August 19, 1922] 



NA TURE 



247 



Letters to the Editor. 



[The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond -with 

 the writers of, rejected manuscripts intended for 

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 taken of anonymous communications.] 



The Acoustics of Enclosed Spaces. 



The acoustics of enclosed spaces intended to hold 

 large audiences is now receiving attention, and it is 

 recognised that good conditions for distinct hearing 

 can be obtained only by eliminating the reverberation 

 due to reflection from the walls. Owing to the high 

 velocity of the transmission of sound in nearly all 

 solid bodies, the angle at which total reflection begins 

 is small ; for oak wood it is about 6°, and for glass as 

 low as 3 . Unless the wave-front is therefore very 

 nearly parallel to a wall it cannot penetrate and is 

 sent back into the room. The simple and partially 

 effective method of deadening the reverberation by 

 covering the walls with a highly porous material, or 

 woven stuffs, is difficult to apply in large spaces, and 

 a more hopeful solution of the problem seems to me 

 to lie in the discovery of a substance that can be used 

 for the exterior lining of walls and has a velocity of 

 transmission not far different from that in air. 



Unfortunately our knowledge of the velocity of 

 sound in different materials is very scanty. I am not 

 aware that the acoustical properties of the substances 

 most commonly used in buildings, such as stones, 

 brick, and mortar or plaster of Paris, have ever been 

 examined. My suggestion is to look for a suitable 

 material which is transparent to sound and can be 

 backed by highly porous matter which will absorb 

 the transmitted vibration. If necessary, a series of 

 alternate layers may be introduced. In referring to 

 the tables of Landoldt-Bornstein I find that the 

 substance which has a velocity of transmission for 

 sound nearest to that of air is cork. This might be 

 taken as a starting point for further investigation, 

 but there are great gaps and inconsistencies in the 

 tables. 



It is to be remarked that at nearly normal incidence, 

 so long as no total reflection takes place, the posterior 

 surface of the wall diminishes very considerably the 

 intensity of the reflected sound. This is illustrated 

 by the analogous problem in the theory of light. 

 Applying the relevant equations (A. Schuster, 

 " Optics," p. 71) to normal incidence we find for the 

 reciprocal of the intensity of a wave transmitted 

 through a wall: i + jt 2 (i - /x 2 )V/\ 2 , where e is the 

 thickness of the wall, X the wave-length in air, and m 

 the refractive index. It is here assumed that the 

 thickness of the wall is small compared with the wave- 

 length measured inside the wall, which will nearly 

 always be the case. For wood the refractive index 

 is about -i, and for stone it will probably be of the 

 same order of magnitude. Applying the equations 

 and assuming the wave-length to be 250 cm. in air, 

 representing a frequency of 130, we find that a wall 

 one metre thick would transmit. 86 per cent, of the 

 incident sound at normal incidence, and this would be 

 increased to 98-5 per cent, if the thickness be reduced 

 to 10 cm. Apart from absorption, it is to be expected 

 that stone walls are fairly transparent to sound 

 falling normally upon them. But, as has been said 

 at the beginning, sound incident at angles slightly 

 inclined to the normal is totally reflected. 



Some interest attaches to the cognate problem of 

 avoiding the transmission of sound from one room to 

 another. I am not referring to the construction of 

 sound-proof spaces of comparatively small dimen- 



NO. 2755, VOL. I IO] 



sions, such as telephone boxes, where the use of 

 absorbing materials is permissible. But we are all 

 familiar with rooms, more especially in hotels, where 

 everything that is said in one room can be overheard 

 next door. This is generally ascribed to the thinness 

 of the walls. Apart from absorption, which is not 

 likely to be very appreciable in a homogeneous 

 material, no large diminution of the intensity of the 

 transmitted sound should be expected from a moderate 

 increase in the thickness of the walls. The above 

 example shows what may be expected from theory. 

 When we deal with bricks and mortar, or lath and 

 plaster, the want of homogeneity may cause a con- 

 siderable amount of scattering, and this would help 

 in making the increased thickness more effective. 



Unless my information as to our present know- 

 ledge is insufficient, it would appear that experimental 

 investigation of the acoustical properties of materials, 

 with regard to absorption, scattering, and the rate 

 of transmission, are much needed at the present time. 

 Such investigations may also have a theoretical 

 interest, as they would include experiments on sheets, 

 the thickness of which bears a much smaller ratio to 

 the wave-length than we are accustomed to deal with 

 in optics. Arthur Schuster. 



Some Spectrum Lines of Neutral Helium 

 derived theoretically. 



It is well known that, owing to the prohibitive 

 nature of the general problem of three (or more) 

 bodies, Bohr's quantum theory has proved so far to 

 be unable to account for any spectrum lines but those 

 forming a series of the simple Balmerian type, i.e. 



, = KW (i-i), 

 \n ml 



where N is the familiar Rydberg constant given by 

 2ir 2 me i /ch 3 , and k the number of unit charges con- 

 tained in the nucleus, or the atomic number. Apart 

 from X-ray spectra of the higher atoms, for which k 

 is replaced empirically by a smaller and not necessarily 

 a whole number (Moseley, Sommerfeld), and where 

 the requirements of precision are not high, this simple 

 type of formula covers, as a matter of fact, only the 

 spectra of atomic hydrogen (it = 1) and of ionised 

 helium (/c = 2), which, having been deprived of one 

 of its electrons, presents again the same problem of 

 two bodies as the hydrogen atom. Accordingly, 

 the known spectrum series of He + , the ultraviolet 

 Lyman series, the principal or Fowler's series, and 

 the Pickering series, are all of the simple Balmer 

 type, with n = 2, 3, 4 respectively. 



The neutral helium atom, however, with its two 

 electrons, emits an entirely different spectrum con- 

 sisting in all of more than a hundred lines (Prof. 

 Fowler's latest report contains, pp. 93-94. a list of 

 105 lines), some apparently " stray " lines, others 

 arrayed empirically into series strongly deviating 

 from the Balmer type, but all alike baffling modern 

 theoretical spectroscopists. In fact, not a single one 

 of these one hundred or so observed lines has, to my 

 knowledge, been accounted for theoretically, the mere 

 desire of attempting this being paralysed by the in- 

 superable difficulty of the three-bodies problem. This 

 is particularly so in the case of lithium (k = 3) and the 

 higher atoms. 



Now, it has occurred to me that, in the absence 

 of a general solution (in finite form, of course), it 

 may be worth while to try some special solution of 

 that classical problem. 



At first a sub-case of Lagrange's famous solution 

 of 1772 suggested itself, namely, the collinear type 

 of motions, in which the three bodies, in our case 



