ON BEATS OF IMPERFECT HARMONIES. 401 



minimum and minimum maximum. The former 

 will be called the phase-relation of coincidences, 

 the latter the phase-relation of oppositions. In an 

 even binary harmony there is a phase-relation of 

 coincident maximums and coincident maximum 

 minimum ; and again an opposite phase-relation 

 of coincident maximum minimum and coincident 

 minimums. The former will be called the phase- 

 relation of coincident maximums, the latter the 

 phase-relation of coincident minimums. The 

 annexed diagrams illustrate and prove these 

 assertions. The horizontal line in each may be 

 either regarded as representing space at any one 

 instant in the direction of propagation of the 

 sound, or it may represent times at which succes- 

 sive phases of the motion are perceived by an car 

 ittj a fixed position. In the left-hand column of 

 diagrams the long vertical cross-bar in each case 

 denotes maximum of air-pressure ; the short 

 vertical cross-bar, minimum. 



For lecture illustrations it is convenient to use 

 long slips of wood with paper pasted on one side, 

 and the short and long cross-bars marked upon it, 



VOL. II. D D 



