CELESTIAL SPACES. 737 



discoveries by means of the invention of the Infinitesimal 

 Calculus. Intellectual labour shows itself in 'all its exalted 

 grandeur, where, instead of requiring external material 

 means, it derives its light exclusively from the sources opened 

 to pure abstraction, by the mathematical development of 

 thought. There dwells an irresistible charm, venerated by 

 all antiquity, in the contemplation of mathematical truths, 

 in the everlasting revelations of time and space, as they 

 reveal themselves in tones, numbers, and lines.* The im- 

 provement of an intellectual instrument of research analysis 

 lias powerfully accelerated the reciprocal fructification of 

 ideas, which is no less important than the rich abundance of 

 their creations. It has opened to the physical contemplation of 

 the universe new spheres of immeasurable extent, in the ter- 

 restrial and celestial regions of space, revealed both in the 

 periodic fluctuations of the ocean, and in the varying pertur- 

 bations of the planets. 



* Wilhelm von Humboldt, Gesammelte Werke, Bd. i. s. 11. 





3 B 



