268 CELESTIAL DYNAMICS. 



will maintain itself as long as motion lasts. It is neverthe- 

 less possible for the weight to move at once to the point ; the 

 probability of its doing so, however, becomes the less as the 

 height from which it is allowed to drop increases, or the string, 

 by means of which it is suspended, is lengthened. 



Similar laws influence the movements of bodies in the 

 space of the solar system. The height of the fall is here 

 represented by the original distance from the sun at which the 

 body begins to move ; the length of the string by the sun's 

 attraction, which increases when the distance decreases ; and 

 the small surface of contact on the floor by the area of the 

 section of the sun's sphere. If now a cosmical mass within 

 the physical limits of the sun's sphere of attraction begins its 

 fall towards that heavenly body, it will be disturbed in its 

 long path for many centuries, at first by the nearest fixed 

 stars, and afterwards by the bodies of the solar system. 

 Motion of such a mass in a straight line, or its perpendicular 

 fall into the sun, would, therefore, under such conditions, be 

 impossible. The observed movement of all planetary bodies 

 in closed curves agrees with this. 



We shall now return to the example of the weight sus- 

 pended by a string and oscillating round a point towards 

 which it is attracted. The diameters of the orbits described 

 by this weight are observed to be nearly equal ; continued ob- 

 servation, however, shows that these diameters gradually di- 

 minish in length, so that the weight will by degrees approach 

 the point in which it can touch the floor. The weight, how- 

 ever, touches the floor not in a mathematical point, but in a 

 small surface ; as soon, therefore, as the diameter of the curve 

 in which the weight moves is equal to the diameter of this 

 surface, the weight will touch the floor. This final contact is 

 no accidental or improbable event, but a necessary phenome- 

 non caused by the resistance which the oscillating mass con- 

 stantly suffers from the air and friction. If all resistance 

 could be annihilated, the motion of the weight would of course 

 continue in equal oscillations. 



