October i;. [918 



NATURE 



125 



membrane into the scala tympani li ma) be due to 

 some oversight on my part, but 1 cannot see how 

 there is a differenci ol pressun on the two sides 

 when the column of liquid i- .1 continuous one. This 



fundamental question in the Wrightson theor; 

 li may further be pointed out that if the vibrations 

 in the liquid to which the basilar membrane responds 

 are the sami a~ thosi ol sound, there is naturally no 

 difficult) with regard to hearing through th< 

 when the stapes has be< ome fixed. 



I n tin li. 



of the basilat ai ting as .1 series ol 1 



t < >r - seem to mi to have forgotten some facts pointed 

 ..in i.\ ll.linhi.il/ himself. The rate of vibration of a 

 string is related, not only to its length, but also to its 

 tension, and there is no reason why the range of the 

 basilai membrane should not be increased i>\ being 

 more tightly stretched at it- narrower end. So fai 

 from it being necessary to have .1 series of separate 

 strings, 1 1. Imholtz demands only that a membrane of the 

 shape of thai of the basilar membran. should bi 

 tightly stretched transversely than longitudinally, and 

 in an appendix to the " Tonempfindungen " in- gives 

 1 compieti mathematical analysis ol the vibration of 

 such a membrane. I regrel that this is beyond. my 

 mathematical capacity, but we may surely accepl it. 

 I'lit McKendrick has shown experimentally thai 

 resonanc is possible in membranes immersed in 

 water, .is would be expected from theory. 



On tin- other si.l.-. Held has stated that a singli 

 fibre of tin' cochleat nervi may supply a compara- 

 tively long stretch ol the basilar membrane— un- 

 doubtedly .1 difficulty in the 1 1. Imln.li/ view. But the 

 menl requires confirmation, and it must be a 

 matter of great difficulty to 



Tlir explanation of the way in which the move- 

 ments of the basilar men altered in direc- 

 tion s,, .1^ I., stimulate tin- hair-cells ; s given very 



clearly by Sit 11 las Wrightson, and 1 havi no 



objections to make to it. On tin other hand, it is 



1 so many t 'orti arches and 



in. ,()in- would have thought that 



a few would suffice to transmit the vibration if it 



s throughout tin- membrane al the same time 



and in iho same form, no analysis taking place. 



sir Thomas Wrightson does nol refer in his book 

 to the interesting experiments ol Yoshii, who found 

 localised lesions in the organ - a result of 



pi olonged 1 tposui ■ in .1 musical note 



Prof. Keith ul the minute 



structure of tin- organ of Corti, ami states that various 

 structui es ci what is demanded by 1 he 



li.in in thai of 1 1 1 Imholtz. 1 would 

 demui s, .111. what in his view that every structure nuisi 

 • ith deference to Pi of. 

 Keith's widr knowledge of tin question. 



It must I..- admitted thai there an- objections to be 



.in I.. Loth theories ; but, hole, il seems 



are no \ ital ones to that of Helm- 



holtz, whereas there are -..111- sir Thomas 



Wrightson unless a satisfactory answei is forthcoming 



to those pointed oul above. W. M. Bayliss. 



University College, London. 



Rainbow Brightness. 



lr would. 1 suppose, bi ult to compute 



theoretically the brightness "i any selected part of a 

 rainbow in terms ..i the -im'» a. mm' brightness. 



Hut ii occurred in me thai wi mi ht compute the 

 relative brightnesses of two selected portions of the 

 primary and the secondary bow, simultaneously- 

 presented and situated along a common radius. 111. 

 luminosities would l..- due to the - le sun, and 1.. 

 raindrops ..f practically the sain, size, so that any 

 NO. 2555. vol.. 102] 



on- would arise from th.- fact that for the 

 primary Low there i- on. internal reflection, but for 



'in secondary tl ire two, and from the fact 1h.1t 



the angular constants diffei lie. difference in the 

 angles will alien both the pol; and the intensi- 



ties ot Mi. lighl reaching th 1 will also 



tsi the iiH adth ol the sei ,v to aboul 



1 t.i of that of the prim.ii \ , 1 1 . . . ; 



1.1 ighl ness ol the s. . ondary. 



But by restricting aiienii.ni 1,, poi io the red 



in each bow, situated along a illinium 1 think 



we may leave out ..I a. 1 ouhl tin- influ i, 



mil, .is. in l.i . .i.ltli 



Lei I'. S di iiiii. the brightnesses of thi 1 * 



-.I'l i.d (along a common radius) from lie 



tin primary and ..f the secondary bow. Then, 



Fresnel's formula-. 



P = 



with u = 



1; 



4 3 



mil the 



" |" rpendi 



Similarh 



20- 



1 gel 



22-40 ' 5220' 



where k is an unknown factor. Thus PS = 2;; for 

 ili. relative brightness of tin- red of the primary to 

 thai ot the secondary, a- viewed l>v the naked eve. 



Now the light of both hows is very considerably 

 polarised in the planes of reflection, which are radial 

 and pass through the sun, the eye, and the element of 

 arc observed. For the primary, 9669 per cent, is 

 polarised in, and only 3-31 per cent, polarised per- 

 pendicular to, the reflection plane. For the secondary, 

 iIh corresponding quantities are .1064 per cent, and 

 ., 36 per cent. 



Through a Nicol prism, placed first so as to trans- 

 in " light, and next -.. .1- to transmit the 

 Hilar" light, we yet for the primary bow . 

 I' in) = . 

 . P 

 1. n 1I1. secondary bow : 



Slill >'= 9 -6 9 . 

 Siperp.) y y 



Thus for the two positions of the Nicol the primary 

 bow is reduced about twenty-nine times, and the 

 -1 1 ondary n< ai lv ten time-. 



I have often experimented on the primary bow 

 and the elemsnt of arc practically disappear- for the 

 second position ol the Nicol. 1 hope to experiment 

 similarly on an element of arc of the secondary bow, 

 which, though losing a smaller fraction of its light, 

 i- originally fainter than the primary, and so may 

 .ils, 1 I..- expected to disappear, though for the "per- 

 pendicular ".azimuth ol the Nicol tie remnanl left of 

 the secondary bow is a trill.- (1-21 times) brighter 

 than that of the primary . 



Finally, we can compan brightnesses of the 



bows, first with th.' Nicol in, and nexl with the Nicol 

 pi 1 1" ndicular to, thi pi ilai ; ition plane : 

 I 1 



S 1 11 

 so thai the relativi brightness with the Nicol slightly 



ceed i, thai in the naked eye, when thi Nicol 



transmits its maximum of each. 



? '"■'I'- -0-83, 

 S-ipi 



so thai the primary bow, as already stated, is sli 

 fainter than the secondary, when each is redui 

 the Nicol to its minimum value. It wool! 

 to tesl these eases by observation. 

 For thi H .1 light 1 gave 2 j j as the ratio 1 

 for the naked eye. But to me the primary bow, 

 viewed generally, appears brighter than this in com- 

 parison with tiie secondary. It i- very difficult to 

 make nnv true corrnarison on account of the varied 

 It we I'i'iv assume that the secondary bow, 



= 2 '49. 



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