmct eotemporary tounds cannot rary f oum } s pr0 . 

 do otherwife than produce diftinct; fenfations. duce diftindt 



In order to make the neceflary diagram as fimple as poffible, 

 let the directions of two eotemporary fets of pulfes be repre- 

 fented by the right lines SM and TN, lying in the fame hori- 

 zontal plane, and interfering in the point A ; alfo, let BCD 

 be the horizontal fection of the hearer's head, made by the 

 fame plane ; and fuppofe the centre of the axis of hearing to 

 be at O; draw OM, ON perpendicular to SM, TN. Now 

 I have (hewn in the preceding paper *, that if a fet of pulfes 

 move in either of the right lines SM, TN, it will excite a 

 fenfation in that part of the head whjch is cut off by a vertical 

 plane, paffing through one of the perpendiculars OM, ON. 

 It alfo appears from the laft proportion, that the impulfes of 

 the vibrating bodies, acting in the lines SA, TA, do not com- 

 pel the particle A to move in any given intermediate direction, 

 as LA. But, according to the fecond propofition, the pofition 

 of the particle A, is fixed in refpect of the planes MO, NO ; 

 that is, though the corpufcle a&ually changes place, in refpe£t 

 of the geometrical point A, it is always found in the interfec- 

 tion of the phyfical right lines SM, TN. Now the two vi- 

 brating bodies continue to act in the directions of thefe right 

 lines, confequently the particle A is conftantly urged in thefe 

 lines by two forces, which, though variable in magnitude, are 

 Combined with time; which circumftance enables the corpufcle 

 to tranfmit the impulfes of one body to M, and thofe of the 

 other to N. What has been demonftrated of the particle A, 

 may be affirmed of any other particle, which is the interfec- 

 tion of two right lines parallel to SM, TN ; in other words, 

 it may be affirmed of two fets of pulfes 5 and the fame de* 

 monftration may be extended to three fets, &c. 



Corollary 1. The fubftance of this and the preceding pro- f hefe propofl- 

 pofition will apply to all elaftic mediums ; hence it happens, {^^co^° 

 that a plate of glafs, &c. in a ftate of vibration, will conduct duded througk 

 a foreign found, whilft it produces one of its own ; for the fohds ' &c * 



* Manchefter Mem. Y. 342, or Philof. Journal, II. 400. 



fame 



