40 M. Arago on Double Stars. 



expanse of the heavens, it is almost impossible to count more than 

 fifteen hundred which have an intensity which can be compared 

 to theirs. 



The problem for solution, then, was this: Fifteen hundred 

 stars being thrown at hap-hazard over the extent of the firma- 

 ment, what probability is there that six of them will be united 

 in the confined space which the constellation of the Pleiades oc- 

 cupies. Mitchel found for this probabihty jooooo 5 that is to 

 say, that it was 500,000 to one that such an approximation of 

 six stars should occur. But since this concentration exists, in 

 spite of the one probability out of the five hundred thousand 

 which might lead to it, we ought to conclude that there has been 

 something erroneous in the ground-work of the calculation. But 

 on closer examination, we find there is only one hypothesis, viz. 

 that the stars are distributed over the heavens at hap-hazard. 

 Hence our hypothesis, the probable consequences of which are so 

 little in accordance with the facts, itself becomes improbable. It 

 is, therefore, the directly opposite theory which ought to procure 

 suffrage. And thus the six stars of the Pleiades are not so 

 closely concentrated by chance ; thus a physical cause has re- 

 gulated their union within so narrow a space ; and thus they are 

 in a mutual dependence upon one another ! But is not this pre- 

 cisely the same conclusion which, much later, has been deduced 

 from the tedious labours of astronomers on the double stars ? 

 Here, it will be perceived, the theory of probabilities had taken 

 the lead of direct observations. 



In applying the same doctrine, remarks the English philoso* 

 pher, to the stars which appear double or triple only through the 

 telescope^ their connexion would appear established upon infi- 

 nitely greater probabilities. And what would Mitchel have 

 said, if in his time certain binary groups had been known, such as 

 ti of Hercules, and y of the Crown, in which the two constituent 

 parts can scarcely be separated with the help of the best telescopes 

 and the strongest magnifiers ? With a little more confidence in 

 the results of the calculations of probabilities, practical astrono- 

 mers would have commenced observations on double stars in 1767. 

 This confidence was possessed by the ingenious author of the 

 remarks to which we have been alluding, to such a degree, that he 

 even then spoke, in his memoir, of the existence of stars which 



