298 



PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 



w 



(0 _ 7,(1) c^(0 



.(1) 



;(i) ^ Ji) 





(2) 



^w^^Wa«+yv-^w^^P)^ 



In this expression, 

 r'(i) 



(T^) 



/ (1)2 



± V 2 K + m„)/'> + 2 g-<" - *^, 





(U5.) 



r^^^, . . r^" *^, being abridged expressions for the distances r^^'", . . r^" *'"^, and 

 /'\ . ./""^\ being abridgements for the functions /^^* "^, . . ./(«"*' ")^ of these 

 distances, of which the derivatives, according as they are negative or positive, express 

 the laws of attraction or repulsion : we have also introduced 2 w — 2 auxiliary quan- 

 tities h!" g^ . . . h>^~ g , to be eliminated or determined by the following equa- 

 tions of condition : 



0-^0) , X'^Sjl^. JO '^ 



^-^ +/.0) 8;i(i) ^^ ' 



0^^(2) . X'^il^^,(^) 



> • • • 



and 



or 



- ^(«-o . /*'" ^-I-: - ^>-i) 



(V^) 



8 ^(1) g ^(2) 



8g(i) ~8gC2) — • • 

 along with this last condition, 



8^C«-i)' 





+ ...+ 



^„-lg("-0 



H/ 





and we have denoted by ^^^\ . . . ^^**"-'), the angles which the final distances 

 • ^ ''~^\ of the first n—l points from the last or nth point of the system, make 



^(1), 



