124 TRANSACTIONS OF THE 



admire that Infinite Power, which planted these concealed capa- 

 cities in elemental nature, to what extent we have just begun to 

 discover. Each new invention is a step forward into this bound- 

 less realm, and widens the scope of our vision, and brightens and 

 enlarges the prospect for the futui-e. We mount, with each in- 

 ventor, to his Pisgah of discovery, from which new lands of 

 promise loom upon the view. 



Why such capacities should be permitted to lie idle and un- 

 known, unless to supply an everlasting field for the employment 

 of man, we can no more tell, than why the sun should dart forth 

 such a profusion of rays, which do not touch any of the worlds, 

 but, so far as we know, uselessly expend themselves in infinite 

 space. This universe is not created on any principle of narrow- 

 ness or stint. The great effulgence floods vacant space as well as 

 tenanted worlds, and innumerable powers, and applications of 

 powers, sleep unknown and unsuspected, waiting development 

 thi-ough the endless years that are to come. 



Each new discovery helps to others. If a new truth shines 

 upon us, its ramifications are inexhaustible. As we continue to 

 explore it, its applications multiply upon us, till it seems illimit- 

 able, and runs its tendrils round the world. If we had but one 

 great original principle to work at, we never could exhaust it, 

 for it links itself to all the universe. The farther back we trace 

 these principles to their original springs amidst the elements of 

 truth, the nearer do we come to their common origin, and the 

 better illustrate the simplicity and unity of all truth. Take the 

 apparently unconnected sciences of music and mathematics. 

 Where will you find more ungenial companions than melody and 

 figures? How can harmonious strains find sympathy in the mul- 

 tiplication table, or concord be developed in the rule of three? 

 What bond is there between the intricate calculations of Le Ver- 

 rier and the massive combinations of Beethoven? Yet music is a 

 mathematical science. In cannot exist independent of numbers 

 and proportion. Its tones are magnitudes of time, or magnitudes 

 of sound. Exact proportions exist between the different scales, 

 the various keys, the protractions of sound, the spaces between 

 sounds : the wht)le science rests on a mathematical basis. These 

 instruments of music, so attractive at your fail-, are as much 

 mathematical as the compass or the rule. The truths that sus- 

 tain both sciences are the same : one phase is abstract numbers ; 

 another, melody. 



If a new power is unfolded, how various are the uses to which 



