THEORY OF COMPOUND SOUNDS. 265 



*ary, as I before omitted to detail the particulars of that au- air or in water 



trior's mifconception, and as Mr. Gough appears wholly to "°f s each other j 

 i 111, ^-^ • i r i • different part j- 



have overlooked the paflage. " Different particles ot the air c i es f the nl ,;,i 

 at the ear" favs Dr. Smitth, " will keep moving conftantly were at the fame 



/». * A & r ,. a a • i* n -i • tlme moved inter 



oppofite ways at the tame time. And m lo rare a fluid as airy e> accor{ ji ng t0 



is, where the intervals of the particles are eight or nine times the refpedtivc 



greater than their diameters, there feems to be room enough un u aaons * 



for fuch oppofite motions without impediment : efpecially as 



we fee the like motions are really performed in water, which 



in an equal fpace contains eight or nine hundred times as many 



fuch particles as air does. For when it rains upon flagnating 



water, the circular waves propagated from different centres, 



appear to interfecl, and pafs through, or over each other, even 



hi oppofite directions, without any vifible alteration in their 



circular figure, and therefore without any fenfible alteration 



of their motions." Harmonics, 1759, p. 105. 



It certainly would have " coft me an effort of ftudy" to de- Whereas the 

 monftrate this, although I could not exadly confider it as the f *™j^ f ' ° u ual 

 " intuitive conclufion of a comprehenfive mind." Such a fluid receive and 

 mind appeared to me to comprehend with equal eafe the dif- trar >fait both 

 tinct and the confuted ; and I am only at a lofs to conceive 

 how the writer of this paflage could ever have compofed a 

 valuable treatife on optics. Mr. Gough's theory differs as 

 widely from this flatement as mine does. My remark on it 

 was this ; " It is furprifing that fo great a mathematician as 

 Dr. Smith could for a moment have entertained an idea, that 

 the vibratious conftituting different founds, fhould be able to 

 crofs each other in all directions, without affecting the fame 

 individual particles of air by their joint forces : undoubtedly 

 they crofs, without difturbing each other's progrefs ; but 

 this can be no other wife effected than by each particle's 

 partaking of both motions. If this affertion flood in need of 

 any proof, it might be amply furnifhed by the phenomena of 

 beats, and of the grave harmonics obferved by Romieu and 

 Tartini, which Mr. Lagrange has already confidered in the 

 fame point of view." Phil. Tranf. 1800, p. 130. 



I have no objection to admitting the whole of Mr. Gough's Sounds may coa* 



propofitions, in the particular cafes which he has confidered • k . ice wh ' ch ar " 

 r r ' l " rive at the ear 



but when he fays that the coalefcence of two founds is impof- in the fame dU 



fible on mechanical principles, he thinks proper to omit the rectionj 



only cafe in which I had afferted its exifience, that is, when 



2 the 



