observed with the great Achromatic of Fraunhqfer. 89 



these numbers, and compared with that which really exists, 

 shows that there are not in the heavens two stars of the first 

 magnitude so near one another that their nearness may not 

 probably be considered as accidental. On the other hand, the 

 magnitudes which follow the first present examples of the 

 most remarkable proximities. Who does not know the three 

 bright stars of the second magnitude in the belt of Orion, of 

 which the two external ones are distant from the middle star, 

 one by a degree and twenty-six minutes, and the other a de- 

 gree and eighteen minutes ? The calculations show that there 

 are 1400 chances to one that their nearness is not accidental. 

 The constellation of the southern cross is still more remarkable. 

 We find there in a space of fifteen degrees square (which does 

 not include the 2700th part of the celestial vault) one star of 

 the first magnitude, two of the second, one of the third, and 

 one of the fourth ; and the probability that such a distribu- 

 tion is accidental is only that of 1 in 20,000. We have thus 

 the best reasons for thinking that these stars depend upon one 

 another. 



These conjectures are confirmed when we consider the stars 

 from the sixth to the seventh magnitude, relative to their dis- 

 tribution throughout the celestial vault. 



From a calculation of probabilities, founded upon the num- 

 ber of the stars which are in the celestial Atlas of Harding, the 

 case where two of them should be distant from one another 

 from thirty- two seconds to one minute, ought to occur only 

 one-and-a-half time, while fifteen instances of it are known. 

 There ought to be but six or seven pairs of stars from the 

 first to the seventh magnitude, where the two stars forming 

 the pair are distant from one to two minutes ; and there are 

 already fifteen cases known. If we consider it for greater dis- 

 tances for stars of the sixth magnitude, we shall find that there 

 ought to be but seven or eight pairs where the stars are dis- 

 tant from one another from two to five minutes ; while there 

 are eighteen cases known. Between five and ten minutes of 

 distance, the calculation of probabilities gives twenty-seven to 

 twenty-eight pairs ; and we know thirty-six cases. We can 

 find in the heavens still more pairs of stars, distant from each 

 other ten and fifteen minutes, than the calculation gives, viz. 



