814 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



tact, separate to an infinite distance, constantly approaching, but 

 never reaching, the zero limit of velocity. 



If the associated force in the approaching atoms is greater than 

 that of the potential of gravity, the atoms, after contact, will also 

 recede never to return, and the limit of ultimate velocity AviU be 

 the excess of the former force over the latter. 



Upon these relations between the associated and potential forces, 

 depends the so-called attraction or repulsion between the atoms ; 

 nor is it necessary to make the comparison between them at the 

 instant of collision, for the diiierence between the entire associated 

 force and that portion due to gravity will evidently be constant. 



When in the case of the two isolated atoms a lateral force is 

 introduced, we" shall have analogous results, arising from similar 

 relations between the amounts of associated force and the potential 

 of gravity, if the comparison is made between the latter and that 

 component of the former, which represents the tendency of the 

 atoms to approach or recede from each other, i. e., the centripetal 

 or centrifugal force. Correspondiug to the described cases of rec- 

 tilinear motion are three classes of orbits, all curves of the sjcond 

 order or conic sections. 



First, the ellipse, including the circle, which is an ellipse having 

 equal axis, Fig. 1 and Fig. 2. These correspond to the vibrating 

 atoms, and will occur when the centrifugal force is less than the 

 potential of gravity. 



Second, the parahola^ Fig. 3, which is an ellipse with an infinite 

 transverse axis. Here the centrifugal or centripetal force is just 

 equal to the potential of gravity. 



Third, the hyperbola, Fig. 4, in which the associated force is in 

 excess, and the atoms merely deflect each other from their courses. 



In all these figures, A and B represent the atoms, and C the 

 centre or common focus about which they move. A, B and C lie 

 always in a straight line, forming a double radius vector, each 

 part of which describes equal areas in equal times. 



If the two atoms are unequal in inertia, the centre of motion or 

 focus of the orbit will be in the centre of gravity, and the paths 

 described Avill be similar, but inversely proportional in dimensions 

 to the inertias of the two atoms. 



The three possible relations of the atoms to each other, then, 

 are first, attraction, second, equilibrium, and third, repulsion, each 

 of Avhich may be changed into the others by adding or abstracting 

 momentum or centrifugal force, ordinarily called heat. The first 



