228 GENERAL CONDITIONS OF SCIENTIFIC RESEARCH. 



movements have been felt, trembling along the far-reach- 

 ing line of our analysis, with a certainty hardly inferior to 

 that of ocular demonstration.' 



'Halley had the glory of having first detected a 

 periodic comet, in the case of that which has since borne 

 his name. But this great discovery was not made without 

 labour. In 1705, Halley explained how the parabolic 

 orbit of a planet may be determined from three observa- 

 tions ; and, joining example to precept, himself calculated 

 the positions and orbits of twenty-four comets. He found, 

 as the reward of his industry, that the comets of 1 607 and 

 1531 had the same orbits as that of 1682. And here the 

 intervals are nearly the same, namely, about seventy-five 

 years. Are these three comets, then, identical ? In look- 

 ing back into the history of such appearances, he found 

 comets recorded in 1456, in 1380, and 1305 ; the inter- 

 vals are still the same, seventy-five or seventy-six years. 

 It was impossible now to doubt that they were the periods 

 of a revolving body ; that the comet was a planet ; its 

 orbit a long ellipse, not a parabola.' 4 But if this were so, 

 the comet must reappear in 1758 or 1759. Halley pre- 

 dicted that it would do so ; and the fulfilment of this 

 prediction was naturally looked forward to, as an additional 

 stamp of the truth of the theory of gravitation.' ' But in all 

 this the comet had been supposed to be affected only by 

 the attraction of the sun. The planets must disturb its 

 motion as they disturb each other. How would this dis- 

 turbance affect the time and circumstances of its reap- 

 pearance ? Halley had proposed, but not attempted, to 

 solve this question.' ' The effect of perturbations on a 

 comet defeats all known methods of approximation, and 

 requires immense labour. " Clairau t," says Bailly, " under- 

 took this ; with courage enough to dare the adventure, 

 he had talent enough to obtain a memorable victory ; " 



