342 Prof. Riicker and Mr. Edser on the 



amplitudes of the vibrations of the notes which give rise to 

 them are so great that powers higher than the first have to 

 be considered. He supported this view by mathematical 

 demonstrations, and stated ( c Sensations of Tone,' transl. by 

 A. Ellis, p. 157) that he had proved their objective existence 

 by making membranes and resonators to respond to combina- 

 tional tones produced by the siren and harmonium. These 

 views and statements have been adversely criticised by Konig, 

 Bosanquet, and Preyer. A very lucid account of the con- 

 troversy was given by the late Mr. Ellis in his translation of 

 the Tonempjindiingen, and the net result of the impression 

 produced in his mind is shown by two notes on pages 156 

 and 157. He there states that the result of Mr. Bosanquet's 

 and Prof. Preyer's experiments is to show that the combina- 

 tional tones are produced in the ear itself, and that it is 

 probable that the apparent reinforcement of the resonators 

 noticed by Helmholtz arose from imperfect blocking of both 

 ears when using them. 



These statements were unqualified, and no condition was 

 made as to the way in which the combination -tones were pro- 

 duced. Helmholtz, for reasons which we need not recount, 

 regarded the siren as the best instrument for producing 

 objective combination- tones ; and we recently determined to 

 submit the question of their existence, which seemed to be 

 decided against him, to another experimental test. 



In this paper we give the result of our investigations, as 

 far as they have at present been carried out. We do not 

 regard them as complete, but they at all events prove that 

 when the conditions under which we experimented are fulfilled, 

 there can be no doubt that difference and summation-tones 

 are produced which are capable of disturbing resonating 

 bodies. 



The resonator employed in the first instance was a tuning- 

 fork. It is well known that this instrument is relatively diffi- 

 cult to excite by resonance, and it was therefore necessary to 

 use an extremelv delicate method of detecting whether it was 

 set in motion. For this purpose a mirror attached to one of 

 the prongs was made one of a system by which Michelson's 

 interference-bands were produced. A movement of the 

 prong amounting to half a wave-length of light (say 1/80,000 

 of an inch) would alter the length of the path of one of the 

 interfering rays by a wave-length. A periodic vibration of 

 this amplitude would cause the band to disappear. 



It is therefore evident that an extremely minute movement 

 could be detected. It was at first open to question whether 

 the apparatus would not be so sensitive to accidental dis- 



