April 21, 192 1] 



NATURE 



233 



Letters to the Editor. 



[The Editor does not hold himself responsible for 

 opinions expressed by his correspondents. Neither 

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 the writers of, rejected manuscripts intended for 

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The Quantum Theory and Homogeneous Vibrations. 



In the quantum theory as usually presented a finite 

 amount ot energy is associated with a periodic dis- 

 turbance which is called "homogeneous." 1 desire 

 to raise the question whether the use of that term 

 is defensible. Both in optics and in acoustics the 

 word ■■ homogeneity " has acquired a definite meaning 

 which is inconsistent with, its application to quanta. 

 In fact, the affirmation of quanta involves a denial 

 of homogeneity. To avoid misunderstandings and 

 obscurities we must either abandon the hitherto recog- 

 nised definition of that word as applied to oscillations, 

 or avoid its use in the formulation of the quantum 

 theory. I submit that the second alternative is 

 preferable. 



A homogeneous vibration as hitherto understood is 

 unlimited in time, just as a homogeneous wave is un- 

 limited in space ; a disturbance having velocities pro- 

 portional to cos nt is homogeneous only if it applies 

 to all values of t, however great, on the positive and 

 negative sides. As soon as limits are imposed the 

 oscillation ceases to be homogeneous. The radiation 

 of a quantum, if expressed by a circular function, 

 being necessarily limited in time, it follows that 

 homogeneity is impossible. If the velocity of the 

 oscillator be represented by e-*'cosnt, the ex- 

 ponential factor admits quanta because it allows 

 us to assign a finite value to the total energy, 

 but it destroys at the same time the homo- 

 geneity. When analysed practically by the spectro- 

 scope or theoretically by Fourier's theorem, all 

 frequencies are represented, though when k is small 

 nearly the entire energy is concentrated in a narrow 

 region closely adjoining that of the maximum intensity 

 which takes place at frequency */n^ — k^. We must 

 conclude that the radiation associated with a quantum 

 is not homogeneous, though its effective energv is 

 confined to a narrow region of frequencies. If an 

 expression be required to represent the nearly homo- 

 geneous radiation of a quantum, we shall perhaps 

 commit ourselves least to any definite views by calling 

 it simply a "quantum radiation." 



Arthur Schuster. 



Yeldall, Twyford, Berks, April lo. 



Variegation in a Fern. 



In the Croonian lecture (Proc. Roy. Soc, B, 

 vol. xci., p. 368) I said that the prothallia of a 

 variegated Adiantum were entirely green, though the 

 ferns which arise from them may be green, or varie- 

 gated, or white. This statement should be corrected, 

 for I find that though the prothallia look all green 

 when growing on the soil, some of them have lighter, 

 occasionally almost white, patches, which are seen 

 as soon as the prothallia are examined by transmitted 

 light. These patches of cells are sharply defined, 

 usually forming radiating bands widening peri- 

 pherally. In some cases the light tissue is an island 

 of cells entirely surrounded by the green cells. The 

 plastids in the light cells are at least as numerous 

 as those of the green cells, but they are smaller and 

 pale in colour, being mostly a faint green, though 



NO. 2686, VOL. 107] 



sometimes almost colourless. The development of 

 this kind of variegation will need careful study. It is 

 difficult to avoid the inference that genetic segrega- 

 tion does here occur in haploid tissue, but the process 

 is not necessarily postponed, as I suggested, tcf the 

 formation of the germ-cells. 



W. Bateson. 

 The John Innes Horticultural Institution, 

 April 14. 



The "Flight" of Flying-fish. 



I HAVE recently received the following information 

 on the "flight " of flying-fish from Prof. Wood-Jones, 

 the well-known anatomist and naturalist. His con- 

 clusions based on his own observations must carry 

 weight, and, in my opinion, should finally settle the 

 points in dispute. 



David Wilso.n-Barker. 



Many years ago I watched flying-fish daily for 

 hours on end, and I think that observations made, 

 as were mine at that time, from the long overhang 

 of the bow-sheaves of a cable ship are far better than 

 those made by casual observers from the decks of a 

 passenger vessel ; for, in the first place, the observa- 

 tion is made many yards ahead of the cut water, and 

 the fish can be observed swimming just below the 

 water and then breaking its surface and taking 

 "flight"; and, in the second, observations can be 

 taken when the ship is steaming no more than 

 i^ knots. As a result of my spell in cable ships in 

 the Indian Ocean I had no doubt as to the manner 

 of "flight" of flying-fish, and, though directly 

 antagonistic ideas seem prevalent to-day, I still, after 

 a further series of observations, have no doubt that 

 flying-fish gather all their impulse by the lateral move- 

 ments of their tail as they leave the water and then 

 sustain themselves in the air by what would now be 

 termed "planing." 



In order to check my previous conclusions, I made 

 observations and notes on this matter during a 

 journey to Australia last year, and also during a trip 

 to Honolulu and back. On both these occasions I 

 took care to interest any children in the question, for 

 children are commonly good judges in such things. 

 On both occasions I secured a specimen which came 

 aboard, and the accompanying rough figures are 

 made from the dissection of one of these. 



These observations may be summarised as 

 follows : 



(i) Flying-fish when disturbed by an oncoming 

 vessel dart about beneath the surface with the greatest 

 rapidity. Some members of a shoal seek safety by 

 their speed below water with their pectoral fins tight 

 adpressed to their sides ; some with a rush break the 

 surface of the water, spread their pectoral fins, and 

 plane away. 



(2) The impulse is gathered by the final very rapid 

 lateral movements of the tail as the fish leaves the 

 water. 



(3) When the fish springs into the air it quivers 

 all over. This quivering is seen in the spread pectoral 

 fins, but this is not a very rapid wing-stroke — as seen, 

 say, in a drone-fly ; it .is merely the vibration due to 

 the great rush with which the creature cleaves the 

 water. 



(4) Once launched in the air the pectoral fins are 

 spread out as planes and remain motionless. 



(5) Fresh impetus can be gained from time to time 

 by the tail dropping to the water and powerful lateral 

 movements being produced with the enlarged lower 

 fluke of the caudal fin. 



