Wave Pattern of a Doublet in a Stream. 523 
slightly curved, and diminishing in height from the central line outwards. 
The remaining curves are for radial lines outside the usual pattern and show 
how the wave disturbance is continued in this region. D is for an angle of 
about 26° 26’ with the rearward central line; it shows an appreciable wave 
effect, but there are indications that it decreases more rapidly with distance 
from the origin than for the previous curves. A similar effect, nore pronounced, 
is shown in E and F, for radial lines at 45° and 90° respectively. 
Fia. 4. 
Fig. 4 is for «gf=0-5, or c=+/(2qf). Here, on account of the labour 
involved in the calculations, only three curves have been drawn; but they 
bring out the points made in the general discussion. The amplitude along 
the cusp line C is now greater than along the central line A. Moreover, the 
greatest amplitude is along the line B, inside the cusp line C, and shows evidence 
of superimposed diverging waves. The radial line B is given by t’ = 3. Now 
for xf = @ = 4, the maximum of the amplitude factor in (19) occurs at ¢ = 1. 
But from (20), when t’ = 3 the positions of stationary phase occur at t = 4 
and t=1; the latter coincides with the maximum of the amplitude factor 
and so in this case we should expect a prominent wave along the radial line 
t’ = 3, or the line B in the diagram. 
A comparison of the curves in figs. 3 and 4 enables us to form some picture 
of the wave disturbance due to the doublet and the changes that occur as the 
doublet is brought nearer the surface ; in the limit, as far as the wave pattern 
is concerned, the effect would approximate to the ideal case of a concentrated 
point disturbance at the surface. 
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