T.ow'i-ic.] Xi/o [Sept. 17, 



ball at the end of a string is swung from right to left around one's hand 

 as one moves rapidly in the same direction around a path, composed of a 

 series of curves or loops all turning to a eonamon centre. If we analyze 

 the motion of the ball, we find that, while, relatively to the hand, it is 

 nearly circular, it i-eally performs a very com]3lex figure relatively to the 

 centre of the greater circle in which the person moves, passing an equal 

 or nearly equal portion of time on each side, and yet with a much shorter 

 path and slower motion on the inner, than on the outer side; this differ- 

 ence being always increased witli the rapidity of the motion in the larger 

 circle and with the slowness of that in the smaller one. Thus the ball's 

 motion may resemble that of the most remote planets or of our moon, 

 consisting of a series of alternate long and short undulations, or that of 

 the other planets and satellites, being a series of scollops or of alternate 

 long and short curves looping into each other. 



And while the ball is performing this motion, the hand does not keep 

 on the line of the greater circle, but performs a series of motions alter- 

 nately on each side of it, corresponding in form to the larger ones of the 

 ball; and in this its motion resembles the small motion of the planet on 

 its orbit, no planet having a satellite ever moving exactly along its 

 theoretic orbit. 



Let the moving ball rejaresent the tangential, and the string the attrac- 

 tive force of the whole movement, and we have the statical condition of 

 a balance of forces. But the tangential force, not being a vis viva, would 

 soon give way to the other-, if there were no recuperative arrangement in 

 relation to it, and our illustration directs us to the actual arrangement. 

 It consists of the constant motion of the central force. This is the key 

 to the dynamics of the system: attraction by a constantly and peculiarly 

 moving central body. Of course both bodies exert this force, though 

 that of the central body is always immensely greater than that of the 

 other: it is all one force acting along the same line. 



This is the moving force that maintains the motions of its dependent 

 bodies, and we find no repulsive force; though, for distinctness of thinking, 

 we find it necessary to analyze the motion into radial and tangential ele- 

 ments, and consider these as representing two colliding forces. A system 

 of forces is an essential element of every system of actual things, and 

 there can be no motion within the systera except what is given or upheld 

 by the very forces that constitute the system, supposing of course no 

 interference from without. 



This is a force constantly acting, and moving as it acts, ever changing 

 the position whence it acts and therefore the direction of its action; always 

 departing from its point of action and therefore from the very results 

 which its action in each moment tends to produce; always fluent in itself 

 and always fluent in its effects. 



As the planet sweeps, with its unsteady rythm of undulations, along 

 its own series of scollops or loops, called its orbit, the satellite sweeps 

 tangentially throughout that orbit ; and thence, obeying the attrac- 

 tive force of the planet without giving up the force of its own motion, 



