28 M. Arago on Double Stars. 



the lesser star of a binary group describes round the greater, pre- 

 sents itself exactly in front, that is to say, when the plane which 

 incloses it is perpendicular to a line drawn from the earth to the 

 central star, the satellite star, throughout the duration of its 

 revolution, continues constantly at the same distance from the 

 earth. The satellite star proceeds, in fact, to occupy succes- 

 sively, in virtue of its individual movement, all possible positions 

 on the circumference of the small circle. And no one doubts 

 that all the points of a circumference of a circle, viewed exactly 

 in front, are equally distant from the eye of the observer. 



Through the centre of the circular orbit of the stellary satel- 

 lite, let us draw a horizontal diameter, which will divide this or- 

 bit into two equal parts, — one superior, the other inferior. Let 

 us then turn the plane in which the circuit is contained round 

 this horizontal diameter, and in such a way, for example, that 

 the lower part shall come to the front, or towards the observer, 

 whilst that the upper will be carried to the back part. Viewed 

 perpendicularly, the orbit of the lesser star was circular. Viewed 

 in its new oblique position, it will appear elongated ; and it is of 

 especial importance to remark, that these different parts will no 

 longer be found at the same real distance from the observer. 

 In the half circle which, on assuming the perpendicular posi- 

 tion, shall have come towards the front, there will necessarily 

 exist a point nearer to the earth than all the others. The point 

 diametrically opposed to this will be the most distant one. In 

 moving from the first point to the second, the satellite star will 

 then gradually recede from the observer. In returning from 

 this second point to the first, it will approach towards him. This 

 double circumstance, on account of the appreciable velocity of 

 light, may bring along with it sensible differences in the manner 

 in which the star shall seem to move along the two halves, — the 

 one the ascendant, the other the descendant half of its course. 

 Let us now proceed to examine in what forms we shall perceive 

 a luminous star, which is endowed with a proper motion. 



Let us take this star in a certain determinate position. From 

 this position it will in all directions dart rays which will propa- 

 gate themselves in straight lines, and the prolonged directions 

 of which, whatsoever may be the place and the time in which 



