852 HISTORY OF THE CONTEMPLATION OF THE UNIVERSE. 



the aid of outward material means, it receives its light 

 exclusively from the pure abstraction of the mathematical 

 development of thought. There dwells a powerful charm, 

 deeply felt and acknowledged in all antiquity, in the con- 

 templation of mathematical truths ; in the eternal relations 

 of time and space, as they disclose themselves in harmonics, 

 numbers, and lines. ( 544 ) The improvement of an in- 

 tellectual instrument of research analysis, has powerfully 

 promoted and advanced that mutual fructification of ideas, 

 which is no less important than their abundant production. 

 It has opened to us new regions of measureless extent in 

 /the physical contemplation of the Universe both in its 

 terrestrial and celestial spheres, in the tidal fluctuations of 

 the Ocean, as well as in the periodic perturbations of the 



