494 



NA TURE 



[March 21, 1895 



torsion of the tliicad instead of the directing force of the 

 magnets. In a lecture delivered before the British Asociation, 

 in Leeds, he exhibited the apparatus, which is sometimes called 

 a mirror re-ocalcr. Prof. Boys has been good enough to make 

 two of these isutnimenis for me, and for reasons, which I will 

 not at the moment enter into, we decided that one of them 

 sboald respond to i6l vibrations per second. It so happens 

 that this coincides almost exactly with the frequency of one of 

 the notes in the experiment under discussion (l6o). It 

 is ibns possible to use the miiror resonator as an auxiliary 

 instrument to test the speed of the siien. AVhen the proper 

 note is reached the spot of light will move, and if the diffrrence 

 tone is objective the interference bands ought to disappear 

 simultaneously. We tried this experiment several times. An 

 observer, so placed that he could not see the interference bands, 

 lifted his hand when the spot of light moved. It was quite 

 extraordinary to note the absolute agreement between his move- 

 ments and the behaviour of the bands. 



By throwing the spot of light and the bands near together 

 on the screen, the coincidences can be watched by a number of 

 persons. We have tried whether the diRetence tone is objective 

 in four cases, and in all have delected it by the disappearance 

 of the interference bands. The details of the experiments are 

 collected in the following table. In the fiist two experiments 

 the first difference tone is, and in the last two it is not, co- 

 incident with K'inig's lower beat note. 



Number of holes j 

 in siren. ' 



Difference Tones. 



Frequencies. 



Difference — and 

 Konig's bc:it-tones. 



15 and 12 



16 ,, 12 



IS .. 9 

 18 ., 8 



I Major third 

 Fourth 



I M.ijor sixth 

 Anoctaveand 

 a major tone \ 



32" 

 256 

 160 

 115-2 



256 

 192 

 96 



51-2 



64 

 64 

 64 

 64 



64 

 64 



32 

 128 



Of course the question at once arises, whether, when it can be 

 distinguished separately, Kunig's beat tone is also objective. I do 

 not wish to express a final opinion on this point, but I may say 

 that when the rows of eight and eighteen holes were opened the 

 speed of the siren was increased till the notes corresponding to 

 256 and 576 vibrations were produced. Knnig's rote would in 

 that case have a frequency ol 576 - 2 x 256 = 64. We tried 

 twice to obtain this. On the second occasion, especially, all 

 the conditions were favourable, and the experiment was carried 

 on for a long time. On neither occasion did we obtain the 

 smallest sign ol an effect on the fork and interference bands. 



We must next turn to the summation tone which Ilelmholtz 

 discovered. It has been a'most universally denied that this 

 note is objective. Without going into details, it is only neces- 

 sary to remark that the late Mr. Elli.=, the translator of the 

 "Tonempfindungcn," \»ho took a dispassionate view of the 

 controversy, thought that the position .issumed by Helmhollz 

 had been disproved. To the statement of Helmholtz that "it 

 was formerly believed that the comMnational tones weie 

 purely subjective and were produced in the ear itself," Kills 

 appended the note ; " the result of Mr. Bosanquet's and I'rof. 

 Preyer"s quite recent experiments is to show that they are so." 



Id 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 rcHeclcd 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 superposed; but 

 when the fork vibrates, they move apart, arc closed by the tin- 

 foil, 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 .-. 3048 = 54'9, or say 55 

 times the distance between two consecutive cogs. If the wheel 

 were viewed 55 times a second, the cogs would appear 



NO. 1325, VOL. 51] 



stationary, as in that interval each would le replaced by the 

 next. As they are really seen aboot 54*4 times a second, they 

 appear to move sltwly lonvatds at ihe rate of about one inter 

 space in two seconds. When this sjeed is attained the bands 

 disappear, thus proving the objective existence of the sum- 

 mation tone. 



We have repeated this observation in various ways, and 

 always with success. The results .trc summed up in the table. 



Summation Jones. 



Numbers of 

 holes in siren. 



10 and S 

 •2 ,, 9 



16 .. 9 



Interval. 



Major third 

 j Fourth 

 Minor seventh 



Frequencies. 



35-5 



56-57 



40-96 



28-4 



27-43 



2304 



Sum. 



64 

 64 

 64 



It is, perhaps, a drawback ihat all the notes in these experi- 

 ments are very low. In order to remtdy this, and also to put 

 the ni.itler to the test by means of another inst'ument, 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, lie noise seemed just to make the resonator move. 

 \\ ben they were sounded together, the spot cf light was driven 

 oft the scale, w hen the upper note coincided with that of a 320- 

 vibration fork, but immediately returned when this pitch was 

 lost. 



The sutrmation lone of 576 vibrations was also obtained by 

 two ether c< mbinaticns of holes. The 320-'oik was used, and 

 the disturlance occurred in the one case whtn the pitch of the 

 upper note given by the siren was nearly the seme as before, 

 and in ihe other case when it was about a tone higher. 



The results are sun.ined up in the table. 



Summation Tones. 



Numbers of 

 holes in siren. 



15 and 12 



16 ,, 12 

 16 ., 9 



lnte^^'aI. 



Major third 



Fourth 

 Major sixth 



Frequencies. 



329-«S 

 360 



256 



24685 



216 



Sum. 



576 

 576 

 576 



I venture to think that these experiments prove the accuracy 

 of von He!mh( II2. They show th.it the siren, at all events, 

 dees prcduce objective tones, the frequencies ol which coincide 

 with those of the fust difference nrd summation tones, .ind that 

 this slaitinent is valid as regards ihe difTeri nee tone, whether 

 it is or is not coincident with Kunig's beat-tone. 



I have now in one single case tried to convey to you some 

 Idea of the complexity of the problems with which von 

 Ilelmholtz dealt. He was the first man who detected a 

 relation between the surging mass of partials and combination 

 tones and our sensations of concord and di.scord. The main 

 facts of his theory are, I believe, generally accepted. On some 

 points modern opinion has tended lo stray from his views ; one 

 of these we have studied afresh this evening. 



It was the fact that I had to deliver this discourse which led 

 me to invesligale the (jucslion anew, and therefore I fell 

 bound to tell you the results we have at present attained. Had 

 it not been for this, I should not have |)ublishcd them as yet. 

 We have several improvements of the apparatus in view. 

 We do not pretend to have covered the field. I do not, there- 

 fore, wish 10 generalise. My object has been to refute hasty 

 generalisations. I am conicnt if I have convinced ygU, as I 

 have convinced myself, that Helmholtz w.is correct in stating 

 that the siren produces oljectivc tones, whose frequencies 

 arc equal to the sum and diflerence of their ])rimaries, and 

 that the methods we have employed have brought to light no 

 facts < p[ oscd to his view that these notes cannot be explained 

 as secondary effects of partials, but as phenomena of the first 

 order — in other woids, as real combination tones. 



But brief space now remains to discuss the vast remainder 

 of his work, and as I have already published an appreciation 



