SKCT. XXXVII. DISTANCE OF BINARY SYSTEMS. 373 



it ought to be, by the whole time its light takes to cross 

 the orbit, and the period of moving through the other 

 half is exactly as much less. Hence the difference be- 

 tween the observed times of these two semi-revolutions 

 of the star is equal lo twice the time thai its light em- 

 ploys to cross its orbit; and as we know the velocity of 

 light, the diameter of the orbit may be found in miles, 

 and from that its whole dimensions. For the position of 

 the orbit with regard to us is known by observation, as 

 well as the place, inclination, and apparent magnitude 

 of its major axis, or, which is the same thing, the angle 

 under which it is seen from the earth. Since, then, 

 three things are known in this great triangle, namely, 

 the base or major axis of the orbit in miles, the angle 

 opposite to it at the earth, and the angle it makes with 

 the visual ray ; the distance of the satellite star from the 

 earth may be found by the most simple of calculations. 

 The merit of having first proposed this veiy ingenious 

 method of finding the distances of the stars is due to M. 

 Savary ; but unfortunately it is not of general application, 

 as it depends upon the position of the orbit, and even 

 then a long time must elapse before observation can fur- 

 nish data, since the shortest period of any revolving star 

 that we know of is thirty years : still the distances of a 

 vast number of stars may be ultimately made out in this 

 way ; and as one important discovery almost always leads 

 to another, their masses may thus be weighed against 

 that of the earth or sun. 



The only data employed for finding the mass of the 

 earth, as compared with that of the sun, are the angular 

 motion of our globe round the sun in a second of time, 

 and the distance of the earth from the sun in miles (N. 

 224). Now by the observations of the binary systems, 

 we know the angular velocity of the small star round 

 the great one ; and when we know the distance between 

 the two stars in miles, it will be easy to compute how 

 many miles the small star would fall through by the at- 

 traction of the great one in a second of time. A compar- 

 ison of this space with the space which the earth would 

 descend through in a second toward the sun, will give 

 the ratio of the mass of the great star to that of the sun 

 or earth. 



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