176 HALLEY'S COMET. 



But a difficulty of a peculiar nature obstructs the solution of this question. 

 It so happens that the only part of the course of a comet which ever can be 

 visible, is a portion such as D, L, G, throughout which the ellipse, the para- 

 bola, and hyperbola so closely resemble one another, that no observations can 

 be obtained with sufficient accuracy to enable us to distinguish one from the 

 other. In fact, the observed path of any comet, while visible, may indiffer- 

 ently belong to an ellipse, parabola, or hyperbola. 



There is, nevertheless, a certain degree of definiteness in the observed 

 course of the body, which, although insufficient to enable us to say what the 

 nature of the entire orbit may be, is still sufficiently exact to enable us to rec- 

 ognise any other comet, which moves, while visible, nearly in the same course. 

 If then, after the lapse of a certain time, a comet should be found following 

 that course, there would be a strong presumption that it is the same comet re- 

 turning again to our system, after having traversed the invisible part of its 

 orbit. This probability would be strengthened, if, on the two occasions, the 

 body should present a similar appearance ; although this is not essential to the 

 identity, since, as has been stated, the same comet is observed to undergo con- 

 siderable changes, even during a single appearance. 



The time between the appearances of comets following nearly the same path 

 being noted, the interval the identity of the bodies being assumed must 

 either consist of a single period, or of two or more complete periods. The 

 epoch which is usually taken as the commencement of a new revolution being 

 the instant of time at which the comet is at its least distance from the sun, the 

 place of the comet at that moment is called its perihelion. The period of a 

 comet may, therefore, be defined to be the interval of time between two suc- 

 cessive arrivals at its perihelion. 



Having succeeded in identifying the path of any two comets, we are then 

 in a condition to predict with some degree of probability the time at which the 

 next appearance may be expected. It is certain providing that it be the same 

 comet that it will arrive at its perihelion after the same interval nearly ; also 

 that it may arrive at half the interval, or a third of the interval, or any other 

 fraction corresponding to the possible number of unobserved appearances which 

 may have taken place in the interval between those appearances from which 

 its return has been predicted. The times, therefore, at which the comet .may 

 be looked for with a probability of rinding it, may without difficulty be predicted ; 

 and if it has been a conspicuous body in the heavens on the occasion of its 

 former appearances, there is a probability that the whole interval between these 

 appearances constituted but one period, and that no return of the comet had 

 escaped observation. 



Such are the circumstances which may have been conceived to have pre- 

 sented themselves when the idea first occurred of attempting to ascertain the 

 identity of former comets, and to discover the means of predicting their future 

 return. The Principia of Newton, which laid the foundation of all sound as- 

 tronomical science, had appeared soon after tie middle of the seventeenth 

 century ; and Halley, the contemporary and friend of Newton, had his atten- 

 tion naturally directed to the physical inquiries which that immortal book sug- 

 gested. 



One of the most curious and interesting of these questions was that to which 

 we now allude. Halley, referring to the records of all former observers, 

 with a view to obtain means of determining, so far as possible, the course 

 of former comets, succeeded in identifying one which he had himself ob- 

 served in 1682, with comets which had appeared on several former occa- 

 sions , and found, that the interval between its successive returns was from 

 75 to 76 years. This discovery has since been fully confirmed, and the comet 



