208 
Mr Cookson, The Oscillations of a Fluid, etc. 
Fig. 3. Circular Trough. 
1 . 
2 . 
3. 
1st gravest mode, when n- 
2nd 
3rd ,, ,, 
These are 
illustrated 
by Lamb. 
4. 
5. 
6 . 
1st gravest mode, when n= 2 
2nd „ „ „ „ 
3rd „ 
7. 1st gravest mode, when n = 3 
8. 2nd ,, „ ,, „ 
9. 3rd ,, ,, ,, ,, 
It will be noticed that the contour lines for an annular trough 
for the gravest mode when n = 1, can be obtained from those for a 
circular trough by cutting a concentric circular piece out of the 
circular basin, the radius being equal to the distance of the crest 
of the wave from the centre of the trough. The reason of this 
similarity is that for the annular trough of the dimensions here 
considered the part of r\ depending on r differs only very little 
from Ji(r): this is seen at once on inspection of the tracing of the 
two curves 
y = B, (kt) : y — J\ («r). 
A little consideration will show why there is this similarity 
between the gravest mode for the annular trough and the second 
gravest mode for the circular trough. (See Lamb, p. 306.) 
