~ Lettir refpeBlng Sound and Light, iGj 



13. The vibration of a chord is fcarcely ever performed In the fame plane. Its revolu- 

 tions, and its fubordinate vibrations, may be rendered diftindlly vifible under the mlcro- 

 fcope, Se£l. XIII. 



14. If a chord be infle£led at any point of aliquot divlfion, the harmonic fecondary note 

 correfponding to that divifion will not be audible ; an experiment contradiftory to fome 

 theories of the origin and of the infeparable nature of harmonic founds, Seft. XIII. 



15. The human voice is analogous to the organ pipe denominated from it, which con- 

 fifts of a tongue piece without any commenfurate tube : .and the falfetto is probably formed 

 by the upper orifice of the trachea afluming the funftions of the glottis, Se£t. XV. 



16. A temperament of progreffive imperfedtion is the moft convenient for pradliQal 

 mufic, and is eafily approximated by tuning fix perfedl, and fix equally imperfe<3: fifths, 

 Sea. XVI. 



From the detached nature of the fubje£ls which I have here enumerated, and the imper- . 

 feft (late of thefe branches of the mathematics to which they refer, it would have been in 

 vain to attempt a very perfpicuous and detailed difcuflion of them. My refearches on thefe 

 fubje£ls have been much interrupted, and probably will not be very fliortly refumed ; but 

 if they r.re of no further ufe to any perfon, I fliall not think my labour loft ; for I flatter 

 myfelf that the inferences, which they have led me to draw refpefting the theory of co- 

 lours, will throw new light on all the moft interefting parts of optics, while by a compa- 

 rifon with the obvious inferences from Dr. Herfchel's important difcoverles, they will alfo 

 lead to fome material illuftrations of the phsenomena of heat. 



I ftiall now trouble you with fome remarks In reply to Profeffor Robifon : the paflage to 

 which I allude is this : ' 



" We are furprifed to fee this work of Dr. Smith greatly undervalued, by a moft Inge- 

 nious gentleman in the Philofophical Tranfa£lions for 1800, and called a large and ob- 

 fcure volume, which leaves the matter juft as it was, and Its refults ufelefs and impradi- 

 cable. We are forry to fee this; becaufe we have' great expedtatlons from the future 

 labours of this gentleman in the field of harmonics, and his late work is rich in refined and 

 valuable matter. We prefume humbly to recommend to him attention to his own admo- 

 nitions to a very young and ingenious gentleman, who, he thinks, proceeded too far in 

 animadverting on the writings of Newton, Barrow, and other eminent mathematicians." 

 Encyclop. Brit. Suppl. Art. Temperament, p. 652. 



According therefore to the author of this article, I have In the firft place taken the 

 liberty of giving fevere advice, to a young mathematician who had never alked It ; fe- 

 condly, this advice is equally applicable to my own prefumption ; and thirdly, Dr. Smith's 

 treatife on harmonics Is a work intitled to the higheft pralfe. 



I did in fail endeavour to (hew, that the gentleman in queftlon had overlooked the la- 

 bours of fome former authors relative to his fubjeft, but I accompanied my remarks with 

 nothing like admonition. After obfervlng that at prefent a geometrician may very eafily 

 fancy he has made difcoverles, when the fame fadls were known and forgotten long befort 

 heexifted, I proceeded in thefe words : 



Y 2 « Aa 



I 



