July i, 1922] 



NA TURE 



solution of sodium chloride, were in good agreement 

 with those found bv analysis. Thus in two samples, 

 for example, the totals for chlorine calculated as NaCl 

 were 6-443 and 6-541 ; the totals found were 6-535 an d 

 6-6i grams. Chlorine likewise is apparently as free 

 as in an aqueous solution. 



The writer is at present developing a calcium elec- 

 trode to determine the state of calcium in the blood. 

 Benjamin S. Neuhausen. 



Johns Hopkins University, Baltimore, Maryland. 



The Dimensions of Area. 



In my " Physics," pp. 423-426, it is maintained 

 that it is incorrect to attribute to area (or volume) 

 the dimensions L 2 (or L s ) ; but no example of an error 

 arising from such attribution could be given. It 

 has since occurred to me that an excellent and 

 important example is provided by Child's high 

 vacuum current law, according to which <r, the 



current density, is proportional to f — J -„-■ 



The laws assumed in the deduction of this relation 

 V 

 are (1) - . A =0 . e (Poisson's equation), (2) a . I . A = 



/3 . e . v, (3) m . v- = 7 . e . V, where A and v are area 

 and velocity, and a, (3, 7 formal constants or no- 

 dimensional magnitudes. If in place of A we write 



1-, we find that a 2 Pm{-J y-" is no-dimensional for 



all values of n. The solution is ambiguous and the 

 Child relation is not deducible by dimensional argu- 

 ment, as it clearly ought to be. If, on the other hand, 



we retain A, a 2 l*[ — JV" a is the only no-dimensional 



magnitude independent of A and v ; we obtain a 

 unique and correct result. 



The removal of the ambiguity must be due to the 

 introduction of some additional law. This additional 

 law is that the ratio of the area in (1) to the area 

 in (2) is independent of /, or that / is perpendicular 

 to A in both cases, or that the electrons follow the 

 lines of force. If we omit the important magnitude 

 shape in stating the dimensions of A, this law cannot 

 be introduced into the dimensional argument, because 

 there remains no magnitude to measure direction. 



The additional law is not quite strictly true because 

 of the inertia of the electrons. It follows, therefore, 

 that if the electrodes are arranged so that the curva- 

 ture of the lines of force is very great, small departures 

 from the Child relation are to be anticipated. But so 

 long as the curvature is small, the relation will hold 

 if the systems compared are geometrically similar, 

 differing only in their size I. So far as I know, the 

 relation has hitherto been proved only for parallel 

 plane and concentric cylindrical electrodes ; experi- 

 mentally it is known to be true over a much wider 

 range. Norman R. Campbell. 



19 Holland Park, W.n, June 4. 



The Resonance Theory of Hearing. 



Mr. Ackermann (Nature, May 20, p. 649) is 

 probably correct when he states that the first in- 

 coming sound wave sets all the resonators of the 

 ear temporarily in vibration, and also, that as the 

 sound waves continue the vibrating resonators 

 decrease in number until only those are left in motion 

 that are executing either sympathetic or forced 

 vibration in time with the incoming sound waves. 

 But surely he has left out of account the probable 



NO. 274S, VOL. I io] 



amplitude of the motion performed by the resonators, 

 and the probable physiological properties of the 

 mechanism, when he judges the intensity of the sound 

 stimuli sent along the auditory nerve to the brain 

 to be directly proportional to the number of re- 

 sonators that are swinging at any moment ? 



At the present time we have practically no in- 

 formation concerning the type of response given by 

 the auditory nerve. It may, like certain motor nerve 

 fibres, obey the all-or-nothing law, or it may conduct 

 with a decrement, or it may be graded in its response. 

 But in all these cases the amplitude will be an 

 important factor in deciding the response given by 

 any one hair cell and nerve fibre. But there are, 

 I think, other physiological factors which Mr. 

 Ackermann has overlooked. For although we cannot 

 directly stimulate the hair cells of the cochlea 

 electrically and ascertain the approximate relation- 

 ship between strength of stimulus and strength of 

 response, so that we can demonstrate clearly that 

 the auditory mechanisms have such physiological 

 properties as threshold, latent period, simultaneous 

 and successive contrast (as we can, for example, in 

 the case of the skin end organs), yet we have sufficient 

 evidence that these properties are exhibited also by 

 the auditory mechanism as by the other organs of 

 special sense. Reconsidering now the case that Mr. 

 Ackermann has taken, and assuming as a basis for 

 calculation — 



(a) that the sound wave energy entering the ear 



in unit time is constant ; 



(b) that the pitch is constant ; 



(c) that the mean amplitude of all the resonators 



in vibration at any one time is inversely 

 proportional to the number in vibration ; 

 and 



(d) that the energy available for distribution is 



proportional to the length of time during 

 which the sound waves have been arriving, 

 i.e. that none of the energy entering the 

 cochlea has been lost in eddies, friction, etc.; 



the following table shows the number of oscillators 



in vibration and their mean amplitude : 



It will be seen that after one sound wave 6000 

 resonators are in vibration with an amplitude of 0-003, 

 whereas after 10 sound waves 150 resonators only 

 are swinging with an amplitude of 1. The table 

 shows that there is a rapid increase in the mean 

 amplitude of the vibrating resonators at the com- 

 mencement of a tone. 



There is no pretence of any exactness in the above 

 values. They merelv illustrate the kind of results 

 to be expected. It should be noted further that at 

 any instant those resonators approximately " in 

 tune " with the incoming sound waves will have 

 amplitudes -considerably greater than the mean 

 value, others nearest to those which are coming to 

 rest will have amplitudes less than the mean value. 



