a < 'Mi.r^ 



M the precursors of same calamity to the human race. Even in tin 

 assent day thU opinion is prevalent among the ruder nation, of the 

 nirth. The intelligence brought by the Overland mail respecting the 

 tenor caused throughout Egypt nd India by the great oomet of 1858, 

 nuwt be f rwh in the recollection of every reader ; and we may eatily 

 infer frv.m thu circumstance what mut hare been the impression pro- 

 duoed on the (till ruder tribe* of Central Africa by the same mysterious 

 object daring the ooane of iu rapid pacatge toward* the southern 

 hemisphere. The ancient |>hilaeophen failed to arrive at any just 

 cuocluaioa* respecting the mature or movement* of comet*. According 

 to Arutotle, comet* are merely bodie* of terrestrial origin, which are 

 geaaiatnil in the upper region* of the atmosphere. Thin opinion team* 

 to bar* been generally entertained by attrouomer* down to the time of 

 Tycho Bnhc 1 , who, by a dieouailon of the observations of the comet of 

 1577, fin illy succeeded in demonstrating tlmt it must have been situate 

 beyond the moon* orbit. Henceforward comet* assumed their true 

 place a* bodie* of cele*tial origin. It (till remained to discover the 

 nature of the paths which they described in the heavens, and to unfold 

 the laws of their movement*. Tycho Brahd imagined that comet* 

 more in straight line* ; and Kepler eeems to have entertained the same 

 opinion. Heveliu* was the first who conjectured that the path of a 

 oomet might be curvilinear; and Doerfel (1681) showed that the comet 

 of 1680 actually described a parabola having the sun in the focus. 



It was reserved for the immortal Newton to discover the real nature 

 of the movements of comets, and to demonstrate that, like the planets, 

 they are mainly regulated by the attractive force of the sun. In the 

 course of his researches on the principle of gravitation, this great 

 philosopher had found that a body which receives an impulse in free 

 space, and is subjected to the attractive force of the sun, will necessa- 

 rily revolve in a conic section having the aim in the focus. The orbit 

 actually described by the body may be either a circle, an ellipse, a para- 

 bola, or an hyperbola, but it mtat be one or other of those curves. By 

 a rigorous investigation, founded on Flamsteed'a observations of the 

 oomet of 1880, Newton discovered that the orbit of that body was a 

 parabola having the sun in the focus. He moreover succeeded in 

 demonstrating that the radius vector of the comet described around 

 the sun equal areas in equal times, conformably to Kepler's second law 

 of the planetary movements. Nor did his researches stop here : he 

 also invented a method by means of which it would be possible from 

 three ol*ervations of a comet to determine the element* of it* orbit. 

 In this investigation, he supposed the species of orbit described by the 

 comet to lie a parabola. His opinion was, that all such bodies revolve 

 in elliptic orbit* of great eccentricity ; but according to the doctrine of 

 conic sections, the curvature of a very excentric ellipse does not sensibly 

 differ from that of a parabola. He therefore adopted the parabolic 

 aosumptiou, which has the advantage of facilitating the solution of the 

 problem. 



Newton's method for determining the orbit of a comet, supplied the 

 means of ascertaining all the elements if the orbit was a jnrabola ; and 

 all the element* except the major axis if the orbit was elliptic. In 

 regard to the latter supposition, the adoption of which, as already men- 

 tioned, accorded with Newton's views, the author of the ' Prinvipia' 

 remarked, " I leave their axe* and times of revolution to be determined 

 from Uie comparison of comets which return in the same orbit* after 

 long periods." (' Princip.' lib. iii., prop, xii, 1st edit., 1687.) 



H.illcv, who was one of the earliest supporters of the theory of 

 gravitation, resolved to reduce to practice Newton's ideas on the theory 

 of comet*. He accordingly collected together all the recorded observa- 

 tion* of those bodies extending down to the year 1700, and with in- 

 credible labour calculated the parabolic elements of their orbits in 

 every instance wherein trustworthy data were available for such a 

 purpose. The comet* whose orbit* were thus calculated amounted to 

 twenty-four in number. They appeared in the following years : 



1480 



1484 



1490 



I486 



1607 





I 



1SJ7 

 1471 

 158! 

 15JJ 

 1546 

 1477 



1111 



18J2 

 1601 

 1664 

 1664 

 1071 

 1677 



I'M, 

 1681 

 1683 

 1684 

 1686 

 1698 



A comparison of the orbit* of the comet* of 1531, ICO", and 1082, 

 clearly indicated to Halley that they referred to the same comet. This 

 will readily ap|*ar from the following statement of their elements, 

 extracted from Halley's table : 



Comet of Comet of Comet of 



1431. 1607. 168]. 



iMtllade of Mwnding node 49 1 14* SO* Jr 11 ] 



iMluution of orbit . . r 17' V \; :.,. 



Loofitoda of perihelion . 301' J9' Sol 1 16* StU'SJ' 



Perihelion punf 

 IMiUM* from perihelion 



U> aMTDdinf nvdo 

 Motion .. 



Auf . 14 

 lion \ . .,, ... 

 . .) ' 



. KetrofTwU 



0483 

 Oct. IS Kept. 4 



I0' ' 108 '2 J' 



Retrograde Retrograde. 



Upon comparing the interval* between two consecutive perihelion 

 passages, it will be found that while for the comets of 1531 and 1607 

 the interval amount* to 76 years and 53 days; the corresponding 



interval for the comet* of 1607 and 1682 amount* to only 74 years and 

 833 days. The difference between the two intervals amount* to 1 year 

 and 95 days, or somewhat more than 15 month*. But acconl 

 the theory of gravitation, a body revolving in an elliptic orbit 

 the sun in virtue of the attractive force of the latter, ought to return 

 to it* perihelion at succeesive intervals of equal magnitude; or. in 

 other words, ought to perform its successive revolutions in equal time*. 

 Halley, however, did not fail to perceive the origin of this apparent 

 discordance. He remarked, in fact, that the disturbing action exercised 

 by the larger planet* upon the comet could not fail to accelerate or 

 retard the passage of the perihelion, a* the case might bo, and would 

 thereby derange the equality in the tunes of revolution which would 

 otherwise ensue. He loona tli.it in the summer of 1681, when the 

 comet was approaching the perihelion, it passed so close to the plan, t 

 Jupiter that it must have been powerfully disturbed by that )><!>. 

 and he clearly perceived that the effect of such a disturbance would 

 have been to retard the arrival of the comet in the perihelion. 



Adopting the interval which elapsed between the perihelion pas- 

 sages of 1631 and 1607, the comet ought to return to the perihelion in ' 

 November, 1758; on the other hand, the adoption of the corresponding 

 interval between 1607 and 1682 would fix the passage of the peri- 

 In-lioii in the month of Auguxt, 1757. Halley very sagaciously infenvd. 

 from a rough estimation of the !!-.( which would be produced l>y the 

 disturbing action of Jupiter (for in bis time there existed n method* 

 for rigorously calculating the amount of such perturbations), tli.it tin- 

 comet would not be visible before the end of 1753, or the beginning of 

 1/59 ; and he appealed to posterity not to lose sight of the fact. 

 the comet should really return about the year 1758, the prediction of 

 such a result was due to an Englishman. 



The ' AstronoiuiiC Cometicas Synopsis,' containing Halley's researches 

 on Comets, was published in the ' Philosophical Transaction*' f< 

 and again at the University press at Oxford, and also in an Knglish 

 translation, published in London in 1705, which was reprinted in 1706, 

 in the ' Miscellanea Curiosa.' It was again reprinted in the second 

 edition of Gregory's 'Astronomy;' in on English edition of tin 

 work, 1715; in Le Mourner's 'Theory of Comets;' and was finally left 

 for publication in an augmented form by Halley himself, and was pub- 

 lixhcd with his 'Astronomical Tables,' in 1749. 



During the period which elapsed between the publication of Halley'.* 

 researches on cometary orbits, and the time announced for the return 

 of the comet of 1082 to the perihelion, on important step h., 

 mode in the application of analysis to physical astronomy. M 

 for solving by on approximative process the problem of planetary 

 perturbation were invented, independently of each other, by KM] i. 

 Claimut, and D'Alcmbert, and were successfully used in com put 

 inequalities of the moon's motion. As the time fixed by Halley for the 

 return of. the comet to the perihelion druw nigh, the suKjeet of it* 

 motion, which was calculated to exercise- an important influenec on the 

 Newtonian theory of gravitation, naturally excited a lively interest 

 throughout every country. in Kurope. Clairaut undertook the arduous 

 task of computing the effects of planetary 



assisted in his calculation- l>y l.alande, who luul just commenced In 

 astronomical career, and also by Madame l.cpaute, the wife of a well 

 known watchmaker of the day. The. principal disturbing bodies in 

 this case were Jupiter and Saturn. It was found that both 

 tended to retard the passage of the comet through the perihelion. 

 According to Clairaut's calculations, he found that t i i],| I., 



retarded 518 days by the action of Jupiter, and 100 days by the 

 of Saturn. Taking these circumstances into considei .iti..n. lie found 

 that the time of revolution would be 76 years, 211 days; and since tin 

 comet had previously passed the perihelion on the 14th of 

 1682, it followed that the next passage of the perihelion would take 

 place on the 13th of April, 1759. Clairaut, however remarked that the 

 omission of many small quantities, which was unavoidable in th 

 ment of so intricate a question, might cause the real time of th. 

 comet's passage of the perihelion to differ as much OB a month from the 

 calculated time. 



The comet was first observed on the 25th of December, 17-' 

 PalitMch, an amateur astronomer of Saxony. It passed through tin 

 IK'rihelion on the 13th of March, 1759; the time was consequently 

 within the limit* assigned by Clairaut. Having revised his 

 lations, the French geometer found that the error in the computed 

 time amounted to only twenty-two days. 



The return of this comet, conformably to the results of calculation, 

 established lieyond doubt the truth of Newton's theory of comet 

 added fresh lustre to the renown of Halley, by whose name it \i.. 

 been justly designated. Before proceeding to give some ace. >unt, . ,f t h. 

 circumstance* connected with it* perihelion passage in 1 - 

 present the reader w ith a brief statement of some of the more i . 

 able comet* recorded in history. 



371 B.C. In thin year there appeared a comet of great splendour, 

 which is alluded to by Diodorus Siculus and also by Aristotle. The 

 fornii r of those writers states that the phciioi. u poised l.y 



the inhabitants of Greece to have presaged the destruction of the 

 Achaian cities, Helix and liuris. According to Aristotle, the t.iil 

 extended over a third of the heavens, or in otlier words, overan HI. 

 of 60*. 



184 B.C. Justin states that there apiwarcJ in this year a splendid 



