212 Frofessor Silvanus P. Thampson [June 13, 



corresponding to the positive remainder, the superior beat you cannot 

 hear. I raise the note of the second fork from re^ to mij^ = 80 ; 

 and the beats quicken to 16 per second. Kaising it to fa^^ = 85^, 

 and then to soli = 96, while the first fork is still kept at ut^, the 

 beats increase in rapidity, but are fainter in distinctness. If I now 

 substitute for the second fork a similar one which begins with soli, 

 and raise its pitch to lai= 106| you may be able to hear two beats, 

 the inferior one rapid and faint at 42f per second, and the superior 

 one slower, but also faint, at 21i per second. Still raising the pitch 

 to the true seventh tone = 112, the rapid inferior beat has died out, 

 but now you hear the superior strongly at 16 per second. I raise 

 it once more to si^ = 120 (the seventh of the ordinary scale) and the 

 beats are still stronger and slower at 8 per second. Finally I bring 

 the pitch lip to the octave ut^ = 128, to find that all beats have 

 disappeared ; there is a perfectly smooth consonance. The facts so 

 observed are tabulated for vou as follows : — 



Suppose now, keeping the lower fork unaltered, we raise the pitch 

 of the higher note (taking a new fork tliat starts at the octave) from 

 ut.2 to sol, by gradual steps, we shall find that there begins a new set 

 of primary beats— an inferior set, which are at first slow, then get 



