SECT. XXXVI. MASSES OF THE STARS. 403 



This circumstance furnishes the means of finding the absolute 

 breadth of the orbit in miles, and from that the true distance of 

 the star from the earth. For, since the greatest and least dis- 

 tances of the satellite star from the earth differ by the breadth of 

 its orbit, the time which the star takes to move from the nearest 

 to the remotest point of its orbit is greater than 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 between the observed times of these two semi- 

 revolutions of the star is equal to twice the time that its light 

 employs 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 dis- 

 tance of the satellite star from the earth may be found by the 

 most simple of calculations. The merit of having first proposed 

 this very ingenious method of finding the distance of the stars is 

 due to M. Savary ; but, unfortunately, it is not of general appli- 

 cation, as it depends upon the position of the orbit, and a long 

 time must elapse before observation can furnish data, since the 

 shortest period of any revolving star that we know of is 30 years. 

 Still the distances of a vast number of stars may ultimately be 

 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. 233). "Now, by 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 attraction 

 of the great one in a second of time. A comparison of this space 

 with the space through which the earth would descend towards 



