May 2, 1892.J 



KNOWLEDGE. 



S3 



vary inversely as the fifth ■ power of the distance from the 

 centre. Such a medium would give a resistance that 

 would just annul the changes arising from tidal friction. 

 Now, Laplace has shown "^ that the action of a resisting 

 medium increasing in density towards the centre, according 

 to any law whatever, causes the major axis and the 

 eccentricity of the orbit of a revolving body to diminish. 

 Therefore, tidal friction must cause the major axis and the 

 eccentricity of the orbit to increase. ' 



The mathematical investigation to which we have 

 referred indicates that the double-stars have arisen from 

 double nebula^,' which are certainly in general figures of 

 equilibrium rendered stable by rotation, as is shown by 

 comparison with figures of similar form mathematically 

 established by Professors Poiucare and Darwin. It also 

 appears that the orbits of the double-stars were originally 

 nearly circular, and necessarily so, because of the very 

 slow process by which double nebulffi separate under 

 gravitational contraction and increasing angular velocity 

 of rotation, whereby a division is accomplished closely 

 resembling-' fission "among the Protozoans, j The resulting 

 masses seem to be comparable and often nearly equal, and 

 this result is in accordance with what we find to be the 

 case among the double-stars. In the course of immense 

 ages the nebulae have condensed into stars, while secular 

 tidal friction in the enormous nebulous masses (for a long 

 time comparatively close together) has expanded the 

 orbits and rendered them very eccentric. The high 

 degree of eificienoy of tidal action in the stellar systems 

 results from the large mass-ratios of the component bodies, 

 their state of fluidity, and their enormous absolute masses 

 (frequently several times surpassing that of the Sun) 

 moving at distances such as the larger planets of our own 

 system. It is shown that if the masses were separated as 

 we have supposed the eccentricity of the orbit would at 

 first slightly diminish, then increase until a high maximum 

 is attained, after which it would again diminish (when the 

 stars have become entirely dark). 



The stellar orbits are on the average more than twelve 

 times as eccentric as those of the planets and satellites. 

 The mean eccentricity of the Gi orbits now roughly known 

 is 0-48, while the corresponding mean for the orbits of the 

 eight great planets and their twenty satellites is less than 

 0-038'J. The orbit of y Virgmis is known with great 

 precision, and here we have the remarkable eccentricity of 

 0-9 ; and the very trustworthy orbit of Sirius. just computed 

 by Dr. Auwers, has the very considerable eccentricity of 



* If ij he tlie density of the medium, p the radius vector, and k 



some constant, then the resistance R varies as " (T y3, but ^2 varies as 



— , ; therefore E varies as -^. The disturbing force F varies as-:;. But 



p' p-" ^ P' 



K must be made equal to F, hence we must suppose c varies as 



\. Then R = F = '. 

 p' P'. 



t Mecaiiiqtte Celeste. Liv. X., Ch VII , Sec. 18; or Watson's 

 ■■ Theoretical Astronomy." p. 552. 



X Wc may add that the increase will usually continue until the 

 rotations of both stars are nearly exhausted, after whicii the eccen- 

 tricity will be reduced by the libratory motion of the sj stem, and the 

 orbit will at length become circiUar. The stars, however, would then 

 perhaps be entirely dark, and hence, if in the immensity of space any 

 such dark rigid double-star systems exist, they cannot be observed. 

 Other relations of rotation and revolution, and various other viscos- 

 ities, give rise to various other results ; but the conclusion above 

 reached is that of chief interest in connection mth the great multi- 

 tude of double-stars hitherto discovered. 



% It is easy to show that double-stars have not been formed by the 

 approach of separate stars (which would describe hyperbolas or 

 parabolas), and hence the double-star systems must have had a 

 nebulous origin. 



§ See also the writer's papers in the Obserrnforii for Februarv and 

 March, 1891. 



0-63. From a number of other orbits whose eccentricities 

 are very well determined the fact seems certain that the 

 double-star orbits are generally highly eccentric, though 

 some few appear to be more circular, in accordance mth 

 the theory of tidal evolution under what are perhaps rather 

 abnormal conditions. Therefore we have in the general 

 elongation of the double-star orbits a visible trace of the 

 action of secular tidal friction, which has played so 

 important a part in the evolution of the stellar systems 

 mainly because of the large mass-ratios of the component 

 bodies, and their comparative proximity during immense 

 ages ; for it must be remembered that double-stars, now 

 condensed and widely separated, were millions of years ago 

 much closer together and more expanded in volume, and 

 hence the tidal action was then very much greater than at 

 present. 



Fig. 3. — A. Circle. B. Mean planetary orbit. ('. Mean stellar 

 orbit. D. Orbit of y A'irginis. E. Parabola. 



Investigation of the double nebuht seems to indicate 

 that double-stars were not formed as rings, but as 

 globular masses ; and since the process of separation thus 

 disclosed would seem to be the normal form of celestial 

 evolution, some doubt is thrown upon Laplace's theory of 

 ring-formation as applied even in our own complex and 

 remarkable system, composed of a gi-eat number of very 

 small planets and satellites moving in nearly circular orbits 

 about central bodies of a much higher order of mass. It 

 seems hardly credible, and yet it is a fact, that our Sun has 

 750 times the mass of all his attendant bodies combined ; 

 the matter of the solar nebula has therefore gone nearly 

 altogether into the Sim, while the planets and satellites are 



