HARMONICS. 107 



must have had, too, a ready familiarity with numerical ratios ; and, 

 moreover (that in which, probably, his superiority most consisted), a 

 disposition to connect one notion with the other — the musical relation 

 with the arithmetical, if it were found possible. When the connection 

 was once suggested, it was easy to devise experiments by which it 

 might be confirmed. 



"The philosophers of the Pythagorean School, 2 and in particular, 

 Lasus of Hermione, and Hippasus of Metapontum, made mauy such 

 experiments upon strings ; varying both their lengths and the weights 

 which stretched them ; and also upon vessels filled with water, in a 

 greater or less degree." And thus was established that connection 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 discovery 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 advance 

 terminated in a single stride. Archimedes had stirred the intellectual 

 world, but had not put it in progressive motion : the science of 

 Mechanics stopped where he left it. And though, in some subjects, as 

 in Harmonics, much was written, the works thus produced consisted 

 of deductions from the fundamental principles, by means of arithmet- 

 ical calculations; occasionally modified, indeed, by reference to the 

 pleasures wdiich music, as an art, affords, but not enriched by any new 

 scientific truths. 



[3d Ed.] We should, however, quit the philosophy of the ancient 

 Greeks without a due sense of the obligations which Physical Science 

 in all succeeding ages owes to the acute and penetrating spirit in which 

 their inquiries in that region of human knowledge were conducted, and 

 to the large and lofty aspirations which were displayed, even in their 

 failure, if we did not bear in mind both the multifarious and compre- 

 hensive character of their attempts, and some of the causes which 

 limited their progress in positive science. They speculated and 



2 Montucla, iii. 10. 



