M. Arago an Double Stars. 41 



x<>ere revolving' round each other, as one of the means by which 

 to resolve some of tlic difficult questions of physical astronomy. 



Although the principles of probabilities begin no\v-a-days to 

 be more extended, we would even say more employed, and aU 

 though, on the other hand, the intimate union — the mutual de- 

 pendence of the t^vo constituent parts of a considerable number 

 of binary stars, is the result of direct and incontestable observa- 

 tions, yet iff is difficult not to concur in the remark of M. Struve, 

 that this union — this dependence, the fruit of so many delicate 

 researches, might have been inferred by all who have eyes to see, 

 from the simple inspection of the table, wherein is enumerated 

 the different classes of the double stars. 



The four classes of Herschel, we ought on no account to for- 

 get, have nothing to do with the intensity of the stars; they have 

 only a relation to their angular distances. The first is composed 

 of all the binary groups, in which the constituent elements are at 

 least separated by a distance of four seconds. The second con- 

 tains those in distances of more than four, and less than eight, 

 seconds. The third commences with eight seconds, and ends with 

 sixteen. Finally, the fourth mounts up to thirty-two seconds. 

 Now every one will understand, that in seeking after the proba- 

 bility in which the stars scattered over the firmament without 

 any rule would present themselves in groups of two, — that this 

 probability, we say, would be less in proportion as the groups in 

 question would be confined within smaller limits. It is, in short, 

 as if we were to calculate what probability, in throwing a certain 

 number of barleycorns on a chess board, there would be of find- 

 ing them collected, in the squares, in groups of two. The pro- 

 bability must evidently diminish in the same ratio as the sizes of 

 the squares. In the proposed problem, the barleycorns are the 

 stars ; the chess-board is the firmament ; the squares, for the first 

 class of Herschel, are those with distances of four seconds at most 

 of diameter ; for the fourth class, the dimensions of the squares 

 extend to thirty-two seconds. In the hypothesis of an absolute 

 independence amongst all the stars with which the heaven is 

 sprinkled, the first class of double stars would be much less nu- 

 merous than the second, still more so than the third, and yet 

 more than the fourth. But the reverse of all this really occurs, 

 as may be seen by a reference to the table (page 3.). Wc 



