Objective Reality of Combination Tones. 353 



Thus 5 x 16^6 X 9 = 26. But if we are to assume that any 

 pair of partials can thus produce objective tones, the number 

 of combinations will be so great that the fork ought to have 

 been disturbed frequently when the note of the siren was being 

 raised to the required pitch. As a matter of fact, when once 

 the C of 64 vibrations was passed, so that all the partials were 

 higher than the pitch of the resonating fork, no such disturb- 

 ances were ever observed except when the difference- or 

 summation-tone of the primaries was produced. Putting, 

 therefore, all such fantastic combinations aside, the experiment 

 may be regarded as a test whether the summation-tone can be 

 produced when it cannot be due to two partials of the same 

 order. 



When the velocity of revolution was 2-56 per second, the 

 16 and 9 holes gave notes of 40*96 and 23*04 vibrations. The 

 sum of these is 64. The 12 holes were viewed through a slit 

 alternately closed and opened by a fork of 15 vibrations per 

 second, and when the holes appeared to move slowly the 

 summation-tone caused the bands to disappear. 



In this experiment, however, the third partial of the lower 

 note corresponds to 69*12 vibrations, and we thought it 

 desirable to make sure that the disturbance attributed to the 

 summation-tone was not in reality due to this partial. This 

 was the more important, because the difference in the speeds 

 of the siren when the summation-tone and the partial in 

 question corresponded to 64 vibrations was very small. 



Thus, when the speed was 2*56 revolutions per second 

 each of the 12 holes would advance through 30*72 intervals 

 in a second, and since the fork gave 30 views per second the 

 holes would appear to move slowly forwards. 



When the speed was 2*37 revolutions per second the 

 third partial of the lower note (9 row of holes) would be 

 3 x 9 x 2*37 = 64, and each hole of the 12 rows would advance 

 through 28*44 intervals — that is, would appear to recede 

 through 1*56 intervals per second. Thus the partial would 

 be most efficient in promoting disturbance when the holes 

 appeared to go backward with moderate speed. 



The question to be answered was whether these two dis- 

 turbances could be confused with each other. 



When care was taken to keep the pressure in the wind- 

 chest the same whether one or both sets of holes were opened, 

 the effect of the partial produced by the 9 set of holes could 

 hardly be detected. The bands were shaken a little when 

 the row of 12 holes appeared to move backwards, but they 

 did not disappear ; whereas they were completely wiped out 

 by the summation-tone when the two notes were sounded. 



