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 

 Brahe proved by their observations that they are situate 

 beyond the moon ; Hevelius, Db'rfel, &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. 



