PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 823 



and reliitive divergence of each towards it is exactly the same. 

 They will, moreover, be cqui-distant from each other on reaching 

 it, the distances MS, HN, lO, JP, KQ, and LR, from the atoms 

 to the points where their original planes of motion cut tlie dynami. 

 cal equator, being all equal, and in one direction around the 

 equator, as represented in Fig. 7. 



The atoms having each crossed the dynamical equator, a reverse 

 action will now take place. The disturbances will go in in exactly 

 the same amounts, but in the opposite orders and directions, so 

 that the atoms will arrive at the six origninal poles of the system, 

 each 90° distant from the point where it is represented in Fig. 5, 

 and the directions of motion will become those represented in 

 Fig. 8. 



Pursuing a similar investigation to that already conducted, in 

 regard to the subsequent motions in the system, we shall find that 

 the atoms, in approaching the dynamical poles, will approach each 

 other ; but from the position of nearest approach, represented in 

 Fig. 9, a reverse action again takes place as before, and the atoms, 

 after eliminating their divergence from the true circles, again occupy 

 the six original poles, as in Fig. 5, each atom being now 180° from 

 its original position, and in that formerly occupied by its com- 

 panion atom. A series of precisely similar semi-revolutions will 

 continue to succeed each other until some disturbance from an 

 external force takes place. 



The application of a similar demonstration to ellipsoidal mole- 

 cules with unequal axis will not be attempted in this paper. It 

 will probably be found not very difficult, however, to the expert 

 mathematician, particularly if the principle of a tendency towards 

 equality of atomic momentum, in aggregated num])ers of unequal 

 inertia as well as in single couples, be admitted. When the mole- 

 cules are made up of single or compound atojns and the pairs are 

 of different weights, the heavier ones must, in accordar.C3 with this 

 law, move in smaller orbits as we have already observed. The 

 companion atoms of each pair, however, must alwaj^s be equal, as 

 otherwise they could not move in the same orbit, either circular 

 or elliptical. 



The thought will doubtless occur here, that the equal atoms of a 

 single pair can move in the same orbit only when that orbit is circu- 

 lar. When the motion becomes excentric or elliptical, it must then be 

 two orbits about a common focus, which is the centre of gravity of 

 the two atoms. (See Fig. 2.) It does not seem unreasonable, how- 



