March i6, 1893] 



NATURE 



459 



the critic should have nearly as much local knowledge as 

 the author, and we pretend to none. To some though 

 not to a great extent the besetting sin of nearly all 

 "Faunists" is evident, and that is the tendency to exalt 

 the importance of the capture of stray individuals, 

 this especially among birds. The occurrence of 

 these wanderers is undoubtedly worth recording ; but 

 that a zoologist should claim consideration for Cumber- 

 land because a Saxicola isabellina was shot there, 

 or for Fumess because a Pelagodroma marina was 

 washed up on Walney, is an indication that he takes 

 rather a narrow view of things — though we are bound to 

 admit that Mr. Macpherson at the same time descants on 

 the merits of the Wheatear as a characteristic Lakeland 

 bird ; and, especially as befits one by descent " servile to 

 Skyey influences ", laments the almost complete absence 

 from the Lakeland seas of the Manx Puffin, due no doubt 

 to its extirpation in the neighbouring island, or its Calf, 

 that gives it an English epithet nowadays inappropriate. 

 Indeed there is no fault to find with our author in his 

 sympathy for the true denizens of his district, and the 

 highest praise is due to him for the labour he has exer- 

 cised, of which almost every page bears witness, in telling 

 their story. To wind up we must add, what perhaps we 

 ought to have said before, that for the purpose of this 

 work " Lakeland " consists of the counties of Cumberland 

 and Westmorland, together with that part of Lancashire 

 known as Lancashire Over-Sands, being identical, the Isle 

 of Man excepted, with the " twelfth Province " of Mr. 

 Watson's Cybele Britannica ; but the want of a map of 

 the entire district is a grievous drawback, for which even 

 the dozen or more excellent etchings, showing as many 

 places of interest, do not wholly make amends. 



THE EVOLUTION OF DOUBLE STARS. 

 Die Entwickelung der Doppelstern-Sysfeme. Von T. J. I 

 J. See. 60 pp. (Berlin : R. Friedlander und Sohn, 

 1893.) 



THE essay which we review is a dissertation for the 

 doctorate of philosophy of Berlin, and the author, 

 Mr. See, is an American, although he writes in German. 



The component stars in double systems appear to be 

 usually of comparable magnitudes, and are found to 

 move in highly eccentric orbits. This case the author 

 holds to be the normal one, whilst the solar system, with 

 its one preponderant mass, and its nearly circular orbits, 

 would be exceptional. 



He attributes the observed high eccentricity of orbit 

 to the influence of tidal friction, and accordingly the 

 greater part of the paper is devoted to the consideration 

 of the results which will ensue from the supposition that 

 each of two bodies raises in the other tidal disturbances, 

 which are subject to frictional resistance. 



If the rotations of the two bodies differ in speed, the 

 problem is an insoluble one, without some postulate as to 

 the law of the frictional resistance. The author is, how- 

 ever, of opinion that sufficient insight may be gained 

 from the solution in the case where two equal bodies 

 rotate with equal speed. This opinion seems justifiable, 

 but it might have been well if the dynamical stability of 

 equality of rotations had been explicitly pointed out. 

 NO. 1220, VOL. 47] 



That there is such stability is clear from the considera- 

 tion that, if one of the bodies rotates more rapidly than 

 the other, it is subjected to a more rapid retardation of 

 rotation, and there is accordingly a tendency towards the 

 restoration of equality. 



The influence of tidal friction on the elements of the 

 orbit of a satellite and on the rotation and obliquity of a 

 planet have been investigated in my several papers, and 

 Mr. See here adapts my conclusions to the case of the 

 double tidal friction of two stars. The adaptation is 

 not difficult, for whilst the rate of change in the rotation 

 of each star remains the same as though the other did 

 not rotate, the rates of change of the elements of the 

 orbit are exactly doubled. Mr. See has then redrawn 

 the curves which exhibit the gradual transformation of 

 the system, and, as might have been expected, finds 

 them to have features closely similar to those of my 

 curves. 



The generality of these solutions is limited by the sup- 

 posed smallness of the eccentricity and of the inclinations 

 of the orbit and of the two equators to the plane of 

 reference. The author, however, then passes to a second 

 case, which is more special in that the equators of the 

 stars remain coincident with the plane of the orbit, but 

 which is more general in that the eccentricity is not 

 treated as being necessarily small. The object is to obtain 

 a numerical solution of the following problem : — Two 

 equal stars, each of three times the sun's mass, revolve 

 in a nearly circular orbit at a distance equal to that of 

 Neptune from the sun, and the rotation of each star is 

 nearly equal to its orbital motion ; it is required to find 

 the greatest mean distance and the greatest eccentricity 

 of orbit to which the system will change under the influ- 

 ence of tidal friction. 



Mr. See solves this problem by methods analogous to 

 those which I have employed, and finds that the mean 

 distance will inc^^ase from 30 (Neptune's distance) to 50, 

 and that the eccentricity will increase from an assumed 

 initial value of one-tenth to a maximum of about three- 

 fifths, which is attained a little earlier than the maximum 

 of mean distance. 



It may be remarked that these results can only be very 

 rough approximations to the truth, because the calculation 

 is conducted on the supposition that the moment of inertia 

 of each star is the same as that of a homogeneous 

 sphere of the same mass and radius, whereas it is obvious 

 that the stars would really be highly condensed spheroids 

 of great oblateness. 



It is to be regretted that the calculation has not been 

 repeated with variations of the assumed initial conditions. 

 It is easy to see that a change in the assumed degree of 

 concentration of the stars would give very different re- 

 sults. Supposing, .for example, the stars had had only 

 half the diameter assumed, the rotational moment of 

 momentum would have had a quarter of its value in Mr. 

 See's example. Now the enlargement of orbit is due to 

 the transference of rotational to orbital moment of 

 momentum, and thus the transferable moment of momen- 

 tum would only have amounted to one quarter of its former 

 value. But the orbital moment of momentum varies 

 as the square root of the mean distance, and hence the 

 enlargement of the orbit could not have been so much as 

 one-sixteenth of its former value. We may feel sure that 



