14 HISTORY OF SCIENCE. 



but this statement has been observed to be inconsistent with the philo- 

 sopher's known objection to all shedding of blood, even on the altars 

 of the gods. 



There is a story of Pythagoras one day passing a smith's workshop, 

 and noticing that the ringing sounds given out by two of the hammers 

 as they struck the anvil formed certain musical harmonies with the 

 note emitted by a third hammer. The story goes on to relate how 

 this led him to think of the cause of those differences of pitch, and 

 how he proceeded to make certain experiments on the subject. Al- 

 though this story is open to doubt, it is tolerably certain that Pytha- 

 goras did actually make experiments on the relations between the 

 several lengths of a stretched cord which would sound the notes of a 

 musical scale. The story about the blacksmith appears to be wholly 

 unnecessary, for so obvious a fact as that a stretched cord will give 

 out a sound more and more acute when we shorten its length, leaving 

 its tension unchanged, could not have escaped the notice of any one 

 who thought about musical sounds at all. It was the scientific con- 

 ception of measuring the lengths of the cord, which has made the name 

 of Pythagoras memorable in connection with acoustics as the founder 

 of the science. He discovered that when a stretched cord is stopped 

 in the centre, each half will, when plucked, give out a note which is 

 precisely the octave above that given out by the full length of the 

 cord ; and that two-thirds and three-fourths of the length of the cord 

 correspond respectively to the musical intervals we call the fifth and 

 the fourth. So that the proportions of the lengths of the cord which 

 will sound a note, octave, fifth, and fourth, are severally i, |, -, and 

 -. The apparatus by which these relations are demonstrated in every 

 course of lessons on acoustics is represented in Fig. 5, and as it con- 

 sists essentially of a single stretched wire, it is called the monochord. 

 The figure shows at B a hollow case or box, the top of which is made 



FIG. 5. 



of thin deal, and forms a sounding-board. The wire M is stretched 

 between two pegs, and below it is placed a stop or bridge, which can 

 be moved to any required point under the wire, the lengths of the 



