SECT. 2.] TO POSITION IN SPACE. 83 



along its optical axis. The observed place of a heavenly body (which is called 

 the apparent, or affected by aberration), is determined by the direction of the 

 optical axis of the telescope set in such a way, that a ray of light proceeding 

 from the body on its path may impinge upon both extremities of its axis: but this 

 direction differs from the true direction of the ray of light in space. Let us con 

 sider two moments of time t, t , when the ray of light touches the anterior ex 

 tremity (the centre of the object-glass), and the posterior (the focus of the object- 

 glass) ; let the position of these extremities in space be for the first moment a, b ; 

 for the last moment a , b . Then it is evident that the straight line ab is the true 

 direction of the ray in space, but that the straight line ab or ab (which may be 

 regarded as parallel) corresponds to the apparent place : it is perceived without 

 difficulty that the apparent place does not depend upon the length of the tube. 

 The difference in direction of the right lines b a, ba, is the aberration such as exists 

 for the fixed stars : we shall pass over the mode of calculating it, as well known. 

 This difference is still not the entire aberration for the wandering stars : the 

 planet, for example, whilst the ray which left it is reaching the earth, itself 

 changes its place, on which account, the direction of this ray does not correspond 

 to the true geocentric place at the time of observation. Let us suppose the ray 

 of light which impinges upon the tube at the time t to have left the planet at the 

 time T and let the position of the planet in space at the time T be denoted by 

 P, and at the time t by p ; lastly, let A be the place of the anterior extremity of 

 the axis of the tube at the time T. Then it is evident that, 



1st. The right line AP shows the true place of the planet at the time T , 



2d. The right line ap the true place at the time t ; 



3d. The right line ba or b a the apparent place at the time t or if (the differ 

 ence of which may be regarded as an infinitely small quantity) ; 



4th. The right line b a the same apparent place freed from the aberration of 

 the fixed stars. 



Now the points P, a, b , lie in a straight line, and the parts Pa, ab , will be 

 proportional to the intervals of time t T, if t, if light moves with an uni 

 form velocity. The interval of time if T is always very small on account of 

 the immense velocity of light ; within it, it is allowable to consider the motion 



