20 A. C. D. CROMMELIN, ESQ., D.SC., F.R.A.S., ON 
Mars and Mercury, to an extremely elongated form. Thus in 
the case of Halley’s comet the breadth is a quarter of the length, 
but the ellipse may be still more flattened than this; there is 
indeed no limit to the amount, and we are led on to the third 
form, the parabola, which we may look on as simply an ellipse 
of infinite length. The fourth form, the hyperbola, does not 
occur much in the heavens, and need not detain us. Newton 
soon saw that comets might be explained by supposing them 
to move in very elongated ellipses, or even in parabolas, 
remaining invisible for most of the time, and only being visible 
for a short time, when in the portion of their orbit nearest to 
the sun. Halley, who had more inclination than Newton for 
the huge arithmetical computations required, entered into the 
new ideas with enthusiasm, and computed the orbits of all the 
comets for which observations of the necessary accuracy were 
available. They were twenty-four in number, and went back 
for about 200 years before his time. By a piece of good 
fortune, which he had most richly merited by his assiduous 
labours, the same comet occurred three times in his list, and 
when he came to tabulate the results he noticed that the 
comets of 1531, 1607, 1682 were travelling in practically the 
same orbit round the sun. It should be mentioned that the 
assumption of parabolic motion was made in the first instance, 
as the necessary computations were simplified, since all parabolas 
are similar curves, and tables can be made which will serve for 
all cases, while in the case of ellipses different tables would be 
required for every case. When he noticed the resemblance of 
orbits he at once conjectured that this was the same body 
returning at intervals of three-quarters of a century. On 
finding the elements of the necessary ellipse to correspond 
with this period, he saw that it satisfied the observations of the 
comet better than the parabolic assumption, and this streng- 
thened his conclusion. The only thing against it was that the 
intervals between the returns were not exactly equal; the first 
being fifteen months longer than the second. This puzzled him 
for a time till he recollected that, even in the case of the 
planets, one revolution was not exactly equal to another. It is 
true that the differences here were only minutes or hours, not 
months or years; the cause of the irregularities he knew to be 
the perturbations which the planets produce on each otber’s 
motion, and he saw that these would be greater in the case of 
the comet, which passed at times very much closer to the giant 
planets than these can do to each other ; further, in an elongated 
orbit a small alteration in the velocity, when not very remote 
