20 THE YEAR. 



rotation pointed directly to the centre of the luminous 

 body ; and in that case the only difference from a state 

 of rest would be, that, to an observer situated any where 

 upon the illuminated side of the opaque body, except 

 on the middle of that side, the luminous body would 

 appear to move round in a circle in the same time 

 that the opaque one turned round upon its axis, and 

 the circle would seem the larger, the farther that the 

 observer were from the middle of the illuminated side. 



If, again, both extremities of the axis of the revolv- 

 ing body were equally distant from the centre of the 

 luminous one, is is evident that the whole surface of 

 the opaque body would be illuminated in the course 

 of every rotation that it made upon its axis ; and that 

 if the motion were uniform, any one point on its sur- 

 face would be for exactly one half of the time of the 

 revolution exposed to the light, and for the other half 

 deprived of it ; the only difference would be, that a 

 point situated just midway between the extremities of 

 the axis of rotation, would be the most strongly illumi- 

 nated, and that other positions would be less and less 

 so according as they were nearer to the extremities of 

 that axis. 



Further, if one extremity of the axis of rotation were 

 nearer the centre of the luminous body than the other, 

 the whole surface of the opaque body would not be 

 illuminated during one rotation ; for there would be a 

 portion round the nearest extremity of the axis con- 

 stantly in the light, and an equal portion round the 

 remotest one, which the light would not reach ; and 

 those portions would be equal to the angular difference 



