THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



JULY 1873. 



I. On the Relations between the characteristic Quantities occur- 

 ring in Central Motions. By R. Clausitjs*. 



IN a memoir published last yearf, I derived for the motion of 

 a material point about a fixed centre of attraction, and for 

 the motion of two material points around each other, some new- 

 relations between period of revolution, vis viva, ergal, and energy, 

 which have the indispensable condition that the motions take 

 place in closed paths. As, however, this condition is generally 

 fulfilled only with particular kinds of attractive forces, it appeared 

 to me important to extend the same method of treating the sub- 

 ject to the case in which the paths do not form closed curves; 

 and I take leave to communicate the following results of this 

 investigation. 



1. Two new equations advanced by me for stationary motions 

 serve as the basis of the inquiry. I will therefore first quote 

 these equations; and as their connexion with equations pre- 

 viously known has recently been mooted in various quarters, it 

 will perhaps be advisable also briefly to discuss this point, in 

 order on the one hand to make evident the connexion, and on 

 the other hand the difference. 



Given a freely movable point with the mass m, which at the 

 time t has the coordinates x, y, z, and is acted on by a force the 

 components of which, taken in the directions of the coordinates, 



* Translated from a separate copy, communicated by the Author, from 

 the Nachrichten der Konigl. Gesellsch. der Wiss. zu Gottingen of Dec. 25, 

 1872. 



t Nachr. d. K. Ges. d. Wiss. May 24, 1871 ; Math. Ann. von Clebsch 

 und Neumann, vol. iv. p. 231 ; Phil. Mag. November 1871. 



Phil. Mag. S. 4. Vol. 46. No. 303. July 1873. B 



