HARMONICS. Ill 



moreover, (that in which, probably, his superiority 

 most consisted,) a disposition to connect one notion 

 with the other the musical relation with the arith- 

 metical, if it were found possible. When the con- 

 nexion was once suggested, it was easy to devise 

 experiments by which it might be confirmed. 



"The philosophers of the Pythagorean School 1 , 

 and in particular, Lasus of Hermione, and Hip- 

 pasus of Metapontum, made many such experi- 

 ments upon strings ; varying both their lengths and 

 the weights which stretched them; and also upon 

 vessels filled with water, in a greater or less de- 

 gree." And thus was established that connexion 

 of the Idea with the Fact, which this science, like 

 all others, requires. 



I shall quit the Physical Sciences of Ancient 

 Greece, with the above brief statement of the dis- 

 covery of the fundamental principles which they 

 involved ; not only because such initial steps must 

 always be the most important in the progress of 

 science, but because, in reality, the Greeks made 

 no advances beyond these. There took place among 

 them no additional inductive processes, by which 

 new facts were brought under the dominion of 

 principles, or by which principles were presented 

 in a more comprehensive shape than before. Their 



1 Montucla, iii. 10. 



