8 4 KINETICS OF A PARTICLE. [159. 



(2) In Ex. (i), write out the equations for the relative motion of 

 either particle with respect to the common centroid. 



159. The theory of central forces is treated with considerable elabo- 

 ration in most works on theoretical mechanics ; a few references only 

 will here be given : P. APPELL, Traite de mecanique rationnelle , Paris, 

 Gauthier-Villars, 1893, Vol. I., pp. 354-405 ; B. WILLIAMSON and F. A. 

 TARLETON, An elementary treatise on dynamics, London, Longmans 

 (New York, Appleton), 2d edition, 1889, pp. 147-205 ; P. G. TAIT and 

 W. J. STEELE, A treatise on dynamics of a particle, London and New 

 York, Macmillan, 6th edition, 1889, pp. 113-166; W. H. BESANT, A 

 treatise on dynamics, Cambridge, Bell (New York, Macmillan), 2d 

 edition, 1893, pp. 120-166, and 267-275 ; W. WALTON, A collection of 

 problems in illustration of the principles of theoretical mechanics, Cam- 

 bridge, Bell, 3d edition, 1876, pp. 248-297. All these works contain 

 numerous examples for practice. The theory of planetary motion is, of 

 course, treated in works on theoretical astronomy. The student will 

 also consult with advantage : W. SCHELL, Theorie der Bewegung und der 

 Kr'dfte, Leipzig, Teubner, 2d edition, Vol. I., 1879, pp. 373-387; 

 E. BUDDE, Allgemeine Mechanik der Punkte und starren Systeme, 

 Berlin, Reimer, Vol. I., 1890, pp. 170-181; B. PRICE, A treatise on 

 analytical mechanics, Oxford, Clarendon Press (New York, Macmillan), 

 Vol. I. (= Vol. III. of A treatise on infinitesimal calculus}, 2d edition, 

 1868, pp. 508-574; O. RAUSENBERGER, Lehrbuch der analytischen 

 Mechanik, Leipzig, Teubner, Vol. I., 1888, pp. 32-102, where the 

 problem of planetary motion is very fully discussed; T. DESPEYROUS, 

 Cours de mecanique, avec des notes par G. Darboux, Paris, Hermann, 

 1884, Vol. I., pp. 336-369, 427-440, and Vol. II., pp. 38-57, 461-466 ; 

 and others. 



