253 
1909-10.] On Waves in a Dispersive Medium. 
time. Remembering that, for n positive, the successive waves of the 
disturbance are of increasing wave-lengths, it is clear from the curves that 
in this case again the most important part of the disturbance at any time 
is on one side of the point where the maximum amplitude occurs, being 
associated in all cases with the greater wave-lengths. 
§ 16. In conclusion, the chief results which have been established are: 
(1) that the wave-length associated with the greatest disturbance at any 
point depends only on the form of the initial disturbance; (2) that the 
wave-length associated with the maximum disturbance at any time is 
constant for any one medium ; (3) that the amplitude corresponding to any 
wave-length falls off according to x~ l , and the energy per wave-length 
therefore according to x ~ x ; (4) that the front of a wave-system, for ^<0, 
continually grows in importance relatively to the rear, while for ^>0 the 
front is always of less importance than the rear. 
These results are proved only for the particular initial disturbance 
chosen, but it seems certain from the nature of the case that they are quite 
general, being applicable to any initial form of disturbance. This has, in 
fact, been verified for several initial forms, including the case of a finite 
constant displacement over a given length of the medium, and also the case 
of a regular sinusoidal displacement over a finite length of the medium. 
(Issued separately February 18, 1910.) 
