NATURE OF MUSICAL SOUNDS. \^\ 



to the theory of the grave harmonics. The Doctor obferves, That two unifons 

 that two unifons, the vibrations of which bifect each other, oftaye ^bifa- 

 ought to give the octave, according to my principles. To this ti«n, infifted 

 I take the liberty to reply, that no two perfect unifons P ro ^ uce ^nof fo r ey a 

 a cycle ; because the arrangement, which is given to their firft eycle. 

 vibrations, will evidently prevail to the end of the experi- 

 ment : no points of divifion can therefore be formed for the 

 feparation of the contiguous cycles ; in other words, no cycles 

 will be produced, confequently no imaginary found can be 

 perceived in the courfe of the Doctor's experiment, becaufe 

 the exiflence of the grave harmonics depends upon a fuccef- 

 (ion of minute cycles, if my idea of their origin be correct. 

 The effect of two imperfect unifons will perhaps appear upon Imperftd nni- 

 examination, not lefs unfavourable to the Doctor's objection, { ° ns P roducc 

 than the preceding cafe : confonances of this defcription, it is 

 true, always run into cycles; but then they are too long to 

 give rife to continuous founds, being better fitted to produce 

 beats. For inflance, let two homogeneous cords of equal dia- 

 meters be ltretched with equal forces; and fuppofe their 

 lengths to be 20 and 20,1 inches, then the longer will make 

 200 vibrations, while the fhorter compleats 201. But the 

 cord correfponding to the grave harmonic of this confonance, 

 vibrates but once in the fame time ; therefore the length of it 

 is to 20,1 inches as 200 to 1 ; or it is 335 feet. The diffi- 

 culty of conducting fuch an experiment mufl be obvious to 

 every one ; for whether firings or pipes be ufed, the lower 

 note of this confonance mufl compleat at leafl twelve cycles, 

 or 2 100 vibrations in a fecond ; otherwife a grave harmonic 

 cannot refult from this combination of imperfect unifons. 

 Having now replied to the Doctor's objection, apparently in How the want 



a fatisfactory manner, I may without the imputation of rudenefs, of direction, &c. 



... _ . . J . , > i • , can be recon- 



requelt him to coniider in what way the teveral properties ot c ij ed t0 rj> r . 



thefe fecondary founds are to be reconciled to his fyflem, more Young's fyftem? 

 efpecially their want of a fixed direction : fhould he fail in the 

 attempt, he needs not be reminded that every theory is im- 

 perfect, which explains a part of a phenomenon, but does not 

 embrace the whole of it. The want of direction appeared to 

 me fo plain a proof of the nature of the grave harmonics, the 

 firfl time I made the experiment, that I immediately explained 

 the fact on the principles, which are given at the beginning of 

 this volume of your Journal, without once fuppoiing the theory 

 4 , to 



