1908. ] Groups of Waves in Dispersive Media, ete. 414 
The predominant value of «, for given time and place, is given by 
K = 4px7/9T??. (54) 
The chief groups, each with approximately constant amplitude, are given by 
nv at3 4irpx? 4px? ) = 
a= B 81T?x«’?t4— 16 p2x4 COS (2n +4) On TE cos ae 4). (55) 
At a given place the maxima of amplitude are those of 
#8 
a (One), 5 
SIP 16 pat 8 2" +2) gota D 
Fig. 2 represents the curve 
3 2 
Y= 08 5.2? (57) 
where « is proportional to the time and « equal to 1 corresponds to « equal 
to x’. 
Fig. 2. 
Comparing this with § 7 we draw the inference that in this case the 
perceptible front of the advancing train is more clearly marked than the rear 
and advances with the half-wave-velocity corresponding to x’, in agreement 
with simple observation. 
(b) Moving line impulse—A line impulse at rest leads to 
7 = Catt~4 cos ie + ir) : 
27T? 
Consequently a moving line impulse will give 
=A if (oar): +2) cos { se (eatew) — +40 } du. (58) 
17 
