M. Arago on Double Stars* 88 



times that CN is contained in LE ; that is to say, to the know- 

 ledge of the distance of the inaccessible object E, for CN is 

 always measureable in leagues. 



And now is the reader put in possession of the principle of 

 the method which astronomers habitually employ for the deter- 

 mination of the distances of the celestial bodies, and which they 

 denominate the method of parallaxes. 



The method of parallaxes, every one may perceive, must give 

 results so much more precise, as in moving from the first to the 

 second station, the angular elevation of the objects shall have 

 more sensibly varied ; or rather, for it is the same thing in 

 other terms, as the traversed base CN, is a larger aliquot part 

 of the distance that is sought after, EL. 



When the object E is a star ; where it is the stars, the dis- 

 stances of which we wish to measure, we take for our first station 

 N, one of the extremities of a diameter of the almost circular 

 ellipse which the earth annually describes round the sun ; and, 

 for the second station, C, the other extremity of this same dia- 

 meter. But the distance which then separates these two points, 

 C and N, is about 20,000,000 of leagues. Notwithstanding, so 

 vast a displacement does not sensibly change the angular ele- 

 vations of the star. The visual rays CE and NE, extended to 

 this star, from the two places separated by 20,000,000 of leagues, 

 form angles very nearly equal with the line which joins the two 

 places. 



We have said the angles were nearly equal, for it rarely hap- 

 pens that there is not found, between the angular elevations 

 measured at the two extremities of the base, discordances, often 

 it is true, irregularities, to the extent of one, two, and even 

 three seconds. These quantities are unquestionably very small ; 

 scarcely do they exceed the errors of the observations ; and yet 

 they are of vast importance. If any one, for example, had suc- 

 ceeded in assuring himself, that for a star Uttle removed from a 

 visual line perpendicular to the diameters of the terrestrial orbit, 

 the angular elevation, from the extremity of one of these dia- 

 meters, really exceeded by three seconds the elevation from the 

 other extremity, calculation would give for the distance of this 

 star from the earth (5,000,000,000,000) five millions of millions 

 of leagues. 



