observed with the Great Achromatic of Fraunhqfer. 83 



the Milky Way, in the Goose, the Fox, and the Arrow. We 

 find also in Perseus, and to the north of the Milky Way, a great 

 accumulation of double stars, while the Milky Way itself is not 

 so well supplied as the constellations Aries, the Triangle, the 

 Fly, and apart of that of Taurus, to the south. In short, the con- 

 stellation of Orion, that region of the Heavens so astonishingly 

 rich, to the south of the Milky Way, contains a surprising num- 

 ber of double stars, while the parts of the Milky Way itself 

 which follow it, such as the Unicorn. &c. contain a very limit- 

 ed number. At a greater distance from the Milky Way to the 

 north, in Gemini, and in the constellations of the Lynx and of 

 the Telescope, in general deficient in bright stars, we find even 

 more double stars than in the parts of the Milky Way situated 

 to the south of these regions. 



At the first glance of the above comparative table, we ob- 

 serve the superiority in the number of double stars of the first 

 class, which may lead us to the following important conclusion. 

 If these stars were only optically double, those in which the 

 little star appears the most distant from the great one ought 

 to be the most numerous, so that there ought to be more double 

 stars of the fourth than of the first class. As the surface of 

 circles whose radii are 4, 8, 16, 32 seconds, (which corre- 

 spond, as we have seen, to the limits of distance of the four first 

 classes of Herschel,) is proportional to the square of the num- 

 bers 1, % 4, 8, or in the ratio of the numbers 1, 4, 16, 64, it 

 follows that the numbers of optical double stars of various 

 classes is, according to the doctrine of probabilities, as the dif- 

 ferences 1, 3, 12, 48, between these last numbers; whence it 

 follows, that of 64 stars optically double there should be only 

 one of the first class. 



Let us suppose now that the 736 double stars of the first 

 class observed were optically so, we ought to find from the pre- 

 ceding ratio 



In the 1st 2d 3d class 



16 47 184 stars optically double. 



But our catalogue contains 987, 675, and 659 double stars of 

 these three classes. We may then conclude with certainty 

 that almost all the stars of the first class are physically double, 

 likewise those of the second class, and a very great part of 



