14 



and «/, c, and h will revolve in three concentric orbits, at diffe- 

 rent distances, and with different velocities, proportional to these 

 distances, b travelling one circumference more than c, and two 

 circumferences more than «, while c will also travel one circum- 

 ference more than «, and one less than b. And this is the real 

 and very simple aiKi obvious cause of the parallelism. The point 

 3, as a part of the circumference, rotates backwards as well as a, 

 and by so retro-rotating loses the value of one circumference in 

 its orbital journey, while a gains one ; but Z>'s place on the outer- 

 most circle or orbit is continually supplied by the other points 

 of circumference in succession, including a itself in its turn, at 

 the 180th degree of the revolution ; and the combined gain of 

 these points altogether is just that one measure of circumference 

 which serves to maintain the parallelism. 



It must be obvious, from the least consideration of the circum- 

 stances, that the outermost point of the revolving body's circum- 

 ference, whether it be a fixed point, as in the moon's case, or a 

 continually changing point as in the case of the earth, must ne- 

 cessarily describe a larger orbit than the innermost point ; so 

 that, whether the body rotate on its axis or not, the outermost 

 half of its mass will move through space with a greater velocity 

 than the innermost half, or, which is the same thing, than the 

 central axis, in the proportion of one circumference more than 

 the length of the orbit which the axis describes ; and the effect 

 of this surplus movement is, that, if the body rotate on its axis 

 once during the orbital revolution, it will present every point of 

 its circumference in succession ticice to every fixed object outside, 

 one of these presentations being the effect of rotation on the axis, 

 and the other being the effect of the superior velocity of the outer 

 half of the mass, that superior velocity itself being directly the 

 effect of the constrained movement of the axis, in obedience to 

 the centripetal force which keeps it in its orbit. When the body 

 revolves without rotating, the same point of circumference will 

 remain continually in one with the radius, on the same side of the 

 axis, and on the inside of the orbit, without the slightest varia- 

 tion in its relation either to these members of the circle, or to its 

 centre, but will present every point of its circumference in suc- 

 cession once to every fixed object outside, and that by virtue of 

 the superior velocity of the outer half of the mass, which pro- 

 ceeds during the revolution, without affecting the rotation on the 

 axis. Let the diagram (Fig. 1) represent the moon as at each 

 of her quarters ; and suppose that she, without quitting these 

 points, turns round on her axis 90° at each. At north, the point 

 a will be facing the earth ; but, by turning round 90°, there 

 a will get into the line of the orbit, 90° from the radius-vector 

 as at W. At W., a will turn away other 90°, and will then 



