22 M. Arago on Double Stars. 



in part of the line AB, where the two objects C and G have the 

 .same angular elevation, where these objects are covered the one 

 by the other. If he proceeds, for a certain space, towards the 

 left, these two heights will increase, at the same time, but un- 

 equally. If, on the contrary, he transport himself from C to- 

 wards the right, the angular heights will both diminish, and the 

 diminutions will not have the same value for the two objects. 



Well, then, calculation and experience agree in demonstrating, 

 that, with regard to each angle of elevation, the variation de- 

 pends, solely, on the propoi'tlon there is betweeji the distances of the 

 object observed from the Vine AB, along which the movement is 

 effected, and the extent of this movement. When the extent CN, 

 along which the observer moves, is a considerable aliquot part 

 of the distance to the object E, the change of elevation is con- 

 siderable between the station C and the station N. If, on the 

 contrary, the line CN is almost infinitely small, compared to the 

 distance of the points to be marked, the angle of elevation will 

 be found to have sensibly the same value at the two points C 

 and N. Hence it may be understood, that if two objects, E 

 and G, which, seen from C, cover one another, the second is 

 at an immense distance, their relative changes of position will 

 depend only on the variations which, by the movements of the 

 observer, will be effected on the angular elevation of the object 

 which is nearest. These variations may thus be almost appre- 

 ciated by the naked eye, or, at least, without the assistance of a 

 large graduated instrument. Particular attention is requested 

 to this remark, as we shall presently again refer to it. 



It has just been remarked, that the change which the angle 

 of elevation of an object E experiences, was dependent on the 

 space over which the observer has moved, and on the distance 

 EL, from the object to the line NCL, passing through the two 

 stations. But such is the intimate connexions of these three 

 quantities, that any twQ of them being given, we can always 

 from them very simply deduce the third. Thus, when the ob- 

 server, in moving from C to N, has measured with precision, 

 by the assistance of his graduated circle, the diminution to 

 which the apparent elevation of the object E has been subjected, 

 two lines of calculation enable us to pass from the numerical 

 value of this diminution, to the determination of the number of 



