j56 THEORY OF COMPOUND SOUNDS. 



perceived by the ear, on which account every particle pre- 

 ferves a fixed pofition in refpeel of this organ and its connec- 

 tions. 



For each corpufcle is confined within the circumference of 

 Thyjica! right a phyfical right line, the diameter of which is determined by 

 &*■ its own abfolute motion. 



Prop. 3. A par- Propofition III. If two founding bodies, affording different 

 te C feaion oftwo notes > a< ^ m conjunction upon the fame particle, through the 

 rows of particles media of two right lines of (imilar particles connecting them 



conveying dif- w \ th it, this particle will be urged at the fame infiant in the 



terent founds, '. ' < Z * _* t . ° . 



will be urged in direction of thefe lines, by two forces having an lnconftant 



thofe lines by ratio. 



their ratS'" 8 ' F° r > ^ ek tne particle A be urged, by the acuter found, in 

 the line SA, and by the graver, in the line TA ; (vide 

 Fig. 2, Plate IX.); then the contiguous particle V, placed 

 in SA, will approach to, and recede from A more fre- 

 quently than W, fimilarly placed in TA, by Prop. I. : conse- 

 quently the force of V upon A will vary in a quicker manner 

 than the force of W upon A ; but this variation of ratio is 

 limited in time ; becaufe it evidently begins and ends with the 

 cycle of the vibrations of the founding bodies, 

 prop. 4. The Propofition IV. The coalefcence of two founds is impof- 

 SSn'tfihe pa°r- flbIe on mechanical principles. 



tide necefTary to For, fuppofe the thing poflible ; then the coalefcence of two 

 Soften "to ^ founds re 4 uires > that a particle of air mould poflefs a motion, 

 fcnpofiible. compounded of the motions which the two founding bodies 



would impart to it feparately ; and that this compound motion 

 fhculd act in a given right line, for an affignable part of time, 

 otherwife it could not excite a fimilar motion in the elaftic par- 

 ticles occupying that given right line. Let A be fuch a par- 

 ticle, and let the conftruclion ufed in the laft propofition, be 

 retained; confequently (Principia, Prop. 2$, Lib. 2.) VA 

 and AW are in the ratio of the forces that act. at any moment 

 in the right lines TA and SA. Make AK as AW, and draw 

 KL parallel to AW, and make it as AV; alfojoin AL; then 

 will the particle A be urged in the direction LA at that inftant. 

 But the ratio of AK to KL varies perpetually, by Prop. III. ; 

 therefore the fpecies of the triangle AKL is equally inconftant; 

 confequently the compound force does not a6t in a given di- 

 rection for an affignable part of time. Now the production 

 and propagation of motion in a given right line requires force 



to 



