APPARENT AND REAL MOTION. 



moon, whose apparent magnitudes are subject, during their revo- 

 lution round the earth, to a slight variation, being a minimum at 

 one point and a maximum at the extreme opposite point, the 

 variation being such as to show that their motions are made in an 

 ellipse in the focus of which the earth is placed. 



87. As the eye perceives the motion of an object only by the 

 change in the direction of the line joining the object with the eye, 

 and as this change of direction may be produced as well by the 

 motion of the observer as by that of the object, we find accordingly 

 that apparent motions are produced sometimes in this manner. 

 Thus, if a person be placed in the cabin of a boat which is moved 

 upon a river or canal with a motion of which the observer is not 

 conscious, the banks and all objects upon them appear to him to 

 move in a contrary direction. In this case the line drawn from 

 the object to the eye is not moved at the end connected with the 

 object, which it would be if the object itself were in motion, but 

 at the end connected with the eye. The change of its direction, 

 however, is the same as if the end connected with the object had 

 a motion in a contrary direction, the end connected with the eye 

 being at rest ; consequently the apparent motion of the objects 

 seen which are really at rest, is in a direction contrary to the real 

 motion of the observer. 



88. In some cases the apparent motion of an object is produced 

 by a combination of a real motion in the object and a real motion 

 in the observer. Thus, if a person transported in a railway car- 

 riage meet a train coming in the opposite direction, both extremes 

 of the line joining his eye with the train which passes him are in 

 motion in contrary directions ; that extremity which is at his eye 

 is moved by the motion of the train which carries him, and the 

 other extremity is moved by the motion of the train which passes 

 him. The change of direction of the line is accordingly produced 

 by the sum of these motions ; and as this change of direction is 

 imputed by the sense to the train which passes, this train appears 

 to move with the sum of the velocities of the two trains. Thus, 

 if one train be moved at twenty miles an hour, while the other is 

 moved at twenty-five miles an hour, the apparent motion of the 

 passing train will be the same as would be the motion of a train 

 moved at forty-five miles an hour passing a train at rest. 



89. If the line joining a visible object with the eye be moved 

 at both its extremities in the same direction, which would be the 

 case if the observer and the object were carried in parallel lines, 

 then the change of direction which the line of motion would 

 undergo would arise from the difference of the velocities of the 

 observer and of the object seen. 



If the observer in this case moved slower than the object, the 



91 



