COMETS. 



341 



that its distance from the earth must be greater than 

 that of the moon, in which this parallax was ap- 

 parent to him. This was one step ; and it was an 

 important one : it removed comets to such a distance 

 from the earth, that their use could not well be sup- 

 posed to be for it, or their influence upon it very 

 great. The general law of the motion of bodies in 

 free space, as well as his own particular observations 

 on the comet of 1680, led Newton to conclude that 

 the orbits of the comets must, like those of the plan- 

 ets, be ellipses, having the sun in one focus, but far 

 more eccentric, and having their aphelions, or great- 

 est distances from the sun far remote in the regions 

 of space. The idea thus thrown out by Newton 

 was taken up by Dr Halley, who collated the ob- 

 servations which had been made of all the twenty- 

 four comets, of which notice had been taken previ- 

 ous to 1680. The results were abundantly curious ; 

 with but few exceptions, they had passed within less 

 than the earth's shortest distance from the sun ; 

 some of them within less than one third of it ; and 

 the average about one half. Out of the number, too, 

 nearlj two thirds had had their motions retrograde, or 

 moved in the opposite way to the planets. While 

 Halley was engaged on these comparisons and de- 

 ductions, the comet of 1682 made its appearance, and 

 he set about observing it with great care, in order to 

 determine the elements of its orbit. Having done 

 so, he found that there was a wonderful resemblance 

 between it and three other comets that he found re- 

 corded the comets of 1456, of 1531, and of 1607. 

 The times of the appearance of these comets had 

 been at very nearly regular intervals, at least, the 

 differences had been only fractional parts of a year, 

 the average period being between 75 and 76 years. 

 Their distances from the sun, when in perihelion, or 

 when nearest to that luminary, had been nearly the 

 same, being nearly six-tenths of that of the earth, and 

 not varying more than one-sixtieth from each other. 

 The inclination of their orbits to that of the earth 

 had also been nearly the same, between 17 and 18 ; 

 and their motions had all been intrograde. Putting 

 them together, Dr Halley concluded, that the 

 comets of 1456, 1531, 1607, and 1682, were re-ap- 

 pearances of one and the same comet, which revolv- 

 ed in an elliptic orbit round the sun, performing its 

 circuit in a period varying from a little more than 

 seventy -six years to a little less than seventy-five ; or 

 having, as far as the observations had been carried, a 

 variation of about fifteen months in the absolute 

 duration of its year, measured according to that of 

 the earth. For this variation in the time of its re- 

 volution, Dr Halley accounted upon the supposition 

 that the form of its orbit had been altered by the at- 

 traction of the remote planets, Jupiter and Saturn, 

 as it passed near to them ; and thence he concluded, 

 that the period of its next appearance would be 

 lengthened, but that it would certainly re-appear in 

 1758 or early in 1759. Its doing so was, of course, 

 the fact that was to be decisive of the orbits of 

 comets, and that they were regular and permanent 

 bodies, obeying the general laws of matter. Halley 

 did not live to see the verification of his prediction ; 

 he died in the year 1742, at the advanced age of 

 eighty-four. 



Soon after his death, Clairault, D'Alembert, and 

 Euler, three of the most eminent mathematicians of 

 Europe, set about the solution of what is called 

 " the problem of the three bodies ;" that is to deter- 

 mine the paths described by three bodies, projected 

 from three given points, in given directions, and with 

 given velocities, their gravitating forces being direct- 

 Ty as their quantities of matter, and inversely as the 

 squares of their distances. The object of this prob- 

 lem is to find the disturbing effects that the bodies 



composing the solar system have upon each other ; 

 and it applies to comets, when within the limits of 

 planetary action, as well as the planets themselves. 

 After some errors, into which all the three had been 

 led, and which gave a result that seemed to overturn 

 the whole doctrine of gravitation, Clairault succeed- 

 ed in obtaining an approximate solution, which 

 agreed with and confirmed that theory. Having 

 done so, he applied it to the calculation of the dis- 

 turbed influence of Jupiter and Saturn, which Hal- 

 ley had predicted would retard the comet of 1682, 

 in its re-appearance about 1758. The results of 

 Clairault's calculations, were, that the comet would 

 be retarded 100 days by the attraction of Saturn, 

 and 51 8 by that of Jupiter, so that it would not come 

 to the perihelion, or point of its orbit nearest the sun, 

 till the 13th of April, 1759. Clairault, however, fix- 

 ed certain limits, within which his calculations might 

 probably be erroneous. It was eventually found that 

 the difference between calculation and observation 

 was less than that which he assigned. Clairault read 

 his investigations to the academy of sciences in No- 

 vember, 1758 ; and, in little more than a month after- 

 wards, the comet made its appearance ; and it reach- 

 ed its perihelion on the 13th of March, in the fol- 

 lowing year, being thirty days earlier than he had 

 calculated. Subsequent calculations enabled him to 

 reduce the error to nineteen days ; and, though the 

 calculations of the disturbing forces were only ap- 

 proximations, enough had been done to prove the 

 return, and determine the orbit of one comet, and 

 give every reason for concluding that all comets, 

 Being bodies of the same class, are subject to the 

 same general laws as the planets, and only vary 

 from each other in the proportion and magnitude of 

 their orbits. There was one further confirmation. 

 Clairault had calculated that the node of the comet's 

 orbit, or the point in which it cut the plane of the 

 orbit of the earth, would advance 2 33' in absolute 

 space, or 1 29' more than the equinoctial points, the 

 precession of which, in the time of the comet's re- 

 volution, was 1 4' ; and observation gave exactly 

 the same result ; so that the only difficulty that re- 

 mained in the doctrine of comets was in the estima- 

 tion of the disturbances to which they are exposed 

 from the other bodies of the system, more especially 

 in the parts of their orbits most remote from the sun, 

 where their motions are comparatively slow. Along 

 with the period of this comet, and its perihelion dis- 

 tance, the magnitude and form of its path were 

 known. Estimating the mean distance of the earth 

 from the sun at 95,000,000 miles, the mean distance 

 of the comet is 1,705,250,000 miles ; its greatest 

 distance from the sun, 3,355,400,000 ; its least dis- 

 tance, 55,100,000 ; and the transverse or largest dia- 

 meter of its orbit, 3,4 10,500,000. Therefore , though 

 its aphelion distance be great, its mean distance is less 

 than that of Herschel; and, great as is the aphelion 

 distance, it is but a very trifling fraction less than 

 one five-thousandth part of that distance from the sun, 

 hearer than which the very nearest of the fixed stars 

 cannot be situated ; and as the determination of their 

 distance is negative and not positive, a distance 

 within which they cannot be, and not one at which 

 they actually are, the nearest of them may be at 

 twice or ten times that distance. The comet of 1 759 

 is, therefore, a body belonging to the solar system, 

 and quite without the attraction of any body which 

 does not belong to that system ; and, as this is de- 

 termined of one comet, analogy points it out as being 

 the case with them all. M. M. Danosseau and Pou- 

 teculant, have calculated the return of this comet, 

 on the 4th or 7th of November, 1835, which differ- 

 ence of three days, arises from their having taken 

 different values for the masses of tne planets. M. 



