652 



NATURE 



[July 21, 1921 



to actuaries who have practical experience of them 

 that the writer of the article may have thought it 

 too obvious for reference. It is, however, an important 

 aspect of the problem of providing pensions which 

 ought not to be overlooked. 



W. Palin Elderton. 

 Mansion House Street, E.G. 2, July 4. 



[The insurance companies selected by the council 

 of the Federated Superannuation System are not all 

 mutual companies, and, in consequence, there are 

 shareholders and dividends to be taken into account. 

 Apart from this, even among mutual companies such 

 matters as directors' fees, palatial buildings, and 

 highly paid officials are not unknown, not to speak 

 of expenses, often heavy, of advertising. If Mr. 

 Elderton wishes to maintain the position that insur- 

 ance companies are purely philanthropic institutions, 

 we fear he has taken on an impossible task. — Ed.] 



Cup and Ring Markings. 



May I query Mr. Carus-Wilson's opinions in his 

 letter in Nature of June 23 (p. 523)? I have, alas! 

 seen only one case (at Ilkley) of these markings, but 

 have long been interested in the peculiar weathering 

 of mortar which is common on the north side of old 

 buildings near the sea. My view is that it is quite 

 distinct from the cup and rings. The change in 

 mortar is, I suspect, one of adsorptive precipitation, 

 so well explained by Mr. S. C. Bradford in Nature 

 of March 23, 19 16, and elsewhere. 



Fig. I. 



After saturation by rain, when drying takes place 

 the lime forms into parallel lines with^ intermediate 

 spaces, and those sand-grains which are thus robbed 

 of their cement are speedily removed by the wind. 

 The. accompanying photograph (Fig. i) is of an old 

 stable wall built of local sandstones and limestones 

 at the Military Arms Inn, The Nothe, Weymouth, and 

 was taken in 1904. The scale is i/io. I presume 

 the cracks, etc., in old oil paintings are also quite 

 unlike either of the above. George Abbott. 



June 26. 



fact that any combination of confused noises will 

 behave in the same manner, such, for example, as 

 the noise of rustling leaves, escaping steam, a 

 shower of rain on trees or tin roofs, or of a 

 distant train in motion. If one stoops towards 

 the road or approaches a reflecting wall while any 

 of these noises are going on, the pitch of the sound 

 rises, and when one is in the act of standing up, or 

 of withdrawing from the wall, it descends. The 

 grating of carriage-wheels on the road, or rather 

 the noises reflected downwards from the body of the 

 carriage, have a like effect when the observer is 

 standing perfectly still. In this case, however, for 

 some reason not clear to the writer, careful listening 

 shows that the pitch falls as the vehicle nears the 

 observer, and rises as it recedes from him. If the 

 sound is a single continuous note, such as that of a 

 whistle blown by a bicyclist riding past the observer, 

 beats are heard as the whistle advances and also as 

 it recedes, these being due to interference between 

 the direct sound-waves and those reflected from the 

 road. The occurrence of beats in such circumstances 

 is perhaps not generally recognised. 



F. M. West. 

 II Downshire Square, Reading, July 12. 



A New Acoustical Phenomenon. 



With regard to Dr. Erskine-Murray's observation 

 of the behaviour of aeroplane sounds (Nature, 

 June 16, p. 490), attention may be directed to the 



NO. 2699, VOL. 107] 



Magnetism and Atomic Structure. 



On the cubical atom theory developed by Lewis 

 and Langmuir it appears that the molecules of CO^ 

 and N2O have almost identical electron configura- 

 tions. A. O. Rankine has shown from viscosity data 

 that each electron system is equivalent to that of 

 three adjoining neon atoms in line. The writer is not 

 aware that attention has been directed to the fact 

 that the specific susceptibilities of gaseous CO, and 

 NjO are -o-423x'io-° and -0429 x 10-' (Tak6 Son6, 

 Science Reports, T6hoku, vol. viii., p. 162, 1919, and 

 Proc. Phys. and Math. Soc. Japan, vol. ii., p. 84, 

 1920) and their molecular susceptibilities — i8-6xio-' 

 and — iS-8xio-' respectively. 



The electron systems of the two molecules are 

 apparently identical, but the net positive charges on 

 the atomic nuclei are 8—6-8 for CO2 and 7 — 8-7 

 for N2O. If, therefore, atomic nuclei possess rota- 

 tions and are a source of magnetic moment, it must 

 be assumed that the redistribution of the positive 

 charges in the manner indicated involves no change 

 of angular momentum. A. E. Oxley. 



Shirley Institute, Didsbury, Manchester, 

 July 14. 



An Algebraical Identity. 



With reference to the letters in Nature of June 9 

 and July 7 by Dr. G. B. Mathews, Dr. H. C. Pock- 

 lington, and the Rev. J. CuUen on the polynomials 

 Y(x), Z(x) satisfying the identity 



Y(jr)2 - ( - )(^-i>/2Z(jr)2 = 4(.jr^ - i )l{x - i ), 



may I point out that Y(x), Z(x) are tabulated as far 

 as p=ioi in Dr. Hermann Teege's inaugural dis- 

 sertation, " Ueber die ^(p—i) gliedrigen Gaussischen 

 Perioden " (Kiel, Peters, 1900)? Connected with 

 these polynomials there is a further point which, so 

 far as I am aware, has not yet been settled. Wheh 

 x = i and p=.i (mod. 4), Y(x) — Py, Z(x) = z, and 

 />y^-2^ = 4. 



I have verified from Dn Teege's results that (y, z) is 

 the primitive solution of pu^ — f = ^, and consequently 

 i(z+y'/p) the primitive unit of the quadratic field 

 [Vp] as far as ^ = 101; but the question whether this 

 unit is always primitive needs further investigation, 



W. E. H. Berwick. 



The University, Leeds. 



