ASTRONOMY. 
mufl; differ a much greater refinance tlian the denfe body 
Of the comet does, and therefore ought to be left behind, 
and would not appear oppofite to the Sun ; and afterwards 
they ought to appear towards the Sun. Alfo, if the fplen- 
dour of the tails be owing to the reflection and refraCtion 
of the Sun's rays, it ought to diminifli the luftrc of the 
(tars feen through it, which would have their light reflect¬ 
ed and refrafted in like manner, and confequently their 
brightnefs would be diminifhed. 
Dr. Halley, in his defcription of the aurora borealis in 
jy 16, fays, “ The ftreams of light fo much refembled the 
long tails of comets, that at firft fight they might well be 
taken for fuch.” And afterwards, “ this light feems to 
have a great affinity to that which the effluvia of eleCtric 
bodies emit in the dark.” Pkii.TranJ'. No.cccxlvii. D.de 
Mairan alfo calls the tail of a comet, the aurora borealis 
of the comet. This opinion Dr. Hamilton (upports by the 
following arguments: A fpeftator, at a diftance from the 
Earth, would fee the aurora borealis in the form of a tail 
oppolite to the Sun, as the tail of a comet lies. The au¬ 
rora borealis has no effeft upon the ftars feen through it, 
nor has the tail of a comet. The atmofphere is known to 
abound with eleCtric matter, and the appearance of the 
eledtric matter in vacuo is exactly like the appearance of 
the aurora borealis, which, from its great altitude, may be 
confidered to be in as perfeft a vacuum as we can make. 
The eledtric matter in vacuo differs the rays of light to 
pafs through, without being affe&ed by them. The tail 
of a comet does not expand itfelf iideways, nor does the 
eledtric matter. Hence he fuppofes the tails of comets, 
the aurora borealis, and the eledtric fluid, to be matter of 
the fame kind. We may add, as a farther confirmation 
of this opinion, that the comet in 1607 appeared to flioot 
out the end of its tail. Le P. Cyfat remarked the un¬ 
dulations of the tail of the comet in 16x8. Hevelius ob- 
fet ved the fame in the tails of the comets in 1652 and 1661. 
M. Pingre took notice of the fame appearance in the co¬ 
met of 1769. Thefe are circumftarrces exactly frmilar to 
the aurora borealis. Dr. Hamilton conjectures, that the 
life of the comets may be to bring the eledtric matter, 
which continually elcapes from the planets, back into the 
planetary regions. “ Thefe arguments (fays Mr. Vince) 
are ttrongly in favour of this hypotheiis ; and, if this 
be true, we may farther add, that the tails are hollow ; for, 
if the eledtric fluid only proceed in its firft direction, and 
do not diverge fideways, the parts direCtly behind the co¬ 
met will not be filled with it; and this thinnefs of the tails 
will account for the appearance of the ftars thro’ thein.” 
With refpeCt to the motions of comets, Kepler, who had 
an opportunity of obferving two of them, concluded, 
“ that comets moved freely through the planetary orbs, 
with a motion not much different from a rectilinear one; 
but of what kind he could not precifely determine.” He¬ 
velius embraced the fame hypotheiis of a rectilinear mo¬ 
tion ; but, finding his calculations did not perfectly agree 
with his obfervations, he concluded, “that the "path of a 
comet was bent in a curve line, concave towards tlieJSun.” 
lie fuppofed a comet to be generated in the atmofphere of 
a planet, and to be difeharged from it, partly by the ro¬ 
tation of the planet, and then to revolve about the Sun 
in a parabola by the force of projection and its tendency 
to the Sun, in the fame manner as a projeCtile upon the 
Earth’s furface deferibes a parabola. At length, the fa¬ 
mous comet in 1680, delcending nearly in a right line to¬ 
wards the Sun, arofe again from it in like manner, which 
proved its motion in a curve about the Sun. G. S. Doer- 
fell, nxinifter at Plaven in Upper Saxony, made obferva¬ 
tions upon this comet, and found that its motion might be 
very well reprefented by a parabola, having the Sun in 
its focus. He was ignorant-, however, of the laws by which 
the motion of a body in a parabola is regulated, and erred 
conliderably in his parabola, making the perihelion diftance 
about twelve times greater than it was. This was pub- 
liftied five years before the Principia, in which work Sir 
ifaac Newton having proved that Kepler’s law, by which 
the motions of the planets are regulated, was a neceffary 
confequence of his theory of gravity, it immediately fol¬ 
lowed, that comets were governed by the fame law ; and 
the obfervations upon them agreed fo accurately with his 
theory, as to leave no doubt of its truth. To prove that 
comets deferibe ellipfes, and not parabolas or hyperbolas, 
Dr. Halley, in his Synopfis of the Aftronomy of Comets, 
advances the following reafons : 
“ Hitherto I have confidered the orbits of comets as ex¬ 
actly parabolic; upon which fuppofition it would follow, 
that comets, being impelled towards the Sun by a centri¬ 
petal force, would defeend as from fpaces infinitely dif- 
tant; and, by their fo falling, acquire fuch a velocity, as 
that they may again fly oft' into the remoteft parts of the 
univerfe, moving upwards with a perpetual tendency, fo 
as never to return again to the Sun. But, fince they ap¬ 
pear frequently enough, and fince none of them can be 
found to move with an hyperbolic motion, or a motion 
fwifter than what a comet might acquire by its gravity to 
the Sun, it is highly probable they rather move in very 
eccentric elliptic orbits, and make their returns after long 
periods of time : for fo their number will be determinate, 
and, perhaps, not very great. Befides, the fpace between 
the Sun and the fixed ftars is fo immenfe, that there is 
room enough for a comet to revolve, though the period of 
its revolution be vaftly long. Now, the latus l^eCtum of 
an ellipfis is to the latus reftum of a parabola, which lias 
the fame diftance in its perihelion, as the diftance of the 
aphelion, in the ellipfis, is to the whole axis of the ellip¬ 
fis : and the velocities are in a fubduplicate ratio of the 
fame : wherefore, in very eccentric orbits, the ratio comes 
very near to a ratio of equality; and the very fmall diffe¬ 
rence which happens, on account of the greater velocity in 
the parabola, is eafily compenfated in determining the fitua- 
tion of the orbit. The principal ufe therefore, continues 
Dr. Halley, of the Table of the elements of their mo¬ 
tions, and that which induced me to conftrudt it, is that, 
whenever a new comet (hall appear, we may be able to 
know, by comparing together the elements, whether it be 
any of thofe which has appeared before, and confequently 
to determine its period, and the axis of its orbit, and to 
foretel its return. And, indeed, there are many things 
which make me believe, that the comet which Apian ob- 
ferved in the year 1531, was the fame with that which Kep¬ 
ler and Longomontanus more accurately deferibed in the 
year 1607 ; and which I myfelf have feen return, and ob¬ 
served in the year 1682. All the elements agree, and no¬ 
thing feems to contradifl this my opinion, befides the ine¬ 
quality of the periodic revolutions : which inequality is 
not fo great neither, as that it may not be owing to phyfi- 
cal caufes. For the motion of Saturn is fo difturbed by 
the reft of the planets, efpecially Jupiter, that the perio¬ 
dic time of that planet is uncertain for fome whole days 
together. How much more, therefore, will a comet be 
fubjefit to fuch-like errors, which rifes almoft four times 
higher than Saturn, and whofe velocity, though increafed 
but a very little, would be fufficient to change its orbit, 
fro-m an elliptical to a parabolical one. And I am the 
more confirmed in my opinion of its being tire fame; for, 
in the year 1436, in the fummer-time, a comet was feci) 
palling retrograde between the Earth and the Sun, much 
after the fame manner; which, though nobody made ob¬ 
fervations upon it, yet, from its period, and the manner 
of its tranfit, I cannot think different from thofe I have 
juft now mentioned. And fince, looking over the hiftories 
of comets, I find, at an equal interval of time, a comet to 
have been feen about Ealler in the year 1305, which is 
another double period of 151 years before the former. 
Hence, ] think, 1 may venture to foretel that it will return 
again in the year 175S.” 
Dr. Halley computed the effefit of Jupiter upon this co¬ 
met in 1682, and found that it would increafe its periodic 
time above a year, in confequence of Which he predicted 
its return at the end of the year 1738, or the beginning of 
1759. Fie did not make his computations with the utmoft 
accuracy, 
