490 Professor A. W. Bucker [March 8, 



the upper note of the siren are judged to be in exact accord, the 256- 

 note be also produced, the bands immediately disappear. Sometimes, 

 of course, a small error is made in the estimate of the pitch, and the 

 effect is not instantaneous, but in every case the bands disappear 

 when the beats between the two notes are so slow that they cannot be 

 distinguished. 



It is therefore evident that Helmholtz was right when he asserted 

 that the difference tone given by the siren is objective. It exists 

 outside the ear, for it can move a tuning-fork. 



Konig has shown that in many cases, when two notes are sounded 

 simultaneously beats are heard, as though the most prominent 

 phenomenon was the production of beats not between the two funda- 

 mental notes, but between the upper of these and the nearest partial 

 of the lower note. Inasmuch as these beats are heard when the 

 lower note (as far as can be tested) is free from upper partials, 

 this rule is not the explanation of the phenomenon, but it is a con- 

 venient way of expressing the results. In the experiment just de- 

 scribed, the frequencies of the two notes were in the ratio 12 to 15. 

 The first partial of the lower note (12) is therefore the nearest to the 

 higher tone ; that is to say, Konig's beat tone and the first difference 

 tone are identical. 



It is easy to arrange an experiment in which these conditions are 

 not fulfilled. Thus let the notes be in the ratio 9 : 15. The second 

 partial of the lower note is 18, which is nearer to 15 than to 9 ; hence 

 the Konig beat-tone would have a relative frequency of 18- 15 = 3. 

 If the siren rotates 10*6 times per second, the frequencies of the two 

 fundamental notes are 9x10*6 = 96 and 15 x 10 • 6 = 160 respectively. 

 As before, the difference tone is 64. 



In this case we can use another method of determining the speed of 

 the siren. In 1880 Lord Eayleigh constructed an instrument in 

 which the mass of air enclosed in a tube is excited by resonance, and 

 the fact of the excitation is indicated by a light mirror, which is set 

 where the motion is greatest, inclined at 45° to the direction of the 

 air currents. In accordance with the general law that a lamina tends 

 to place itself perpendicular to the direction of a stream, the mirror 

 moves when the air vibrates. In the original apparatus the amount 

 of the movement was controlled by magnets. Since that date Prof. 

 Boys has modified the instrument by substituting a quartz thread 

 suspension for a silk fibre, and using the torsion of the thread instead 

 of the directing force of the magnets. In a lecture delivered before 

 the British Association, in Leeds, he exhibited the apparatus, which 

 is sometimes called a mirror resonator. Prof. Boys has been good 

 enough to make two of these instruments for me, and for reasons 

 which I will not at the moment enter into, we decided that one of 

 them should respond to 161 vibrations per second. It so happens 

 that this coincides almost exactly w T ith the frequency of one of 

 the notes in the experiment under discussion (160). It is thus 

 possible to use the mirror resonator as an auxiliary instrument to 



