308 PROFESSOR HAMILTON ON A GENERAL METHOD IN DYNAMICS. 



which gives, rigorously, 



if we establish by analogy the definition 



U, = t + 2.^{(||y + (f)Ven; (F3, 



and therefore approximately 



S,= r{V-V,)dt, , . (G8.) 



*y 



the parts Sj Sg being chosen so as to vanish with the time. These remarks may all 

 be extended easily, so as to embrace relative and polar coordinates, and other marks 

 of position, and offer a new and better way of investigating the orbits and pertur- 

 bations of a system, by a new and better form of the function and method of this 

 Essay. 



March 29, 1834. 



