186 HALLE Y'S COMET. 



stances ; and both of these astronomers agree in stating that the tail was dis- 

 tinctly visible by the naked eye, and varied in length at different periods from 

 ten degrees to forty-seven degrees.* These circumstances are obviously in 

 perfect accordance with the former appearances of the same be Jy. 



On its departure from the sun it continued to be observed until the middle 

 of April, when its southern position caused the time of its rising to follow that 

 of the sun ; consequently it ceased to be visible in the morning. By a further 

 change in its position, however, it again appeared after sunset on the 29th, and 

 Messier then describes it as having the appearance of a star of the first mag- 

 nitude. But here again unfortunately another circumstance interposed a dif- 

 ficulty the light of the moon was at that time so strong as in a great degree 

 to overcome the effect of the comet. The body disappeared altogether in the 

 beginning of June. 



The comet had now commenced a new period under circumstances far more 

 favorable than had ever before occurred. An interval of seventy-six years 

 would throw its return into the year 1835. But during that interval, the 

 science of analysis, more especially in its application to physical astronomy, 

 has made prodigious advances. The methods of investigation have acquired 

 greater simplicity, and have likewise become more general and comprehensive ; 

 and mechanical science, in the large sense of that term, now embraces in its 

 formularies the most complicated motions and the most minute effects of the 

 mutual influences of the various members of our system. These formulre ex- 

 hibit to the eye of the mathematician a tableau of all the evolutions of these 

 bodies in ages past, and of all the changes they must undergo (the laws of na- 

 ture remaining unchanged) in ages to come. Such has been the result of the 

 combination of transcendent mathematical genius and unexampled labor and 

 perseverance for the last century. The learned societies established in the 

 various centres of civilization, have more especially directed their attention to 

 the advancement of physical astronomy : and have stimulated the spirit of in- 

 quiry by a succession of prizes offered for the solution of problems arising out 

 of the difficulties which were progressively developed by the advancement of 

 astronomical knowledge. Among these questions the determination of the re- 

 turn of comets, and the disturbances which they experience in their course, by 

 the action of the planets near which they happen to pass, hold a prominent 

 place. The French Academy of Sciences, in the year 1778, offered a high 

 mathematical prize for an essay on this subject, which was the means of call- 

 ing forth the splendid Memoir of Lagrange, which formed at once a complete 

 solution and a model for all future investigations of the same kind. Lagrange's 

 investigation was, however, of a general nature, and it remained to apply it to 

 the particular case of Halley's comet, the only one then known to be periodic. 

 In 1820, the Academy of Sciences at Turin offered a prize for this application 

 of Lagrange's formula, which was awarded to M. Damoiseau. In 1826, the 

 French Institute proposed a similar prize, having twice before offered it with- 

 out calling forth any claimant. On this occasion M. de Pontecoulant aspired 

 to the honor. " After calculations," says he, " of which those alone who have 

 engaged in such researches can estimate the extent and appreciate the fatigue- 

 ing monotony, I arrived at a result which satisfied all the conditions proposed 

 by the Institute. I determined the perturbations of Halley's comet by taking 

 into account the simultaneous actions of Jupiter, Saturn, Uranus (Herschel), 

 and the earth; the comet having passed in 1759 sufficiently near our planet to 

 produce in it (the comet) sensible disturbances ; and I then fixed its return to 

 its nearest point to the sun for the 7th of November, 1835." Subsequently to 

 this, however, M. de Pontecoulant made some further researches, which have 



* Mcmoires de 1' Academic des Sciences, 1760. 



