$Q M. Arago (m Double Stars. 



sitions to the other, it will appear then to occupy more time 

 than in reality it requires. The reverse of this necessarily hap- 

 pens, when, during its course, the star is approaching nearer to 

 us. But the two halves of the orbit of a double star are in pre- 

 cisely the condition which we have been describing, when the 

 plane which includes them is oblique, as it regards the visual 

 ray proceeding from the earth to the central star. Mathema- 

 tically speaking, the stellary satellite, viewed from the earth, 

 will employ then more time to run through the a&cendant half 

 of its orbit, — the half in which it is continually removing itself 

 from us, than to run through the other half, — that in which it is 

 approaching towards us. Well, then, we proceed to shew, that 

 the distance of the satellite from the earth may be deduced from 

 the difference observed between the direction of the ascendant 

 semi-revolution, and the duration of the opposite semi-revolu- 

 tion, whenever this difference shall have been observed with pre- 

 cision. 



If we revert to the preceding explanations, it will be easily 

 perceived, that the duration of the ascendant semi-revolution of 

 the satellite surpasses the duration of the real semi-revolution, 

 by the number of days and the fractions of a day which the 

 light may employ to traverse the number of leagues by which 

 the distance of the satellite from the earth is increased during 

 this semi-revolution. It is not less evident, that the duration of 

 the descendant semi-revolution is less than the duration of the 

 real semi-revolution by the same number of days, and fractions 

 of a day, since, in its retrograde course, the satellite approaches 

 us quite as much as previously it had removed itself. Finally, 

 the two observed semi-revolutions differ from each other the 

 double of the time which the light takes to pass through the num- 

 ber of leagues by which the distance of the satellite from the 

 earth varies in these two extreme positions. 



Let us, then, subtract the duration of two observed semi-revo- 

 lutions, the one from the other ; let us take the half of the dif- 

 ference ; let us, then, transform this half into seconds, at the rate 

 of 86,400 seconds for a day ; let us multiply the total number 

 of seconds thus obtained by 80,000, the number of leagues which 

 light moves in a second, and the product will be the valiLe, also 

 expressed in leagues^ of the quantity which the satellite star re- 



