486 Professor A. W. Bucker [March 8, 



All ordinary calculations as to the production and mingling of 

 different waves of sound are based upon the supposition that the 

 displacements of the particles of air, or other body through which 

 the sound is travelling, are very small. If this is so, the force which 

 tends to restore each disturbed particle to its ordinary position of 

 equilibrium is accurately proportional to the amount of the displace- 

 ment. 



In von Helmholtz' view, objective combination tones were in 

 general produced when the disturbance was so great that this con- 

 dition was no longer fulfilled. Violence is of the essence of the 

 explanation. Hence the siren, where both sets of holes open into the 

 same small wind chest — the harmonium, in which two reeds alternately 

 close and open slits in the same enclosure, are the instruments best 

 suited to produce them. Of these the siren is the more efficient. 

 Von Helmholtz convinced himself that the combination tones pro- 

 duced by the harmonium are for the most part ear-made. He 

 expressly stated that " when the places in which the two tones are 

 struck are entirely separate and have no mechanical connection, as, 

 for example, if they come from two singers, two separate wind 

 instruments, or two violins " — to which we may add two tuning-forks 

 — " the reinforcement of the combinational tones by resonators is 

 small and dubious." * 



Now this reinforcement by resonators has been altogether denied 

 by most of those who have taken an interest in the matter, while, if 

 an exception is allowed, it is in favour of the beats of a disturbed 

 unison, the observed effects being ascribed to the beats, and not to 

 the difference tone. 



Some writers make no exception whatever in their denial of the 

 objective reality of what may be broadly termed secondary tones. 

 Thus Mr. Bosanquet, who made a most careful series of experiments 

 some fourteen years ago, stated that " the ordinary first difference 

 tone ... is not capable of exciting a resonator. ... In short, the 

 difference tone of Helmholtz ... as ordinarily heard, is not objective 

 in its character." "f 



Prof. Preyer, too, using very sensitive tuning-forks, found that 

 the differential tone given by two forks did not affect a fork the 

 frequency of which corresponded with its own, except in cases where 

 the difference tone was itself a partial of one of the forks. 



It must be remembered that the assertions of Helmholtz as to the 

 experimental proof of the objective nature of the tones were made 

 with reference to those instruments which he regarded as most likely 

 to produce objective notes, viz. the siren and the harmonium, and that, 

 therefore, experiments with forks hardly affect his position. 



Let us now try with the siren whether it is possible to confirm or 

 to disprove the validity of his views. 



* * Sensations of Tone,' translated by Ellis, p. 157. 

 t Proc. Phys. Soc, iv. 1881, p. 233. 



