Ti7o THE EAR. 



guished. 1 These results are a remarkable testimony to the sensitiveness 

 of the ear. 



Konig has investigated the phenomena of beats by large tuning-forks 

 specially devised to produce the purest tones by simple pendular movements, 

 and he has found that with such it is possible to obtain primary and secondary 

 sets or orders of beats, and even beats of high orders. "When two simple 

 tones interfere, the primary beats belong to either an inferior or superior set, 

 corresponding in number to the two remainders, positive and negative, found 

 by dividing the frequency of the higher tone by that of the lower. 2 Thus, 

 suppose two tones having frequencies of 40 and 74. Then 74-^40 = 1+ a 

 positive remainder of 34; or 74 40 = 2 6, a negative remainder of 6. 

 Kbnig finds that if two such forks are sounded there are two sets of beats, 

 one at 34 per second and the other at 6 per second. The inferior beat is heard 

 distinctly when its number is less than half the frequency of the lower 

 primary, but if its number is greater, the superior beat comes out the stronger. 



Beat tones. Much discussion has taken place as to what occurs 

 when very rapid beats fall on the ear. Lagrange and Thomas Young 

 held that they blend into a tone, but Helmholtz and others maintain 

 that this is not the case. It is possible to experience a double sensa- 

 tion at the same time, both of a beat tone and of individual beats ; just, 

 as in listening to a syren, we may, as it were, feel the puffs and hear the 

 beginning of a musical tone. Konig has undoubtedly given strong 

 evidence in favour of the existence of true beat tones. He uses pure 

 tones, instead of the mixed tones of the syren and of reeds. These beat 

 tones are best heard when large forks of high pitch are struck. Thus, 

 take ut 9 = 2048 and re G = 2304. Then 2304 - 2048 = 256 = ut s . Strike 

 ut 6 , then re G , and ut 3 sounds. This is an example of the grave or inferior 

 beat. Again, take i** 6 = 2048 and st' 6 = 3840. Then (2048) 2 -3840 

 = 256, a negative remainder ut 3 , as before. Sound both forks 

 and ut 3 will be heard. Again, take w 6 = 2048 and so 6 = 3072. Then 

 3072 -2048 = 1024 = ^ 5 . Sound ut B separately, so that the sound 

 may catch the ear. Then sound ut 6 and sol^ and we hear ut 5 ringing 

 out. 



Strong as this evidence appears to be, it does not satisfy some 

 observers. Lord Eayleigh, 3 in particular, declares that the question 

 " must still be regarded as an open one," and he states that no evidence 

 has been adduced that the intensity of the beat tone is proportional to 

 that of the generators. 



Audibility as affected by intensity. In considering the action of 

 sound on the minute mechanisms in the cochlea, it is important to take 

 into account the degree of sensitiveness of the ear, both as to ampli- 

 tude and as to energy of vibration. When an open organ-pipe is 

 sounded, there is a condensation and rarefaction of the air, and there is a 

 position of maximum condensation, data regarding which can be deter- 

 mined experimentally. From these data, Topler and Boltzmann 4 con- 

 cluded that " plane waves, of pitch 181, of which the maximum con- 

 densation is 6 '5 x 10~ 8 , are just audible." These observers also stated the 

 matter thus : The ear is affected by vibrations of molecules of the air 



1 Preyer, op. cit. ; Ellis, Proc. M^ls. Assoc., 1877, p. 1. 



2 Konig, "Quelques experiences d'acoustique," Paris, 1882, p. 87. An excellent 

 account of Konig's researches is given by Silvanus P. Thompson, Notices Proc. Roy. Inst. 

 Gr. Britain, London, June 13, 1890. 



3 Rayleigh, op. cit., vol. ii. p. 469. 



4 Ann. d. Phys. u. Chem., Leipzig, 1870, Bd. cxli. S. 321. 



