the summer of the year 1456 a comet was seen, which passed in a retrograde direction between the earth and the sun, in nearly the same manner; and although it was not observed astronomically, yet, from its period and path, I infer that it was the same comet as that of the years 1531, 1607, and 1682. I may, therefore, with confidence predict its return in the year 1758. If this prediction be fulfilled, there is no reason to doubt that the other comets will return.'

Later, in his Astronomical Tables, published in 1749, ten years before the return of the comet, Halley recurs again to his prediction in the most decided terms. 'You see, therefore,' he says, 'an agreement of all the elements in these three, which would be next to a miracle if they were three different comets; or, if it was not the approach of the same comet towards the sun and earth in three different revolutions, in an ellipsis around them. Wherefore, if according to what we have already said, it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.' *

Posterity has remembered and science recognised the claim of the English astronomer, by giving his name to the first comet whose periodical return, announced beforehand, was confirmed by the event. But the same posterity will not be unjust: it will give a legitimate share of honour to the French astronomers Clairaut and Lalande, who completed the work of Halley by calculating the retardation the comet would be subjected to in its voyage of seventy-six years. This second part of the history of a great discovery is perhaps still more surprising and instructive than the first.

As the epoch of the return predicted by Halley drew near,

[Halley died on January 14, 1741-2, and his Tabulæ Astronomicæ were published seven years after his death, in 1749. In 1752 a second edition appeared, and to it was appended an English translation, from which the passage cited in the text is extracted.-ED.]

all astronomers in France and Europe, occupied with this great event in the annals of science, held themselves in readiness to make observations of the comet. The time of its reappearance was uncertain. The known periods, as Halley had himself remarked, were unequal. Between 1531 and 1607 the interval was 27,811 days; from 1607 to 1682, 27,352 days, with a difference of 459 days between the perihelion passages. Would the new period be still shorter, or, on the contrary, after having been diminished by fifteen months and a half, would it return to its old value, or even exceed it? Several savants made calculations and offered various hypotheses respecting the path of the comet on its return and the date of its apparition, which was watched for from 1757.

It was then that Clairaut, a great mathematician, undertook the rigorous solution of the problem which Halley had only indicated-viz., the calculation of the perturbations which the comet of 1682 would experience whilst passing in the vicinity of the planets, especially of Jupiter and Saturn. It was a work of immense difficulty, and Clairaut, pressed for time, sought the assistance of Lalande, one of the most illustrious of French astronomers. Mdlle. Hortense Lepaute, the lady who has given her name to the Hortensia, undertook part of this laborious work. Thanks to the devotion to science. of these three worthy collaborateurs, the work was brought to a close in November 1758, and Clairaut presented to the Academy of Sciences a memoir from which the following is a short extract:

'The comet which has been expected for more than a year has become the subject of a curiosity much more lively than that which the public generally bestows upon questions of astronomy. True lovers of science desire its return because it would afford striking confirmation of a system in favour of which nearly all phenomena furnish conclusive evidence.

Those, on the contrary, who would like to see the philosophers embarrassed and at fault hope that it will not return, and that the discoveries of Newton and his partisans may prove to be on a level with the hypotheses which are purely the result of imagination. Several people of this class are already triumphing, and consider the delay of a year, which is due entirely to announcements destitute of all foundation, sufficient reason for condemning the Newtonians.

'I here undertake to show that this delay, far from invalidating the system of universal gravitation, is a necessary consequence arising from it; that it will continue yet longer, and I endeavour to assign its limit.'

Let us say at once that Clairaut found that the perihelion passage of the comet would be delayed 618 days, and that it would take place in 1759, a hundred days being due to the action of Saturn, and 518 days to that of Jupiter, bringing the perihelion passage to the middle of the month of April. Nevertheless, he made reservations with a modesty not less to his honour than his immense work, reservations necessitated by the terms omitted from the calculations, such as unknown causes of perturbation, and the fear that some errors might have been committed in the numerous and delicate operations performed. All these accumulated uncertainties might, according to Clairaut, make the difference of a month in the appointed time. The comet was actually seen on the 25th of December, 1758, by a Saxon peasant of the name of Palitsh in the environs of Dresden. Observations were made of the comet, and astronomers were soon able to prove that the perihelion passage would take place on the 13th of March, 1759, thirty-two days before the epoch calculated by Clairaut. Such a triumphant success of the theory produced in the scientific world a deep impression, and Lalande said with very legitimate enthusiasm:

'The universe beholds this year the most satisfactory phenomenon ever presented to us by astronomy; an event which, unique until this day, changes our doubts to certainty, and our hypotheses to demonstration. . . . M. Clairaut asked one month's grace for the theory; the month's grace was just sufficient, and the comet has appeared, after a period of 586 days longer than the previous time of revolution, and thirtytwo days before the time fixed; but what are thirty-two days to an interval of more than 150 years, during only one twohundredth part of which observations were made, the comet being out of sight all the rest of the time? What are thirtytwo days for all the other attractions of the solar system which have not been included; for all the comets, the situation and masses of which are unknown to us; for the resistance of the ethereal medium, which we are unable even to estimate, and for all those quantities which of necessity have been neglected in the approximations of the calculation? . . . A difference of 586 days between the revolutions of the same comet, a difference produced by the disturbing action of Jupiter and Saturn, affords a more striking demonstration of the great principle of attraction than we could have dared to hope for, and places this law amongst the number of the fundamental truths of physics, the reality of which it is no more possible to doubt than the existence of the bodies which produce it.'

Another return of Halley's comet took place in 1835. It furnished an opportunity of testing the progress made by theoretical astronomy during the period of seventy-six years occupied by the comet in once more performing its revolution. Taking the perihelion passage of 1759 as the point of departure, and following in the steps of Clairaut, two French astronomers, Damoiseau and Pontécoulant, independently undertook the laborious task of determining the epoch of the perihelion passage of the comet, taking into account the perturbating

action of the planets. Amongst the unknown disturbing causes which Clairaut had been unable to take into account, but which entered into the researches of the two above-mentioned savants, was the planet Uranus, discovered by Sir William Herschel in 1781. According to Damoiseau the comet should have passed its perihelion on November 4; according to Pontécoulant not till November 13, 1835. Two other astronomers, Lehmann and Rosenberger, had fixed the dates of November 11 and 26. On August 5 the comet was seen at Rome. Observations gave for the exact date of the perihelion

1. As seen by the naked eye October 24. 2. As seen in the telescope the same day.

passage November 16, at half-past ten in the morning, the difference between the observed date and the mean of the calculated dates being less than three days. The result showed an increase of sixty-nine days above the length of the preced

*

On re-computing the disturbing influence of the planets Pontécoulant calculated that a period of 28,0063 days should have elapsed between the perihelion passages of 1835 and 1759. Observations proved it to be 20,006 days. The difference, which is only two-thirds of a day, shows what progress had been made both in theoretical and practical astronomy.