704 APPENDIX TO De. VVHEWELL'S MEMOIR ON 



that course. To this it is that attention should be directed. We have to do with a conscious- 

 ness relative to the deluging of physical Mechanics with an mco7icewable (unsaglichen) 

 Metaphysic, which — contrary to experience and conception — has those mathematical deter- 

 minations alone for its source. 



It is recognized that what Newton — besides the foundation of the analytical treatment, 

 the developement of which, by the bye, has of itself rendered superfluous, or indeed rejected 

 much which belonged to Newton's essential Principles and glory — has added to the Keplerian 

 Laws is the Principle of Perhtrbations, — a Principle whose importance we may here accept 

 thus far ; (hier in sofern anzufuhren ist) ; namely, so far as it rests upon the Proposition that 

 (k) the so-called attraction is an operation of all the individual parts of bodies, as being material. It 

 (/) lies in this, that matter in general assigns a center for itself, (sicli das centrum setzt), and the 

 figure of the body is an element in the determination of its place ; that collective bodies of the 

 system recognize a reference to their Sun, (sich ihre Sonne setzen) but also the individual 

 bodies themselves, according to the relative position with regard to each other into which 

 they come by their general motion, form a momentary relation of their gravity (schwere) 

 towards each other, and are related to each other not only in abstract spatial relations, but at 

 the same time assign to themselves a joint center, which however is again resolved [into the 

 general center] in the universal system. 



As to what concerns the features of the path, to shew how the fundamental determina- 

 tions of Free Motion are connected with the Conception, cannot here be undertaken in a 

 satisfactory and detailed manner, and must therefore be left to its fate. The proof from reason 

 of the quantitative determinations of free motion can only rest upon the determinations of 

 Conceptions of space and time, the elements whose relation (intrinsic not extrinsic) motion is. 



(m) That, in the first place, the motion in general is a motion returning into itself, is founded 

 on the determination of particularity and individuality of the bodies in general (^ 269), so that 

 partly they have a center in themselves, and partly at the same time their center in another. 

 These are the determinations of Conceptions which form the basis of the false representatives 



(«) of Centripetal Force and Centrifugal Force, as if each of these were self-existing, extraneous 

 to the other, and independent of it ; and as if they only came in contact in their operations and 

 consequently externally. They are, as has already been mentioned, the Lines which must 

 be drawn for the mathematical determinations, transformed into physical realities. 



Further, this motion is utiiformly accelerated, (and — as returning into itself — in turn 

 uniformly retarded). In motion as free, Time and Space enter as different things which are 

 to make themselves effective in the determination of the motion, (§ 266, note.) In the so- 



(0) called Explanation of the uniformly accelerated and retarded motion, by means of the 

 alternate decrease and increase of the magnitude of the Centripetal Force and Centrifugal 

 Force, the confusion which the assumption of such independent Forces produces is at its 



{p) greatest height. According to this explanation, in the motion of a Planet from the Aphelion 

 to the Perihelion, the centrifugal is less than the centripetal force, and on the contrary, in 

 the Perihelion itself, the centrifugal force is supposed to become greater than the centripetal. 

 For the motion from the Perihelion to the Aphelion, this representation makes the forces pass 

 into the opposite relation in the same manner. It is apparent that such a sudden conversion 

 of the preponderance which a force has obtained over another, into an inferiority to the other, 

 cannot be anything taken out of the nature of Forces. On the contrary it must be concluded, 

 that a preponderance which one Force has obtained over another must not only be preserved, 

 but must go onwards to the complete annihilation of the other Force, and the motion must 

 either, by the Preponderance of the Centripetal Force, proceed till it ends in rest, that is, in 

 the Collision of the Planet with the Central Body, or till by the Preponderance of the Centri- 



