Sounding of tivo Notes. 523 



largest opening we could certainly perceive, beside the note 88 

 and the very powerful note of the period 16, the two notes 80 

 and 96 ; but they were very faint, and on account of the great 

 roughness of the deep note somewhat difficult to observe. 



In the second arrangement I endeavoured directly to imitate 

 the change of phases in the vibrations in the change from one 

 undulation to another. For this purpose I divided two con- 

 centric circles working close together into 88 parts, and dis- 

 posed the openings which were to produce successive undulations 

 alternately upon the two. As with 88 openings and 16 periods 

 5 J holes would have come upon each of the latter, I always 

 took two periods together, and bored therefore on the first 

 circle the divisions 1, 2, 3, 4, 5, 6, and on the second 6, 7, 8, 

 9, 10, 11 ; then, again, on the first circle the divisions 12, 13, 

 14, 15, 16, 17, and on the second 17, 18, 19, 20, 21, 22, and 

 so on. If these two circles of holes were now blown upon, 

 one from above and the other from below, through two tubes 

 each of the diameter of the largest opening of its own circle, 

 there ensued at each revolution of the disk a series, of 88 iso- 

 chronous impulses, varying periodically 16 times in intensity, 

 which at every change from one intensive period to another 

 changed their signs. In this experiment the two notes 88 

 and 96 appeared much more distinctly than in that previously 

 described with the circle of holes blown upon from one side, 

 which had upon it the periods of holes divided from one 

 another by the length of a half vibration. 



It only remains further for me to mention that Tyndall has 

 cited the slight intensity of the resultant notes as a proof that 

 they cannot have been produced by the beats of the primary 

 notes (On Sound, p. 350). After setting forth clearly 

 that, when two equally powerful notes produce beats, the note 

 always changes periodically from cessation to a doubly greater 

 amplitude than either of the primary notes singly had had, 

 Tyndall says literally: — " If, therefore, the resultant notes were 

 due to the beats of their primaries, they ought to be heard 

 even when the primaries are feeble ; but they are not heard 

 under these circumstances." Now, of course, beat-notes must 

 always have a greater intensity than their primary notes, if 

 vibrations of equal amplitude always produced the same inten- 

 sity in all notes ; but this is not the case, as may be proved 

 by a very simple experiment. If a c tuning-fork, vibrating 

 in the amplitude of 1 millim., is held so far from the ear 

 that the note is barely audible, and if at the same time 

 the same experiment is made with a second, </ fork, whose 

 prongs are of the same thickness and breadth, while it also 

 vibrates in an amplitude of 1 millim., it will be found that 



