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TENTH ANNUAL REPORT OP 



outside of the orbit. The sun, for example, outside of the moon's 

 orbit, operates powerfully on it, and causes its apsides to advance 

 rapidly. The superior planets, outside of the earth's (n-hit, exert but 

 a feeble influence, and the motion of its aphelion is almost insensible. 

 An exterior body always operates to draw a planet away from its 

 centre ; that is, it diminishes its attraction towards the centre, and, of 

 course, it does this most efficiently when the planet is farthest removed 

 from the central body ; in other words, when at its aphelion. Hence 

 it advances a little beyond its former aphelion before it turns to go 

 back to the perihelion. Thus each aphelion point is a little further 

 onward than the preceding. 



This may be illustrated by a long pendulum. I suspend the small 

 globe by a'cord six or eight feet in length. Instead of swinging it- 

 back and forth, however, like a pendulum, I throw it round, so as to 

 describe an elliptical orbit. Now, in order to describe this orbit, 

 there must be a central force. That force is the component part of 

 gravity, which would, if I should stop the ball, 

 cause it to fall towards the centre, and which 

 would hold it there, and only there, when at rest. 

 I now swing the globe in such a manner, that it 

 will describe from west to east a long narrow 

 orbit, whose longest axis lies north and south. 

 After a few revolutions, the axis is seen shifting 

 a little to the southeast and northwest ; and in 

 a few minutes the south has become east, and the 

 north has become west, the apsides having ad- 

 vanced ninety degrees. To show that the two 

 revolutions are necessarily in the same direction, 

 I stop the globe, and revolve it from east to west. You presently 

 notice the axis of the orbit making progress from east to west also.* 

 To explain this change in the pendulum's orbit, I must state a law 

 demonstrated in Newton's Principia ; that, when a body revolves in 

 an ellipse about the centre, instead of the focus, the attraction to the 

 centre varies as the distance. When a long pendulum is swung in a 

 smcdl orbit, this law is proved to obtain almost exactly ; and experiment 

 corroborates it. But if the cord is shortened, or the orbit enlarged, 

 the deviation increases, and always in this way — that the central force 

 is not great enough at the extremities of the long axis. Hence, as 

 the body is passing one of these points, the central force being too 

 feeble to bring it back in the former path, it shoots forward a little 

 before turning to come back ; that is, the apsis is advanced slightly. 

 This occurs at every semi-revolution. Now here is a known cause, 

 operating just like the attraction of external bodies in the solar sys- 

 tem, and producing just such an effect. Thus, again, we have an in- 

 stance, in which a mechanical experiment, that can be performed in 



«In Fig. 11, the globe, siispended from the ceiling, and drawn aside, is urged by a com- 

 ponent of gravit}' towards G, where it would hang, if at rest. Being thrown obliquely 

 so as to describe the ellipse in the direction of the single-shaft arrows, it will, at its suc- 

 cessive returns, pass tlirough the points A, B, C, D, &e. The douUe-shaft arrows show this 

 motion of the apsides to be in the direction in which the globe describes its orbit ; that 

 is, the apsides advance. 



