266, 26?] Motion subsequent to Fission 



from equation (581). Using equations (579) this becomes 



Introducing the polar equation of the orbit in the form 



a (1 - e 2 ) 



we find 



= 1 + e cos 0, 

 (1 - g) = ? [(1 - e 9 ) - (I + e cos <9) 2 ], 



255 



As G acts in the direction of 6 increasing, G/h will be positive, while 

 e(l+cos 2 #) is necessarily positive. Tidal friction acts mainly when the 

 masses are closest together i.e. when cos is nearest to + 1. Hence it is 

 readily found that G cos 0/h is preponderatingly positive and de/dt integrated 

 through a whole orbit will be positive. 



Thus tidal friction increases both a and e, and as the evolution of a binary 

 star progresses we ought, on the tidal-friction theory, to find (i) increasing 

 separation, (ii) increasing period, (iii) increasing eccentricity. 



267. Campbell has attempted to test these conclusions with the help of 

 material provided by his studies of spectroscopic and visual binaries*. The 

 general summary of Campbell's classification of spectroscopic binaries is 

 shewn in the following table : 



In this table the values of e are mean values for all the binaries for which 

 the eccentricity can be calculated, no entry being inserted when the eccen- 

 tricity is known only for a single star. 



* "Second Catalogue of Spectroscopic Binary Stars," Lick Obs. Bull. No. 181 (1910) ; Stellar 

 Motions, Chap. VIII. 



