DISCOVERIES IN TIIK (*KT,F,STIAL SPACES. 327 



sounds of aerolites traversing our atmosphere and becoming 

 ignited within its confines, impart a new stimukis, for a cer- 

 tain time, to the general interest in problems, which appear 

 to the people at large even more mysterious than to the dog- 

 matizing physicist. 



My reason lor more particularly naming Kepler in these 

 remarks on the influence of direct sensuous contemplation has 

 been to point out how, in this great and highly-gifted man, a 

 *aste for imaginative combinations was combined with a re- 

 markable talent for observation, an earnest and severe meth- 

 od of induction, a courageous and almost unparalleled perse- 

 verance in calculation, and a mathematical profoundness of 

 mind, which, revealed in his Ste7'eometria Dolicntt77i, exer- 

 cised a happy influence on Fermat, and, through him, on the 

 invention of the theory of the infinitesimal calculus.* A man 

 endowed with such a mind was pre-eminently qualified by 

 the richness and mobility of his ideas,! and by the bold cos- 

 mical conjectures which he advanced, to animate and aug- 

 ment the movement which led the seventeenth century unin- 

 terruptedly forward to the exalted object presented in an ex- 

 tended contemplation of the universe. 



The many comets visible to the naked eye from 1577 to 

 the appearance of Halley's comet in 1607 (eight in number), 

 and the sudden apparition already alluded to of three stars 

 almost at the same period, gave rise to speculations on the 

 origin of these heavenly bodies from a cosmical vapor filling 

 the regions of space. Kepler, like Tycho Brahe, believed 

 that the new stars had been conglomerated from this vapor, 

 and that they were again dissolved in it.$ Comets to which, 



* Laplace says of Kepler's theoiy of the measurement of casks {Ste- 

 reometria Doliorum), 1615, " which, like the sand-reckoning of Archi- 

 medes, develops elevated ideas on a subject of little importance;" 

 " Kepler presente dans cet ouvrage des vues sur I'infini qui ont influe 

 sur la revolution que la Geometrie a eprouvee k la fin du l?""® siecle ; 

 et Fermat, que Ton doit regarder comme le veritable inventeur du calcul 

 differentiel, a fonde sur elles sa belle methode de maximis et minimis. 

 {Precis de VHist. de VAstronomie, 1821, p. 95.)" On the geometrical 

 power manifested by Kepler in the five books of his Harmonices Mundi, 

 see Chasles, Aperqu Hist, des Miihodes en G^omitrie, 1837, p. 482-487. 



t Sir David Brewster elegantly remarks, in the account of Kepler's 

 method of investigating triith, that " the influence of imagination as an 

 instniment of research has been much overlooked by those who have 

 ventured to give laws to philosophy. This faculty is of greatest value 

 in physical inquiries ; if we use it as a guide and confide in its indica- 

 tions, it will infallibly deceive us; but if we employ it as an auxiliary, 

 it will aflbrd us the most invaluable aid" {Martyrs of Science, p. 215). 



X Arago, in the Annvaire. 1842. p. 434 {Dc la Ti-ansformation dej 



