552 



NATURE 



[January 22, 1920 



ship, in draughtsmanship and graphical representa- 

 tion, and in the interpretation and explanation of 

 statistical results. In this last field the Director him- 

 self would, of course, be the expert par excellence, 

 and not a mere administrator. It was also pointed 

 out that to put the whole of the work in the hands of 

 a mere administrator would lead to failure. The staff 

 would, of course, include persons who specially studied 

 demography, trade, production, finance, labour and 

 industrial affairs, shipping, railways, tramways, and 

 transport and communication. 



In concluding, the author said that if the United 

 Kingdom, by appropriate effort, were to supplement 

 the efforts of some of the autonomous Dominions, it 

 would be possible to build up a statistical edifice for 

 the whole British Empire which, in meeting the needs 

 of a great people — with its reactions upon the human 

 race — would constitute the bureau a sort of temple 

 expiatoire for our remissness in the past. The key- 

 note of the whole paper was that an important duty 

 has been left unfulfilled, and that we must not go on 

 neglecting it, for such a work is needed by publicists 

 and statesmen, and for the general purposes of intel- 

 ligent criticism and intelligent government. 



ITALIAN PAPERS ON RELATIVITY. 



DR. AITILIO PALATINI, of the University 

 of Padova, Italy, dedicates a special paper 

 (Ac. d. Lincei, April, 1919), entitled "Traiettorie 

 dinamiche dei sistemi olonomi con tre gradi di liberty," 

 to the investigation of what may shortly be called 

 irreversible systems, i.e. systems the Lagrangian func- 

 tion of which contains the velocity (apart from its 

 square) also linearly. The paper is but a generalisation 

 of Birckhoff's investigation on " Dynamical Systems 

 with Two Degrees of Freedom " (Trans. Amer. Math. 

 Soc, vol. xviii.. No. 2, 1917) to three degrees of freedom. 

 The result arrived at is that the trajectories of «uch 

 a system coincide with those of an ordinary system 

 of three particles with appropriate constraints moving 

 in a conservative field of force which spins uniformly 

 about an axis. The analogy with such systems 

 leads Dr. Palatini to take up in a second note, en- 

 titled " Moti Einsteiniani stazionari " (1st. Veneto, 

 May II, 1919), the relativistic problem of what the 

 author proposes to call stationary motions, i.e. such 

 for which the four-dimensional line-element ds' 

 contains non-vanishing, though constant, coefficients 

 S\t, ^2*7 ^31 (coefficients of the mixed, space-time 

 terms, as dx dt, etc.). The chief result is again the 

 equivalence to a three particles system in a uniformly 

 revolving conservative system. It strikes one that this 

 result could be read off the ds' almost directly. The 

 result concerning the "anisotropic and irreversible" 

 behaviour of energy is again obvious and, physically, 

 of comparatively small interest. 



The paper is inspired by Prof. Levi-Civita's recent 

 investigations on static Einsteinian motions (Ac. d. 

 Lincei, 1917, et seq.), for which ^,4, etc., are per- 

 manently zero — elegant investigations, no doubt, but 

 of purely formal interest. 



Dr. Palatini's third recent article, "La Teoria 

 di Relativiti nel suo sviluppo storico " (Scientia, 

 September-October, 1919), which, though not without 

 many happy ideas as to the popular presentation 

 of the "old" (1905) and the new or generalised rela- 

 tivity and gravitation theory, lacks that plasticity and 

 freshness which would be imparted to it by a more 

 intimate contact with existing phvsical ideas. This 

 absence of contact goes in the present case (conclud- 

 ing section of part i., dedicated to the older theorv 



of Einstein) even so far as to ignore the numerous 

 and famous experimental proofs of the variability of 

 mass with velocity. The author does not seem ever to 

 have heard of the beautiful experiments of Kaufmann, 

 Bucherer, Hupka, and others which have made the 

 variability of /3-particles an almost tangible fact. The 

 second part of the article, devoted to general rela- 

 tivity, has the indisputable positive feature of being 

 very enthusiastic, and gives, no doubt, some general 

 idea of Einstein's newest doctrine. Yet even here 

 one cannot help being surprised at one or two mis- 

 conceptions, marring the introductory section on the 

 concept of space-curvature, defects the more inex- 

 plicable as they emanate from a pure mathematician. 

 Thus on pp. 16-17 we are invited to imagine some 

 practically one-dimensional beings or animalcules 

 living in three kinds of capillary tubes, a straight, a 

 circular, and a hyperbolic one (devices not unfamiliar 

 to any reader of the great Clifford). Having endowed 

 these unfortunate beings with a sufficient amount 

 of intelligence, Dr. Palatini (speaking of the first of 

 them) proceeds to say : " In order to arrive from one 

 to another point of its space, the being would state 

 (constatare) that it had to follow the straight road." 

 As if that poor thing had a choice in its one-dimen- 

 sional abode ! Equally misleading is not only the 

 remainder of the historv of these fictitious three beings, 

 but also the presentation (p. 18) of our own concepts 

 of the " spazio ambiente " in which we live. 



Carlotta Longo gives, in her doctorate dissertation of 

 1918 (Padova), published in Nuovo Cimento (vol. xv. , 

 1918, pp. 191-211), a very attractive and geometrically 

 elegant investigation on the elementary electrostatic 

 law according to Einstein's generalised relativity and 

 gravitation theory. She confines herself to the special 

 but most important case of a radially symmetric 

 electrostatic distribution, and, integrating the field- 

 equations in Prof. Levi-Civita's form adapted to the 

 present case, finds for the electrostatic force a l.iw 

 which differs from Coulomb's inverse square law only 

 in so far as the distance r from the centre of the 

 field is replaced by the curvature radius of the geodetic 

 sphere passing through the point in question. ."V 

 further result of the investigation is that, in a 

 radially symmetric field at least, there can be electric 

 charge only where "there is also matter," unless 

 it be a point-charge at the centre (f = o) itself. Tliis 

 striking result would deserve a more definite and 

 critical enunciation. We are not told what kind of 

 " matter " is meant, while, on the other hand, the 

 energv of an electrostatic field is, for Einstein, also 

 a kind of "matter." Yet another very interesting 

 result is reached at the end of the paper. It relates to 

 the " mechanical " force exerted by an electron, if 

 its usual "electromagnetic mass" is assumed to be 

 not only an inert, but also a gravitating- (heavy) mass. 

 The result is that, in addition to the quasi-Newtonian 

 attraction, there is a repulsion, which, however, 

 is comparatively small. Thus, for example, at a 

 molecular distance from the centre the repulsion would 

 be only one-hundred-thousandth of the gravitational 

 attraction. 



The paper is clearly written, and, being very 

 suggestive, will certainly attract the attention of 

 Einstein's followers. Nevertheless, one cannot 

 help mentioning here that an excellent paper on this 

 subject (which pushes the analytical, if not the geo- 

 metrical, solution much farther) was published in 1910 

 bv H. Reissner (Annalen d. Physik, vol. 1.. pp. 106-20). 

 This paper, however, seems to have entirelv escaped 

 the notice of the author, whom nobody will fail to 

 congratulate upon her elegant results. 



L. SlIBFRSTFIN. 



NO. 2621, VOL. 104] 



