3^ M. Arago on Double Stars, 



Suppose that it shall have resulted, from the minute exami- 

 nation of a series of measures of angles of position, that the du- 

 ration of the ascendant semi-revolution of a stellary satellite 

 only surpasses^ by twenty days, the duration of the descendant 

 <3emi. revolution, hence it follows, that the total quantity which 

 the star removes from, or approaches to, the earth, in proceed- 

 ing from the one of its extreme positions to the other, cannot^ 

 in its turn, be greater than the number of leagues traversed by 

 the light in ten days. 



Let us, for a moment, adopt this superior limit as the real 

 value of the total change of the distance of the star, and let us 

 enquire, as is done every day, for the extent in leagues, of the 

 axis of the stellary orbit. In parting from a hmit, it is a 

 limit which we must find. Thus, the calculation will give us a 

 number of leagues which the real length of the diameter in ques- 

 tion cannot surpass. In other words, it will conduct us either 

 to the real length or to a length greater than it. 



Now, if we inquire, by the known methods of land-surveying, 

 to what distance must be extended a right line of a length 

 equal to that number of leagues which constitutes the superior 

 limit, that it may appear to us under the angle which the mi- 

 crometrical direct observations have assigned to the axis' of 

 a stellary orbit, what will be found will be, without other alter- 

 native, either the truth or a quantity greater than the truth ; 

 ^he truth, if the number of leagues employed has happened to 

 be exactly equal to the diameter of the orbit, a quantity greater 

 in every other case, since then the number on which we have 

 operated will itself have been too great ; but that it may be 

 brought to subtend a certain determinate angle, a line must evi- 

 dently be transported further, as it is made longer. We are 

 thus, then, brought to the determination of a distance, beyond 

 which we cannot suppose the star situated, without placing our- 

 selves in opposition to the facts. 



If, from another part of the investigation, the discussion of 

 the angles of position should permit us to affirm that the dura- 

 tion of the ascendant semi-revolution of a stellary satellite is su- 

 perior to the duration of the descendant semi-revolution, by 

 at least a certain definite number of days, the calculation ap- 

 plied to this new result, instead of a superior limit, would lead 



