December 30, 1920] 



NATURE 



567 



ment official 1 am discreet enough not to venture on a 

 public . discussion of the merits of so controversial a 

 topic as the closure of the Moray Firth. 



December 21. Henry G. MAiRtcK. 



Propagation of a Finite Number of Waves. 



It has been stated as a general proposition by 

 physicists that it is impossible to propagate a finite 

 number of simple harmonic waves without change of 

 type, the reason being that the discontinuity of motion 

 at the beginning and end of the train of waves cannot 

 be represented by a simple sine or cosine function. 



The proposition as stated is too general, and should 

 be qualified. It would be true, however, to say that a 

 finite number of simple harmonic waves cannot be 

 propagated without change of type if the mean pres- 

 sures in the wave-train and in the undisturbed medium 

 are the same. 



That a finite train of waves of unchanging type can 

 actually be propagated in a medium in which the 

 wave-velocity and group-velocity are the same may 

 be seen from the following illustration : 



Let the medium be enclosed in an indefinitely long 

 pipe containing a piston on which a simple harmonic 

 motion of amplitude a may be imposed. Let the 

 medium and piston be at rest when the latter is in one 

 of the extreme positions. If the motion is then 

 started there is no discontinuity either in the velocity 

 or in the acceleration. So long as the motion of the 

 piston is maintained, simple harmonic waves are pro- 

 pagated through the tube in both directions, the mean 

 pressure in one set being p,{i + aj\) and in the other 

 /»,(!- a/A), where p, is thii undisturbed pressure. 



At the moment when the motion is started the pres- 

 sure on both sides of the piston is p„ and this is the 

 maximum or minimum pressure in each wave scries, 

 according as the direction of motion of the piston 

 tends to dilate the medium or to compress it. The 

 necessary increase and decrease of mean pressure in 

 the two wave series are automatically >upplied by the 

 work done by the exterior force which must be applied 

 to the piston to generate the successive waves. If the 

 motion is stopped where the piston is in the same 

 extreme position in which it was started, a finite 

 number of simple harmonic waves afe left travelling 

 alont; the tube in opposite directions. 



.\. Mallock. 



Solar Variation and the Weather. 



Mk. Ci.avion's re|>re>enl.iti<>ii in N.xriRE of Decem- 

 ber c) that, .ipart from seasonal and diurnal changes, 

 the ■' chief, if not the only,'" cause of weather change 

 lies in solar variations overlook-; an important source 

 of variation in the atmosphen- which could not be 

 allowed for on the lines of his investigation. No one 

 will dispute that if Mr. Clayton finally substantiates 

 his correlation results, which have been severely 

 criticised in .America by Dr. C. F. Marvin (Monthly 

 Weather Review, March, iqjo) they will be of great 

 value in forecasting deviations from the norm.il otpar- 

 licular elements, such as temperature and rainfall, in 

 coming seasons. But they will not help us to foresee 

 the actual sequence of atmospheric phases embodying 

 the combination of alt elements which we call 

 weather ; and it is the precise sequence of changes, 

 not the departure of one or more elements from 

 normal during a given period, which, after all, is the 

 primarv aim in weather forecasting. 



It seems almost certain that however closely types 

 may recur, the atmosphere is never twice in the same 

 condition, and this, I believe. i« a prominent convic- 

 tion in the minds of those meteorologists with a 

 lengthy experience of daily weather maps. If a series 

 "f phases in the circulation of the atmi»spherc be repre- 



NO. 2670, VOL. 106] 



sented by .\, Bj C, D, . . ., it is conceivable that by 

 an odd chance there might be a recurrence some time 

 later of the particular phase .A; ; but unless, which 

 seems almost infinitely improbable, all the external 

 forces acting upon the atmosphere at the moment A, 

 are identical with those which were in operation at 

 the moment .A,, there will be no cyclic repetition 

 A, B, Cj Dj . . . to be maintained for a longer or 

 shorter period. In place of the repeating cycle a 

 very different series of phases might emerge ; and it 

 is on this principle that no two seasons are ever alike 

 in the actual sequence of phases. 



In other words, once set a fluid system like the 

 earth's atmosphere in motion and change, it will 

 possess an internal source of variability because iden- 

 tical dispositions of external forces never act upon 

 identical phases. No doubt, with a sufficient number 

 and quality of simultaneous observations, meteoro- 

 logists could so diagnose the condition of the atmo- 

 sphere as to be able to calculate what phase would 

 grow out of a present phase a few hours later; but 

 the prevision of distant phases, w-hich is really at the 

 root of the weather problem, seems at present quite 

 impossible. L. C. W. Bonacina. 



27 Tanza Road, Hampstead, N.VV.3, 

 December 19. 



Name for the Positive Nucleus. 



While the word "hydrion" docs strictly express 

 the meaning conveyed by the symbol H+, yet in the 

 minds of chemists' it connotes all those properties 

 associated with its hampered state in solutions, 

 especially aqueous solutions. Even if hydrion is not 

 hvdrated like other ions, yet there is probably some 

 sort of electrical double layer which modifies its pro- 

 perties. The " wet " physical chemist might abandon 

 his term " hydrion " and the symbol, recognising that 

 the real hydrion (H+) will have entirely different pro- 

 perties if ever these are known. He is in possession, 

 however, and is not likely to do this unless, perhaps, 

 some variant term, such as " hydro-ion," might be 

 found acceptable. The alternative .symbol H is, of 

 course, already to hand, and, indeed, more widely 

 used than H+i which could be left to the physicists. 



In spite of these minor difficulties, it appears to me 

 that Prof. Soddy's suggestion (Nati?re, December 16, 

 p. 502) should be acceptable to chemists, largely 

 bec.'iuse it is provisional in character and avoids the 

 multiplication of words and symbols. .Mthough it 

 expresses a view as to the ultimate constitution of 

 matter which may not prove correct, yet it _ is only 

 the existence of such a view which necessitates a 

 word and a symbol. If the other words suggested are 

 to be taken as entirely non-committal, then the choice 

 of one is less important at present, and, if effected, 

 the word will probablv soon acquire different mean- 

 ings when used bv different schools of thought. 



E. B. R. PRIDRAttX. 



I'niversity College, Nottingham, December 18. 



The Physieal Meaning of Spherical AbwratlM. 



May I rorrert an obvious mistake of mine which I 

 notice in my letter on spherical aberration appearing 

 in Nati-rk of December 0? The second expression for 

 intensity should read : 



I » const X ll I J,faa)eo$ 7^(<i*) \ 



+ {/;.(««>) sin ,. «/(<.»)}*]• 



L. C. Martin. 

 Imperial College, S.W.7, December 17. 



