208 



Mr Gookson, The Oscillations of a Fluid, etc. 



(m 





v||Sj 





Fig. 3. Cikculae Though. 



1. 1st gravest mode, when n = l] These are 



2. 2nd „ ,, ,, „ L illustrated 



3. 3rd „ „ „ „ j by Lamb. 



4. 



1st gravest mode, when n—2 



7. 



1st gravest mode, when n=B 



5. 



2nd 



8. 



2nd ,, „ „ 



6. 



3rd 



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 1 (at) : y = J x (*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.) 



