SECT, i.] ROTATION AND TRANSLATION. 



nutation (N. 33) in the axis (N. 34) of rotation, and the re- 

 action of that matter on the moon is the cause of a corre- 

 sponding nutation in the lunar orbit (N. 35). 



If a sphere at rest in space receive an impulse passing 

 through its centre of gravity, all its parts will move with 

 an equal velocity in a straight line ; but, if the impulse does 

 not pass through the centre of gravity, its particles, having 

 unequal velocities, will have a rotatory or revolving motion, 

 at the same time that it is translated (N. 36) in space. These 

 motions are independent of one another ; so that a contrary 

 impulse, passing through its centre of gravity, will impede 

 its progress, without interfering with its rotation. As the 

 sun rotates about an axis, it seems probable, if an impulse in 

 a contrary direction has not been given to his centre of 

 gravity, that he moves in space, accompanied by all those 

 bodies which compose the solar system a circumstance 

 which would in no way interfere with their relative motions ; 

 for, in consequence of the principle, that force is propor- 

 tional to velocity (K 37), the reciprocal attractions of a 

 system remain the same, whether its centre of gravity be at 

 rest, or moving uniformly in space. It is computed that, 

 had the earth received its motion from a single impulse, 

 that impulse must have passed through a point about twenty- 

 five miles from its centre. 



Since the motions of rotation and translation of the planets 

 are independent of each other, though probably communi- 

 cated by the same impulse, they form separate subjects of 

 investigation. 



