Secondary Undulations of Oceanic Tides. 91 
3. In a bay o£ considerable area, or in a shallow bay witli 
a narrow opening towards the ocean, the secondary 
undulation is in ordinary cases imperceptible. 
4. In a deep bay or estuary, the breadth of which is not 
large in comparison with its length, the secondary 
undulations are most pronounced. 
5. In bays or open coasts, which are not far from each 
other, a common undulation is observed. 
6. The secondary undulations in many bays change their 
periods continuously and through certain ranges. 
7. In some bays the periods of the undulation are fairly 
constant. 
8. In many cases the same trains of secondary undulations 
appear in the same phase with respect to the tidal 
wave, on consecutive days of ordinary weather. 
9. The phases of the prominent, fundamental -Jindulation 
at different parts of a bay are equal. 
10. The periods T of the most pronounced undulations are 
fairly given by the relation 
U 
where / is the length of the bay measured along its 
depth, li the mean depth of the bay, and a the force 
of gravity. 
11. Just outside a bay the undulation, which inside has 
been observed to be of considerable amplitude, may 
also be traced, but its amplitude is very small. 
12. In a bay, the periods of the conspicuous undulation 
observable in the case of a storm, or in that of a sea- 
wave of distant origin, are the same as those ordinarily 
observable in the bay. 
It has long been believed that the secondary undulation in 
a bay is the seiche between two opposite sides of the bay ; 
but according to our observations, the phases of the most 
conspicuous undulation are the same throughout the bay, so 
that this view cannot be universally true. Napier Denison 
considers the undulation to be long waves continued from 
the ocean into the bay, on which supposition all the con- 
clusions above enumerated, except the 9th, 10th, and 12th, 
can easily be explained. But the fact that there is a pro- 
minent undulation peculiar to each bay, cannot be explained 
by merely considering progressive waves. 
This undulation, however, can be explained in the following- 
way. As a representative example, take a rectangular bay 
