A SYSTEM OF PARTICLES. 267 



In order to ascertain this, I have adopted an approximative process 

 of finding and comparing the integrals, and the result being negative, 

 we may conclude that the tendency is to restore the equilibrium in 

 this case. It is true an objection may be adduced from the enormous 

 complication of disturbances which must affect the equilibrium. The 

 only answer I can offer to this, is, that the rapidity with which a 

 disturbance is transmitted is enormous in the same proportion, and 

 hence we may conclude that the disturbances are easily righted. 



34. Adopting then a series of attractive particles, or two series, 



each of which attracts its own, but repels the others, we obtain, as 



our equations of motion, (the direction of transmission being that of 

 tlie axis of x) : 





2P h' + r-2f 



buti^^^"^^'U4^^^^"V 





■ dt' 



4P P-r . ,7r6f 

 —^ a . r^- Sm- ^ . 



e' r' \ 



(It e I r J X ^ 



2P (f + r-2/ 



e-" 



M — ^ — r'"-x^- 



/3 



Vol. VI. Part II. M .m 



