M. Arago on Double Stars. Hi 



viz. one having a graduated circle furnished with a plummet- 

 line, or a level, and a moveable telescope. Let us suppose that 

 above the line AB, there is found at the unequal heights EL, 

 GH, two small objects E and G. 



When the observer stands in C, the two objects E and G 

 will be situated, as an effect of perspective, on the same visual 

 ray. In the glass of the instrument, the nearer will cover the 

 more distant ; but as soon as the station C is abandoned, as 

 soon as the observer advances or retires, this state of things will 

 be wholly changed. If he remove to M, the object E will no 

 longer cover the object at G : it will appear more elevated, since, 

 after having seen it, it would be necessary to depress the tele- 

 scope to find G. A removal, on the other hand, towards N, 

 for example, would give an exactly opposite result ; the object 

 E, as the diagram clearly shews, would then exhibit it as un- 

 derneath G. 



It thus, then, is clearly established, that the relative positions 

 of two objects, at different distances, necessarily change when 

 the observer alters his position. 



But it is not enough for the science to have established the 

 existence of the relative apparent motions, which are deter- 

 mined by a change in the position of the observer ; it is requi- 

 site, moreover, to know what is, in the total apparent mo- 

 tion, the part which each of the two objects plays ; what is nu- 

 merically the share, in the phenomenon, which the distances of 

 these two objects from the observer bears, to the distance which 

 he himself has gone over in the course of the horizontal line. 



All this results immediately from the simple inspection of the 

 analytic processes employed by astronomers in their calculations ; 

 but we must abstain from quoting any formulas, that we may 

 preserve for this contribution that popular character which we 

 have designed. We must be contented with pointing out, as 

 clearly as it is possible, the results which follow from them. 



To avoid troublesome circumlocutions, it will be proper, at 

 once, to designate the angular elevation of an object, the angle 

 which is formed by the horizon, and the visual line proceeding 

 from the eye of the observer to that object. This is, besides, 

 the technical expression. 



Let us consider the observer again placed in C, that is to say, 



