492 



Professor A. W. BiicJcer 



[March 8, 



In an experiment on the summation tone, as the total number of 

 vibrations must not exceed 64, the notes will be too low to be well 

 heard. I shall therefore use a third method of determining the rate 

 of speed of the siren. A mirror attached to the lower plate of the 

 instrument rotates with it. Concentric with, and lying on this, is a 

 circle of paper with eighteen cogs. Light reflected from the mirror 

 passes through holes in two pieces of tinfoil attached to the prongs 

 of a tuning-fork. When the fork is at rest, these holes are super- 

 posed ; but when the fork vibrates, they move apart, are closed by 

 the tinfoil, and only cross each other twice in each complete vibration. 

 The tuning-fork makes 27*2 vibrations per second, and thus allows 

 the light to pass 54 • 4 times per second. But when the siren makes 

 3*048 revolutions per second, the rows of nine and twelve holes 

 give a summation tone of 64 vibrations, and each cog moves over 

 18 x 3*048 = 54*9, or say 55 times the distance between two con- 

 secutive cogs. If the wheel were viewed 55 times a second, the 

 cogs would appear stationary, as in that interval each would be 

 replaced by the next. As they are really seen about 54 * 4 times a 

 second, they appear to move slowly forwards at the rate of about one 

 interspace in two seconds. When this speed is attained the bands 

 disappear, thus proving the objective exsistence of the summation 

 tone. 



We have repeated this observation in various ways, and always 

 with success. The results are summed up in the table. 



It is, perhaps, a drawback that all the notes in these experiments 

 are very low. In order to remedy this, and also to put the matter 

 to the test by means of another instrument, we have employed a 

 mirror resonator which responds to 576 vibrations per second. 



The rows of 15 and 12 holes being opened, notes of 320 and 256 

 vibrations were produced. When they were sounded separately, the 

 noise seemed just to make the resonator move. When they were 

 sounded together, the spot of light was driven off the scale, when the 

 upper note coincided with that of a 320-vibration fork, but immedi- 

 ately returned when this pitch was lost. 



The summation tone of 576 vibrations was also obtained by two 

 other combinations of holes. The 320-fork was used, and the dis- 

 turbance occurred in the one case when the pitch of the upper note 



