April, 191J. 



KNOWLEDGE. 



131 



periodic time of revolution the total mass of a 

 binary system may be obtained from the extension 

 of Kepler's third law, assuming the motion due to 

 an action of a gravitative character. Let M t and M 2 

 be the masses of the two components respectively, 

 M and in the mass of the Sun and Earth. 



Then 



Mi + Mi = 



R :1 



-11 



where T = Earth's period of revolution = 1 year and 



R = the semi-axis major of its orbit, the astronomical 



unit ; a and p being the semi-axis and periodic time 



respectively of the stellar system. Thus our formula 



becomes ., 



Mi + Mt = -^r 

 P 



giving the mass of the system in terms of the Sun's 

 mass as unity.* Thus we find the masses of many 

 of the binary systems are comparable with that of 

 the Sun, some being rather smaller, others consider- 

 ably greater. 



Of fifty-three orbits of spectroscopic binaries dealt 

 with by Dr. See, he finds that the mean eccentricity 

 of these orbits is considerably less than that of the 

 visual binaries, being only 0-23 instead of 0-5, as 

 for the latter, a point which has important bearings 

 on Cosmogonic theory. The average period for 

 these fifty-three systems is about thirty-seven days, 

 but if we exclude a few long period stars, the 

 average period of all the rest is about ten days. 

 From the formula , 



M! + M a = ~ 



p~ 



assuming the average mass of the spectro- 

 scopic binaries to be about the same as that 

 of the visual ones, and taking M 1 + M 2 = 1, 

 we find the average value of the mean distance 

 to be 0-2173 astronomical units, when p = 37 

 days or 0-09 when p = 10 days. Thus the average 

 dimensions of these orbits are less than that of 

 the planet Mercury, and it seems probable that 

 for such orbits the efficacy of tidal friction as 

 a possible agency in changing their forms may 

 not be overlooked. The late Sir George Darwin, 

 whose recent death we have to deplore, and whose 

 researches on the problems of fluid motion and tidal 

 friction generally are well known, was of opinion 

 that many double stars have been generated by the 

 division of primitive and more diffuse single stars, in 

 a manner somewhat analogous to that in which he 

 supposed that our own Moon came into being. 

 Many difficulties, not altogether ignored by Darwin 

 himself, prevent our acceptance of his views as 

 regards the origin of our satellite, but there appears 

 more reason to consider that the fission theory of 



the origin of double stars is a true one. Such fission 

 would give rise to nearly circular orbits, and though 

 this is not the case with the known systems, it is 

 more true for the nearer spectroscopic binaries than 

 for the more widely separated visual ones. But it has 

 been shown that when two bodies of not very unequal 

 masses revolve round one another in close proximity 

 the conditions are such as to make tidal friction as 

 efficient as possible in transforming the orbits. 

 Hence we have in tidal friction a cause which may 

 have not only sufficed to separate the two component 

 stars of a double star system from one another, but 

 also to render the orbit eccentric (Darwin). Thus 

 it may be that under this influence in the course of 

 time the orbits of the spectroscopic binaries will 

 increase and become more eccentric, more nearly 

 like those of the " visual " binaries. On the other 

 hand, it is not impossible that some of these orbits 

 ma\' be shortening and becoming more nearly 

 circular under the action of the resisting medium, 

 whose long-continued action affords the best explan- 

 ation yet advanced of the comparative circularity of 

 the orbits of the planets in our own Solar system. 

 The efficacy of tidal friction (whose tendency is to 

 produce increase of eccentricity and distance) is 

 greater as the mass-ratios of the bodies acting and 

 acted upon are more nearly equal, as in the compo- 

 nents of a double star system, and least when one 

 mass greatly preponderates, as in our own Solar 

 system, where the mass of the Sun exceeds that of 

 all the planets put together more than six hundred 

 times. " The preponderance of high eccentricities 

 amongst the equal pairs seems to be an indication of 

 the higher efficacy of tidal friction, or of the lesser 

 importance of the action of a resisting medium in 

 such systems," and so, whilst deducing one confirma- 

 tion of the action of tidal friction and the resisting 

 medium from the small size and roundness of the 

 orbits of the spectroscopic binaries, we ma)' find an 

 additional verification of this theorv in the larger 

 eccentricities occurring amongst binary stars with 

 nearly equal components. We may, too, if we 

 please, derive important conclusions as to the relative 

 ages of the various systems. Thus from the 

 theoretical researches of Sir G. Darwin on tidal 

 friction, supplemented by the long imperfectly recog- 

 nised agency of the resisting medium, Professor See 

 has for the first time succeeded in giving a reasonable 

 account of many remarkable features in the phe- 

 nomena of the starry heavens, and has securely laid 

 the foundations and much of the superstructure of 

 a rational cosmogony. But there will always remain 

 " the immeasurable magnitude of the undiscovered " 

 to humble our pride ; and ever upward progress, we 

 trust, in our knowledge of the wondrous universe of 

 God, will not lead us to imagine that we have 

 " solved the universe." 



The Earth's mass being only .i^oVtttt that of the Sun, is here neglected. 



