PHYSICAL SCIENCES IX ANCIENT GREECE. 501 



ma, ol which the notes are in the ratio of 80 to 81. That the ear 

 really detects this defect of musical coincidence of the two notes nn- 



*/ 



der the proper conditions, is a proof of the coincidence of our musical 

 perceptions with the mathematical relations of the notes ; and is there- 

 fore an experimental confirmation of the mathematical principles of 

 harmony. But it seems to be represented by Plato, that to look out 

 for such confirmation of mathematical principles, implies a disposition 

 to lean on the senses, which he regards as very unphilosophical. 



Hero of Alexandria. 



THE other branches of mathematical science which I have spoken 

 of in the History as cultivated by the Greeks, namely Mechanics and 

 Hydrostatics, are not treated expressly by Plato ; though we know 

 from Aristotle and others that some of the propositions of those sciences 

 were known about his time. Machines moved not only by weights 

 and springs, but by water and air, were constructed at an early period. 

 Ctesibius, who lived probably about B. c. 250, tinder the Ptolemies, is 

 said to have invented a clepsydra or water-clock, and an hydraulic or- 

 gan ; and to have been the first to discover the elastic power of air, 

 and to apply it as a moving power. Of his pupil Hero, the name is 

 to this day familiar, through the little pneumatic instrument called 

 Hero's Fountain. He also described pumps and hydraulic machines 

 of various kinds ; and an instrument which has been spoken of by 

 some modern writers as a steam-engine, but which was merely a toy 

 made to whirl round by the steam emitted from holes in its arms. 

 Concerning mechanism, besides descriptions of Automatons, Hero com- 

 posed two works : the one entitled Mechanics, or Mechanical Introduc- 

 tions ; the other Barulcos, the Weight-lifter. In these works the ele- 

 mentary contrivances by which weights may be lifted or draw r n were 

 spoken of as the Five Mechanical Powers, the same enumeration of 

 such machines as prevails to this day ; namely, the Lever, the Wheel 

 and Axle, the Pulley, the Wedge, and the Screw. In his Mechanics, 

 it appears that Hero reduced all these machines to one single machine, 

 namely to the lever. In the Barulcos, Hero proposed and solved the 

 problem which it was the glory of Archimedes to have solved : To 

 move any object (however large) by any power (however small). This, 

 as may easily be conceived by any one acquainted with the elements 

 ->f Mechanics, is done by means of a combination of the mechanical 

 powers, and especially by means of a train of toothed-wheels and axles 



