514 Dr. K. Konig on the Simultaneous 



Tuning-forks for the notes af } e' ', </, c n , with prongs 6 mil- 

 lims. thick, upon sounding-boxes, as they are generally used 

 in physical experiments, notwithstanding their somewhat con- 

 siderable intensity, form only such weak summation-notes that 

 auxiliary forks which give beats with them are necessary to 

 prove their existence beyond doubt. If we possess a series of 

 tuning-forks for the harmonic notes of the fundamental note c, 

 the intervals c? : g' and g' : c" are specially adapted for the proof 

 of the summation-notes by means of the beats, as the aux- 

 iliary forks for these can be easily arranged by untuning, by 

 means of a little wax, the forks of the series mentioned for e' 

 and for the seventh upper note of c. But with such strong- 

 notes as I have made use of, the summation-notes are in them- 

 selves sufficiently loud to be perceived without auxiliary forks. 

 At d :g / (2 : 3) we can distinctly hear e" (5), which with d 

 and <J again forms the summation-notes of the second order 

 7 and 8 (c w ), which makes itself known by boats with the 

 suitable auxiliary forks ; and other auxiliary forks allow even 

 the summation-notes of the third order 2 + 7 = 9 (d'"\ 2 + 8 

 and 3 + 7 (e f// ), and 3 + 8 = 11 to be noticed, though only by 

 very faint beats. In the same way we hear also at c' : e' (4:5) 

 the note 9 = d /f , and by means of the auxiliary forks can prove 

 the notes 9 + 4 = 13, 9 + 5 = 14, and the summation-notes of the 

 third order 17, 18, and 19. Intervals with the fundamental 

 note c' = 512 v. s. are generally the best suited for the observa- 

 tion of the difference- and summation-notes, as in these, on 

 the one hand, the rattle of the discontinuous beats causes little 

 if any disturbance, and, on the other hand, the beat-notes, on 

 account of their great depth, have only a very slight intensity. 



From the observations here given it follows, therefore, that 

 difference-notes and summation-notes can be demonstrated by 

 the simultaneous sounding of simple notes produced from 

 separate sources of sound if these have a very great intensity, 

 but that they are extraordinarily weaker than the beat-notes; 

 so that at the simultaneous sounding of two clangs with toler- 

 ably powerful overtones, in most cases the audible notes, whose 

 vibrations are equal to the sum of the primary notes, will in 

 all probability be beat-notes of the upper notes, and not sum- 

 mation-notes of the primary notes. 

 , These combination-notes are as little reinforced by sounding- 

 boxes as the above-described beat-notes. 



IV. Upon the nature of Beats, and their operation compared 



with the operation of Primary Impulses. 



As the number of the vibrations of the summation-notes 



does not agree with the number of the beats of the two pi 



