sf.ct.iv.] DISSERTATION SECOND. II b 



must be a conic section, having the sun in one of its 

 foci, and might either be an ellipse, a parabola, or even 

 an hyperbola, according to the relation between the force 

 of projection and the force tending to the centre. As 

 the eccentricity of the orbit on every supposition must be 

 great, the portion of it that fell within our view could not 

 differ much from a parabola, a circumstance which rendered 

 the calculation of the comet's place, when the position of the 

 orbit was once ascertained, more easy than in the case of the 

 planets. Thus far theory proceeded, and observation must 

 then determine with what degree of accuracy this theory 

 represented the phenomena. From three observations of 

 the comet, the position of the orbit could be determined, 

 though the geometric problem was one of great difficulty. 

 Newton gave a solution of it ; and it was by this that his the- 

 ory was to be brought to the test of experiment. If the 

 orbit thus determined was not the true one, the places of the 

 comet calculated on the supposition that it was, and that it 

 described equal areas in equal times about the sun, could not 

 agree with the places actually observed. Newton showed, 

 by the example of the remarkable comet then visible (1680), 

 that this agreement was as great as could reasonably be ex- 

 pected ; thus adding another proof to the number of those 

 already brought to support the principle of universal gravita- 

 tion. The comets descend into our system from all different 

 quarters in the heavens, and, therefore, the proofs that they 

 afforded went to show, that the action of gravity was confined 

 to no particular region of the heavens. 



Thus far Newton proceeded in ascertaining the existence, 

 and in tracing the effects, of the principle of gravitation, and 

 had done so with a success of which there had been no in- 

 stance in the history of human knowledge. At the same time 

 that it was the most successful, it was the most difficult re- 

 search that had yet been undertaken. The reasonings up- 



