160 On Binari/ or Multiple Stars. 



tiple stars), constitutes of itself an argument for a more than 

 apparent connection between the members of those groups. 



It is evident that two stars may constitute an apparently 

 double star without any real proximity between them, merely 

 because a line passing through the eye of the spectator and 

 the nearer star may, if prolonged into space (no matter how 

 far), pass somewhere near a second star, whose position 

 would therefore seem almost to coincide with the first, al- 

 though the distance which separates them might be indefi- 

 nitely great. Such stars are sometimes said to be " optically" 

 double. On the other hand, it may happen that the two 

 stars are really as well as seemingly near, and may act upon 

 one another by their mutual attractions, after the manner of 

 sun and planet. Such stars are called " physically" double. 



Nearly a century ago the Rev. John Mitchell attempted to 

 deduce from the theory of probabilities, the chances against 

 the fortuitous approximation of two or more stars, supposing 

 the stars generally to be " scattered by mere chance as it 

 might happen." He concludes that there is a probability of 

 80 to 1 that the two stars j8 Capricorni are physically con- 

 nected, and above 500,000 to 1 that the stars of the Pleiades 

 are so. These results have been implicitly adopted by most 

 subsequent writers on probabilities and on astronomy. 



The author denies in toto the legitimacy of the influences, 

 and the possibility of putting a numerical value upon such 

 evidences of physical relation. As inductive presumptions of 

 such a connection he admits that they have a certain evidence 

 in their favour ; but one not more expressible by numbers 

 than that of any physical theory, such as that of gravity. 

 The author endeavours to show that Mitchell has confounded 

 the mere expectation of an event which may or may not 

 occur, with the inherent probability that a particular event 

 which has occurred, should happen rather than any other 

 possible event. He also shows that Mitchell's mathematical 

 expression of the result of random scattering leads to absurd 

 results, and must therefore be erroneous and delusive. 



The following was stated to the meeting as the results at 

 which the author had at that time arrived : — 



(1.) The fundamental principle of Mitchell is erroneous. 



