31C SPECIAL RESULTS IN THE URANOLOGICAL 



Syrens,, or sometimes in their place the Muses, as celestial 

 songstresses, have been preserved in several remains of 

 antique art, particularly on cut stones. In Christian anti- 

 quity, and throughout the middle ages, from Basil the Great 

 to Thomas Aquinas and Petrus Alliacus, we find frequent 

 allusions, most often, however, in terms of censure, to 

 this idea of the Harmony of the Spheres ( 514 ). 



All the Pythagorean and Platonistic views of the Uni- 

 verse, both the geometric and the musical, re-awoke at the 

 end of the sixteenth century in the imaginative Kepler. 

 He built up the planetary system, first in the Mysterium 

 cosmographicum, on the basis of five regular solids which 

 could be placed in the intervals between the planetary 

 spheres ; and next, in the Harmonice Mundi, according 

 to the intervals of musical notes ( 515 ). Persuaded of 

 the conformity to law of the relative distances of the 

 planets, he thought to solve the problem which he had 

 thus proposed to himself by a happy combination of his 

 earlier and his later views. It is remarkable that Tycho 

 de Brahe, who, on all other occasions, we find so rigidly 

 attached to actual observation, had, before Kepler, expressed 

 the opinion, contested by Rothmann, that the revolving cos- 

 mical bodies may, by agitating the celestial air (that which 

 we now call the " resisting medium"), produce musical 

 sounds ( 516 ). It appears to me, however, that the analogies 

 between the relations of musical tones or notes and the dis- 

 tances of the planets, however long and laboriously traced 

 or sought after by Kepler, yet in the mind of that ingenious 

 thinker never passed out of the domain of abstractions. 

 He, indeed, at one time rejoices in having discovered, to 

 the greater glory of the Creator, musical relations of num- 



