318 , LAPLACE. 
has enabled us to ascend to the earliest ages of our 
planet.* 
In the time of Alexander comets were supposed by 
the majority of the Greek philosophers to be merely 
meteors generated in our atmosphere. During the mid- 
dle ages, persons, without giving themselves much con- 
cern about the nature of those bodies, supposed them to 
prognosticate sinister events. Regiomontanus and Tycho 
Brahé proved by their observations that they are situate 
beyond the moon; Hevelius, Dérfel, &c., made them 
revolve around the sun; Newton established that they 
move under the immediate influence of the attractive 
force of that body, that they do not describe right lines, 
that, in fact, they obey the laws of Kepler. It was 
necessary, then, to prove that the orbits of comets are 
curves which return into themselves, or that the same 
comet has been seen on several distinct occasions. This 
discovery was reserved for Halley. By a minute inves- 
tigation of the circumstances connected with the appari- 
tions of all the comets to be met with in the records of 
history, in ancient chronicles, and in astronomical annals, 
this eminent philosopher was enabled to prove that the 
comets of 1682, of 1607, and of 1531, were in reality 
* The results of Clairaut’s researches on the figure of the earth 
are mainly embodied in a remarkable theorem discovered by that 
geometer, and which may be enunciated thus:—The sum of the frac- 
tions expressing the ellipticity and the increase of gravity at the pole is 
equal to two and a half times the fraction expressing the centrifugal force 
at the equator, the unit of force being represented by the force of gravity 
at the equator. This theorem is independent of any hypothesis with 
respect to the law of the densities of the successive strata of the earth. 
Now the increase of gravity at the pole may be ascertained by means 
of observations with the pendulum in different latitudes. Hence it is 
plain that Clairaut’s theorem furnishes a practical method for deter- 
mining the value of the earth’s ellipticity.— Translator. 
