249 
1909-10.] On Waves in a Dispersive Medium. 
where for n we take its absolute value. The greatest amplitude of the 
disturbance at any point therefore varies inversely as the square root of its 
distance from the centre of the initial disturbance, no matter what value we 
give to n. 
To find the wave-length of the disturbance at x, when the amplitude 
there has its maximum value, we put 
B 
i 
U 
n + 1 
n 
= 27T 
• ( 27 ), 
since the phase varies by 27 r in passing along one complete wave-length. 
From this we obtain, as in § 16 of my former paper, 
or by (23), 
2ft7T 
(n+ 1)B 
A. — 4-7ra 
©H 
. (28), 
which shows that the wave-length at any point when the displacement 
there is greatest depends only on the form of the initial disturbance, and 
is the same in all dispersive media for the particular disturbance we are 
considering. 
§ 11. If, on the other hand, we regard t as fixed, and proceed to find 
the place at which the disturbance has its maximum amplitude at the time 
chosen, we differentiate with respect to x, and then by proceeding exactly as 
before obtain 
X = (29), 
1 - n 
as the value of the wave-length at the place of maximum displacement, for 
all times. The place of maximum displacement at a given time is deter- 
mined by 
n ^~ n ) . . . . (30), 
2(l+«)Ba 
and the amount of the maximum displacement at the time and place so 
determined is given by 
—( l . 
2af\ nx ) 
(31), 
where, as before, the absolute values of n and (1 — n) are to be taken. 
§ 12. Remembering that in these equations the presence of a indicates 
in what manner the wave-length, amplitude, etc., of the displacement curve 
at the point of the medium observed are determined by the form of the 
initial disturbance, and the presence of n indicates in what manner they 
depend on the dispersive nature of the medium, we can state the results con- 
