July 29, 1897] 



NA TURE 



295 



But Prof. Muraoka, in WiedematuC s Annalen, describes, as 

 fohaimiskiifcr, a Japanese insect which undoubtedly is not the 

 Lampyris nocliltica, but a luminous flying insect, very abundant 

 at the end of June. Therefore it would be a Luciola, but a 

 little larger than our famous Luciola ilalica, which appears very 

 numerously in all Italy at the end of June. 



Gemminger and Harold mention in Japan two LucioUt: 

 Luciola japanica, Linn. , and Luciola chinensis, Thunb. , but 

 no kind of Lampyris. Carlo Del Lungo. 



R. Liceo Galileo, Florence, Italy, July ii. 



THE EVOLUTION OF STELLAR SYSTEMS} 



ABOUT a century ago Laplace presented to the 

 world an hypothesis concerning the mechanics of 

 the heavens, basing it on sound dynamical principles, and 

 working it out with that genius which he alone at that 

 time could bring to bear. This hypothesis, grand 

 and general as it was and still is, has made his name 

 familiar to every student of astronomy of to-day ; and 

 the equipment of a modern observatory enables us to 

 observe more minutely the stellar systems (which he 

 could not see, but only imagine), and wonder at his far- 

 reaching mind in expounding such a simple scheme of 

 evolution for them. Modern investigations have neces- 

 sitated, however, a modification of Laplace's original 

 hypothesis. In his time the view was held that figures 

 of equilibrium of rotating bodies were necessarily surfaces 

 of revolution about the axes of rotation, but thanks to the 

 mathematical researches of Jacobi, Darwin, Poincare, &c., 

 this is found now not to be universally true. To-day, for 

 instance, if we consider the revolution of two separate 

 fluid masses so close to one another that they are caused 

 to coalesce and form a rigid system, through tidal distor- 

 tions, then the form of the resulting mass will be dumb- 

 bell shaped, approximating to Poincare's apioid. It is 

 regarding the mutual reaction of two such bodies as these 

 that the author of the volume under consideration has 

 recently made matheinatical investigations, and he has not 

 limited himself to the purely mathematical side of the prob- 

 lem, but has extended the view to the stars in space, which 

 according to the ideas now held are not solid bodies, but 

 masses of matter in which tidal action can have full play. 

 It seems exceedingly probable, he says, "that the great 

 eccentricities now observed among double-stars have 

 arisen from the action of tidal friction during immense 

 ages : that the elongation of the real orbits, so un- 

 mistakably indicated by the apparent ellipses described 

 by the stars, is the visible trace of a physical cause which 

 has been working for millions of years. It appears that 

 the orbits were originally nearly circular, and that under 

 the working of the tides in the bodies of the stars they 

 have been gradually expanded and rendered more and 

 more eccentric." 



Dr. See, in the first of the three chapters which com- 

 poses this volume of inore than 250 pages, gives a short 

 historical sketch of double-star astronomy from the time 

 (1779 of Sir William Herschel down to that of Mr. 

 Burnham. The next three sections are devoted to the 

 solution of several probleins referring to Laplace's 

 demonstration of the law of attraction in the planetary 

 systems, investigation of the law of attraction in the 

 stellar systems and the analytical solution of Bertrand's 

 problem based on that developed by Darboux, together 

 with the solution given by Halphen. The three following 

 sections treat of problems which Dr. See has previously 

 published in the Astrononiischen Nachrichten. In the first 

 of these he develops the theory by which, by a simple 

 spectroscopic observation, the absolute dimensions, paral- 



1 " Re<iearches on the Evolution of the Stellar Systems. Vol. i. On the 

 Universality of the Law of Gravitation and on the Orbits and General 

 Characteristics of Binary Stars." By T. J. J. See, A.M., Ph.D. (Lynn, 

 Mass, VS.X. : The Nichols Press, 1896.) 



laxes, and masses of stellar systems may be immediately 

 ascertained assuming the orbits are known from micro- 

 metrical measurement. In a later chapter he points out 

 how this method may be applied to the best-known 

 doubles. Those most suitably situated for such measure- 

 ments of relative motion are : rj Cassiopeoe, a Canis 

 Majoris, 9 Argus, | Bootis, y Coronie Borealis, 2 2173, 

 70 Ophiuchi, /3 Delphini, and a Centauri. The second 

 section gives us a means of rigorously testing the law of 

 gravitation by comparing the observed motion in the line 

 of sight of a companion with the theoretical value. 



Sections 8-12 are devoted to a survey of the chief 

 methods of determining the orbits of binary stars. 

 Ainong these attention may be drawn to a very simple 

 graphical process of finding the apparent orbit from the 

 given elements. Dr. See also properly brings to the 

 fore that admirable graphical method of solving Kepler's 

 equation which was originally invented by J. J. Waterson, 

 and subsequently rediscovered by Dubois. This method, 

 which Klinkerfues describes in his treatise on theoretical 

 astronomy, and which is used by many continental 

 astronomers, is suited to ellipses of all eccentricities, and 

 can be applied, by the addition of a simply determined 

 correction, to the orbits of comets and planets, giving all 

 the accuracy required. 



As regards chapter ii. much could be written, since 

 this part of the volume extends over 178 pages out of the 

 258, and is of great importance. The author has brought 

 together the detailed researches on the motions of the 

 forty stars whose orbits can be best determined at this 

 epoch. For the completion of this work Dr. See has been 

 able to obtain measurements by double-star observers 

 which have not been previously published, and by this 

 means he has carefully determined independently the 

 orbits of these forty doubles, a piece of work which must 

 have involved an immense amount of labour. In the 

 case of each binary are given the observed measures up 

 to date, the previously determined elements and his own 

 elements, and a comparison of the observed with the 

 computed places. There further follow an ephemeris up 

 to the year 1900, and sometimes up to a later epoch, 

 general remarks on the binary in question, and in each 

 case a plate showing the apparent orbit and the positions 

 of the observed companion. 



As an illustration of one of the orbits, we may mention 

 that of 70 Ophiuchi, as this is of special interest since 

 the motion of the comparison indicates that a third body 

 is probably in question. Several investigators have 

 worked out the orbit of this double, but there seems 

 always to have been a certain amount of dissatisfaction 

 about the resulting ellipse. The figure shows very clearly 

 the wavy line of motion of the observed with the com- 

 puted position. Prof Schur, who made a most rigorous 

 investigation of this binary in 1868 and 1893, discussing 

 400 observations in the latter year, inspired the belief 

 that at length a definite orbit was obtained, but sub- 

 sequent comparison of the observed with the computed 

 positions indicated that there must probably be an unseen 

 body disturbing the elliptic motion. Prof Burnham, who 

 has specially searched for this third perturbatory body, 

 has as yet failed to see it, although he has used the 36- 

 inch Lick refractor in the attempt. 



Coming now to the third and last chapter. Dr. See 

 sums up the results of the researches on these forty 

 binaries. A general glance at the table shows that the 

 elements T, a, ^, /, X have no relation to physical 

 causes; but, in the case of the eccentricities, "a most 

 remarkable law " is established, which is " of fundamental 

 importance in our theory of the origin and development 

 of the stellar systems, and is besides of practical value 

 to working astronomers." Perhaps the following table 

 will best show the number of orbits corresponding to 

 different eccentricities : — 



NO. 1448, VOL. 56] 



