Objective Reality of Combination Tones. 351 



The pitch of the notes given by the siren was again 

 determined in different ways on different occasions. The 

 summation-tone being produced in the lower box, the 15 row 

 in the upper box was also opened, thus producing a note of 

 15x3*5 = 53*3 vibrations per second. The required speed 

 was determined by making the beats vanish between this 

 note and a Konig's fork tuned to give 53'3 vibrations. With 

 this method it was difficult to keep the speed constant for a 

 length of time sufficient to disturb the resonating fork appre- 

 ciably. When the pitch was altered very slowly the bands 

 disappeared just as the right note was reached, and did not 

 disappear at any other time during the experiment. 



On another occasion the 9 and 12 rows of holes were 

 opened, so that the summation-tone of 64 vibrations would be 

 given when the siren made 3*05 revolutions per second. The 

 18 row of holes was watched through a fork of 27*2 vibrations, 

 so that 54*4 views would be obtained while a hole moved over 

 18 x 3*05 — 54*9 intervals. Hence the right pitch was obtained 

 when the holes moved slowly forwards. The bands invariably 

 disappeared when this state of things was attained. 



On a third occasion the lower cover of the siren was covered 

 with a thin piece of silvered glass as above described, carrying 

 a concentric circle of black paper, the edge of which was 

 divided into 18 equidistant cogs. An image of these was 

 produced on a screen by a lens, and made intermittent by 

 the 27-vibrations fork. The disturbance due to the sum- 

 mation-tone was again and again made evident when the 

 images of the cogs appeared to be moving slowly. In the 

 intervals the bands were beautifully steady. 



The earlier of these experiments were performed before, and 

 the later ones after, the apparatus had been taken down and 

 set up again in another room. They left in the minds of those 

 who saw them no shadow of doubt as to the objective reality 

 of a note corresponding in frequency with the summation- 

 tone. 



We now turn to experiments intended to throw light on 

 the cause of the production of this note. 



Experiment V. 



It has been suggested that the summation-tone may be the 

 difference-tone of partials. Konig (Acoustique, p. 127) 

 remarks that it may occasion some surprise that the particular 

 harmonics whose difference-tone corresponds to the summa- 

 tion-tone should be especially prominent ; but he points out 



