November 22, 1S94] 



NATURE 



79 



became iuappUcabU, what assumptions became invalid? — why, 

 if Dr. Watson's method of generalised coordinates were valid, 

 the ether, the solar system and the universe generally were not 

 subject to the Maxwell-Boltzmann law, so that the mean kinetic 

 energy of every coordinate in the universe should be the same 

 and so on, insisting that what he wanted to know was w!iy the 

 theory failed, what assumptions were invalid. 



After the other speakers had concluded, Prof. Boltrmann 

 arose to reply, and he took up a perfectly logical position. He 

 said that the theory as it left his hands was a mathematical 

 theorem, a piece of pure mathematics, and that it was for 

 physiiisls to say how far it applied to gases — that the reason of 

 any disagreement between the theory and the facts was "a 

 mystery, as Lord Salisbury had said." 



That appears an unassailable position, and the only mis- 

 apprehension which, so far as I can see, could arise, would be 

 that Boltzniann had admitted not only that his work was a piece 

 of pure mathematics, but that it was nothing; more, a bare 

 theorem without the promise that future adaptations would lead 

 to an even closer accord between the theory and the facts. If 

 such an impression as that has got abroad, Mr. Bryan has done 

 good service in calling attention to the matter. 



There seem many difficulties about the suggestion (made by 

 Dr. I. armor at Oxford, and referred to by Mr. Bryan in his 

 letter) that the spectra of gases need not be explained by the 

 Boltzmann law, as they arise not from molecular but from 

 ethereal vibrations set up by the molecules. Surely if so, the 

 molecules cannot be regarded as an independent system, and 

 Dr. Watson's generalised coordinates must include ethereal co- 

 "rtlinates also, and the Maxwell-Boltzmann law must be 

 ^apposed to hold for matter and ether alike, which does not 

 lOem to get over the difficulty. 



November lo. Edwd. P. Cui-Verwell. 



Homogeneity of Structure the Source of Crystal 

 Symmetry. 



Mr. Barlow's letter on this subject (p. 58) raises a problem 

 of considerable interest, which may be stated in simple words. 



He has inquired in the most general manner possible how 

 anything can be uniformly distributed in space so as to con- 

 stitute a homogeneous system ; the word homogeneous may be 

 taken lo signify that round any one member of the system the 

 distribution of the remainder is the same as round any other. 

 It is not necessary to say that the units of which the system 

 consists are figures or solids, but merely that, whatever the unit 

 may be, it is homogeneously repeated. 



Now repetition may conceivably take place by sliding the 

 unit from one position to another, by rotating it about an axis, 

 by reflecting it across a plane, or by a combination of these pro- 

 cesses ; in other \>ords, by translation, rotation, and inversion. 

 If the last process be excluded, we cannot arrive at all the types 

 of symmetry presented by crystals ; if it be included, we obtain 

 all those types and no others. Therefore the crystal structure 

 is one in which this process is operative. Mr. Barlow himself 

 does not include inveision as a mode of homogeneity, but 

 regards it as an additional property possessed by some 

 crystal structures. Earlier writers have specialised the 

 problem by taking a particular unit. Bravais and Sohncke, 

 for example, to whom the modern treatment of the subject is 

 entirely due, have investigated systems of points. Now the re- 

 flection of a point is an identical point, so that it is useless to 

 introduce the principle of reflection or inversion as distinct from 

 translation in order to derive any one point of such a regular 

 system from another. The same is true of spheres and many 

 symmetrical fi;;;ures, and unfortunately molecules have usually 

 in such investigations been treated as points or spheres or 

 symmetrical figures. 



Mr. Barlow does not consider that his solution of the 

 geometrical problem supplies a theory of crystal structure or 

 settles the question whether the seat of the symmetry is in the 

 arrangement or in the configuration of the molecules. 



But it appears to me that a step of very great importance has 

 been made, for, surely, these investigations prove that the 

 symmetry of such a structure can be entirely explained by the 

 arrangement of the unit?. I would go farther, and a^k whether 

 the result does not suggest that the units which determine the 

 symmetry of a crysial are units capable of repetition by the 

 processes of translation, rotation, and inversion. If this be so, 

 we are not justified in treating them generally as points or as 

 symmetrical figures. 



Many things besides unsymmetrical figures can be conceived 

 which are capable of such repetitions ; for example, a solenoid, 

 a vortex motion, a system of forces in statical equilibrium. 



I would add that Mr. Barlow's investigation cannot be said 

 either to support or to contradict the theories of Fedorow and 

 Schunflies ; it is, as he remarks, purely geometrical, and in this 

 respect is identical with their researches, and leads to the same 

 results. It is true that Fedorow has proposed a theory of 

 crystal structure, but this is only an application of the 

 geometrical principles which he had previously established. 



H. A. MiERS. 



British Museum (Natural History), November 19. 



Gravitation. 



I REGRET that I cannot agree with Dr. Joly's suggestion 

 (vide p. 57 supra) that the curious adhesion which I observed 

 between solids immersed in a stretched liquid, lends itself to 

 any explanation of gravitation on the lines that he indicates. 

 The phenomenon is, and was described by me as, one of 

 adhesion, and not, as Dr. Joly puts it, of attrac/ion, for there 

 was no evidence of any approach of bodies separated by a 

 measurable thickness of liquid, and there is, further, no reason 

 to suppose that the phenomenon would occur unless the medium 

 were already modified in the neighbourhood of the solid sur- 

 faces, i.e. unless a condition which we may provisionally ascribe 

 to gravitation already e.xisted. For this reason Dr. Joly's 

 suggestion appears to me to be an invitation to argue in a 

 circle. 



If there were evidence, which there is not, that the ether 

 round celestial bodies was modified to a great distance, the sug- 

 gestion would, I think, be legitimate, but it would then be 

 necessary to explain the modification. 



Devonport, November 18. A. M. Worthington. 



The Foucault Pendulum Experiment. 



Prof. Greenhill gives currency to quite an erroneous idea 

 in last week's Nature (p. 50). He says " in the Foucault 

 experiment of the pendulum which shows the rotation of the 

 earth, the slightest current of air will destroy and reverse the 

 desired motion ; so that it is advisable in showing the experi- 

 ment to have an elastic ball concealed in the palm of the hand, 

 which can send a slight current of air on the bob of the pendulum , 

 and thus accelerate the initial precession of the plane of the 

 vibration so as to gratify the eyes of the audience and diminish 

 their impatience at the slowness of the motion." If Prof. 

 Greenhill will go to the Western Galleries of the South Iven- 

 sington Museum any day, he will be able to see a Foucault 

 pendulum fulfilling its purpose without being particularly pro- 

 tected from draughts, and without the accessory pufts to which 

 he refers. The pendulum is suspended in a place where people 

 are continually passing to and fro, yet its plane of vibration 

 always rotates in the same direction as watch-hands, or rather 

 the table under the pendulum turns in the opposite direction. 

 I have watched the pendulum dozens of times without seeing 

 it Tail. G. A. R. 



November 19. 



An Observation on Moths. 



An experiment was tried in 1S94, on a number of pupa: of 

 Samia promethea and .Samia cecropia, which brought out a point 

 of which I have seen no mention. When the moth is almost 

 ready lo burst through the thin shell which encloses it, this 

 outer skin becomes dark-coloured and friable, and the insect can 

 often be seen moving wiihin. 



If the enclosing envelope is then removed with a scalpel and 

 forceps, the moth struggles out, apparently as lively as when 

 legitimately hatched. 



The only hitch in the proceedings seems to be in the non- 

 expansion of the wings, the development of which usually lakes 

 place at once. The moth crawls about, like a forlorn penguin, 

 for a period varying from one to three days, when the wings 

 seem to realise the absurd state of affairs, and make a brave 

 effort to fulfil their part of the contract. The effort, however, 

 is only partially successful, for owing to their dry condition the 

 expansion is irregular and incomplete, and the poor moth 

 remains a helpless cripple. 



This would seem lo demonstrate that the wings do not mature 

 as rapidly as the test of the body, and that until complete 

 maturity is reached, no eflbrt towards expansion is made. 



L. C Jones. 



N<^. 1308, VOL. 51] 



