436 PHYSIOLOGICAL PHYSICS. [Chap. xxxn. 



line of rest, are all + , that is to say, and consequently 

 the three distances added together give the distance 

 A6' above the line of rest. Take the vertical line cc', 

 the position of a point of the compound wave in that 

 line is obtained by taking the algebraical sum of the 

 distances c'c 2 , c 3 c 4 , and c 5 c 6 . c c 2 and c 5 c 6 are 

 negative, c 3 c 4 is positive ; the result is a negative 

 quantity, the distance AC below the line of rest. So 

 the position of any other point in the compound 

 wave may be determined. It is, consequently, 

 apparent that the compound wave could be resolved 

 into the simple waves 1, 2, 3. It can, moreover, be 

 shown that any complex wave can be analysed into 

 simple waves, whose corresponding number of 

 vibrations are in the proportion of 1, 2, 3, 4, etc. 

 That is to say, a compound wave may be resolved 

 into one simple wave, representing a number of 

 vibrations that may be taken as 1, and into a series of 

 other simple waves, representing each a number of 

 vibrations that is a multiple of the first, 2, 3, 4, 5, 

 and so on. Vibrations whose numbers are in this 

 proportion, 1, 2, 3, etc., are said to form a HARMONIC 

 series. 



Of course, sounds do not produce transverse waves, 

 such as are depicted in the figure. These are simply 

 graphic representations of waves. The varying dis- 

 tances of the curves above or below the middle line 

 represent varying degrees of condensation and rare- 

 faction of the atmosphere in which the sound is propa- 

 gated. 



Now if a string be fixed at both ends, pulled by 

 the centre to one side and let go, the string will 

 vibrate in its whole length, first to one side then to 

 the other, and if riders of paper be placed at different 

 points on the string, they will be all thrown off 

 (Fig. 188). The string while it vibrates will utter a 

 note of a definite pitch and particular quality, the 



