M. Arago on Double Stars. 19 



termined this space for our globe. We have seen how much it 

 would cause to fall in the same interval of time, a body which 

 would also be at the distance of 39,000,000 of leagues. The 

 distances in these two cases being equal, the falls must needs be 

 proportional to the masses. In searching, by a simple division, 

 how many times the fall towards the earth is contained in the 

 fall towards the sun, we should learn how many terrestrial globes 

 it would require to make a mass equal to that of the luminary 

 which illuminates it. It is thus fundamentally, if not formally, 

 that the number 337,000, already cited in page 12, is discovered. 



What elements, then, have we employed to arrive at this re- 

 sult ? Only the quantity of the angular motion of our globe 

 around the sun in a second of time, and the value in leagues of 

 a radius of the terrestrial orbit, — none other. But the direct 

 observation of the double stars supplies us with the angular velo- 

 city of the lesser star round the greater ; if we had, in leagues, 

 the radius of the orbit which this lesser star tuns, we might 

 easily find what is, in the fraction of a league, or, in yards, the 

 distance which it falls in a second towards the central star. This 

 distance, compared to the fall of a body towards the earth, or to 

 the fall of a body towards the sun, since previously the three 

 numbers, as we have already explained, would have been redu- 

 ced to a common distance, by the inverse proportion of the 

 squares, would give the relation of the mass of the greater star 

 to the mass of the earth, or to that of the sun. Hitherto, un- 

 fortunately, we have known, respecting the radii of the orbits of 

 the stellary satellites, only the angles which they subtend, as 

 seen from the earth. To transform these angles into measures 

 of length in leagues and yards, it would be necessary to have the 

 value of the distances which separate us from the stars. When 

 these distances shall have been determined, the radii of the orbit 

 in leagues may be deduced, and the remainder of the calculation 

 will be accomplished without difficulty. 



The science, in being enriched with a knowledge of the move- 

 ments of the double stars, has made an immense stride in the so- 

 lution of a problem which seems far removed above the intelli- 

 gence of man. The day in which the distance of a double star 

 shall be determined, will be the day in which it may be weighed, 

 in which we shall know how many millions of times it contains 



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