i, 2] Survey of the Problem 3 



examined by Hertzsprung* in the Ursa Major cluster, nine, or 60 percent, of 

 the whole, are certainly binary, while Frost f finds that in the Taurus cluster 

 the corresponding proportion is 50 per cent. Frost also finds that 40 per cent, 

 of stars of B type are binary, while Campbell J finds that out of 1600 stars 

 considered by him, the spectroscopic binaries alone number 25 -per cent., 

 a ratio which must of course be increased by the addition of visual and 

 eclipsing binaries. [Thus there is' every reason to suppose that throughout 

 our universe fully one-third of the stars, and probably more, are binariesH 



To an observer who was so far removed from our system that the light 

 from Jupiter was visible while that from the other planets was not, our system 

 would appear to be a binary system. From observations, either spectroscopic 

 or visual, our imaginary observer might be able to determine the ratio of the 

 masses, and would find it to be '00095. But when in the same way, we 

 determine the ratio of the masses in the binary systems visible to us, this 

 ratio is found never to be very far from unity. Boss has found that in ten 

 visual binaries in which the ratio of the masses is well determined, this ratio 

 is never one of greater inequality than 0'33 to 1, the average being 0*69 to 1, 

 while Campbell 1 1 finds for nineteen spectroscopic binaries an average mass- 

 ratio 079, the greatest inequality of mass being one of ratio 0'39 to one. 



Thus it appears that the binary system formed by our sun and Jupiter is 

 of a very different character from the binary systems observed in other parts 

 of the sky, and the same is true of all the planetary systems inside our solar 

 system. In these latter systems the closest approach to equality of masses of 

 primary and satellite is found in our earth-moon system, in which the ratio is 

 0*0123 to 1. Next, after a very long interval, come Saturn and Titan having 

 a mass-ratio of the order of 0'0002 to 1, and Jupiter and its third satellite 

 having a ratio of the order of O'OOOl to 1. 



Thus, although it may be open to question whether or not our moon 

 stands in a class by itself inside the solar system, there appears to be no 

 question at all that the planetary arrangements inside our system stand in a 

 different class from the binary arrangements outside. 



Not only binary but also triple and multiple systems are observed. It 

 is stated by Russell 11 that of the double and multiple stars contained in 

 Burnham's General Catalogue of Double Stars, combined with Lewis' catalogue 

 of the Struve stars, about 800 appear to have common proper motion. And 

 of these 74 are triple or multiple, this number being 9'25 per cent, of the 

 whole. The proportion in Jonckheere's more recent Catalogue and Measures 

 of Double Stars** which contains 3950 stars is 9'7 per cent, of the whole. 



* Astrophys. Journ. 30, p. 139. t Astrophys. Journ. 29, p. 237. 



Stellar Motions, p. 245. Prel. Gen. Catalogue, p. 23. 



II Stellar Motions, p. 259, or " Second Catalogue of Binary Stars," Lick Obs. Bull. 181. 

 U Astrophys. Journ. 31 (1910), p. 199. ** R.A.S. Memoirs, Vol. 71 (1917). 



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