312 GREEK SCIENCE. 



mathematicians have written upon it treatises which are still extant. 

 Their principal researches consisted in determining the value of the 

 intervals between different notes of their scale, and arranging them 

 into systems of four contiguous notes, which they called tetrachords : 

 which, however, do not make the successions of the notes so clear as 

 our arrangement of them in octaves. Any further discussion of this 

 subject might be considered out of place ; we shall only notice, that 

 the scale above referred to was called the diatonic ; that besides this 

 they had the chromatic, in which all the half notes were introduced ; 

 the old enharmonic, which, according to Dr. Burney, resembled the 

 Scotch scale ; and the new enharmonic, which contained all the quarter 

 notes, and to which we have nothing exactly corresponding. It ap- 

 pears certain that the music of the Greeks was confined to melody, or 

 the pleasing succession of sounds ; and that it was left for modern 

 times to produce what we now call harmony ; that effect of simul- 

 taneous sounds which may almost be considered as having a rightful 

 claim to the reward offered for the discovery of a new sense of plea- 

 sure. 



Mechanics. In the view of the state of mathematics in the time of Plato we can 

 hardly enumerate the two sciences of mechanics and optics, which had 

 scarcely then begun to exist, though they soon afterwards engaged 

 some attention. The doctrine of motion, indeed, was not destined for 

 the Greeks, for they never had any but the vaguest notions on the 

 subject, and continued ignorant of the first law of motion, " that a 

 moving body will go on uniformly, except so far as it is acted upon 

 by external causes :" nor was any light thrown on this subject, till the 

 time of Galileo. In the ' History of Astronomy n the reader may see 

 the speculations of Aristotle ; and a fragment on this subject, which 

 is attributed to Euclid, contains nothing more definite or important. 

 The doctrine of equilibrium, in which Archimedes made such extra- 

 ordinary progress, seems to have been little better before his time. 

 In ARISTOTLE'S mechanical problems, he thus accounts for the fact 

 that, by means of the lever, a small weight may move a larger which 

 is at the end of a shorter arm. The extremities of the arms describe 

 circles, and the motion of a point in a circle is twofold ; viz., a motion 

 perpendicular to the radius, which is according to nature, and a motion 

 towards the centre, which is contrary to nature. This unnatural 

 motion is smaller in a larger circle, if the space described be the same ; 

 and hence in a larger circle a force will with equal ease move a body 

 through a larger space. It is manifest that such reasoning as this can 

 lead to nothing ; and we do not know of anything better till the time 

 of Archimedes. 



Optics- Optics was in a similar imperfect state at this time. The vagueness 



of Aristotle's speculations on the subject has been mentioned in the 



history of it given in another part of this volume, 2 and the reader will 



there find an abstract of the remarkable treatise of Euclid ; the earliest 



1 Page 346 of this volume. 2 Page 353. 



