1908. | Groups of Waves in Dispersive Media, ete. 424 
Table II. 
n. Gas Coca Grell 
5 15 35 2:3 
10 10°8 28 °6 2°6 
15 9 25 PAY 
20 asi 23 3 
50 & / 3°74 
| 100 3°6 13 °6 3°8 
eid 
ne 4 
J 
G wa al 
pee a 1 Nl =; poke | 
7t \00 85 65 45 25 5. @ 
Fie. 6. 
§ 14. Point Impulse for Different Media. 
Consider a point impulse moving with uniform velocity ¢ over the surface 
of a dispersive medium for which U and V are respectively the group- and 
wave-velocity for a value « of 27/2. 
A Cz d) 
Fig. 7. 
Let the disturbance from the impulse when in the neighbourhood of 
a point A combine so as to produce waves « at P at the present moment 
when the impulse is at O. Then the problem of finding the possible 
persistent wave systems is contained in the equations 
JX 10h ramets 
AO LE ccos@=V; (101) 
that is, in (w?—2cum cos a+ cu*)?/u = U, (102) 
¢ (cu—o cos «)/(o?— 2cun cos a+c7u*)? = V. (103) 
The wave pattern depends upon the character of the positive roots of 
these equations for cw and «; each such value of cw defines a wave system 
27 
