114 Messrs. K. Honda, T. Terada, and D. Isitani on the 
many cases the corrections due to the mouth and the varia- 
tion of the section seem to be superfluous. This probably 
arises from the fact that in many bays the correction due to 
the section nearly cancels the correction due to the mouth ; 
for such bays gradually contract and the depth decreases 
as we approach the end, therefore the correction due to the 
variation of the section is negative, and the mouth correction 
being always positive, the two tend to annul each other. As 
a good example, we may refer to the bays of Ofunato and 
Tsuruga. If, however, the mouth of a bay be contracted 
and shallower than the inside, the correction due to the 
section is positive, and the total correction may, in some 
cases, amount to a considerable quantity. In such cases, 
the value calculated by the simplest formula must be de- 
cidedly less than the observed value, and can be brought into 
agreement only by taking the two corrections into consider- 
ation ; a good example of this is furnished in the case of the 
bay of Aomori. That the calculated periods for the bays of 
Mororan and Okirai, both of which have rather narrow 
mouths, are a little less than the observed values, is also 
explained on the same view. 
§ 7. Sea- Waves and Secondary Undulations. 
As already remarked, Professor F. Omori found that the 
periods of sea-waves observed in a bay are the same as those 
of the usual secondary undulation. We have made a like 
investigation for different bays, and our findings confirm his 
conclusion, especially in the case of sea- waves of distant 
origin. This fact now may be explained in the following way. 
Sea-waves are probably of such a complex nature, as to be 
represented by the sum of a series of long waves of different 
periods and amplitudes. If a group of these waves proceed 
towards a bay, the bay takes up and resonates to the undu- 
lation whose period coincides with that of the free oscillation 
of the bay. Thus the prominent undulation in a bay, what- 
ever the component waves of a sea- wave may be, is the 
undulation whose period is nearest to that of the free oscillation. 
The above consideration applies chiefly to sea-waves that 
are of distant origin, and consequently of small amplitude. 
If, however, the origin is not very far from a bay or an open 
coast, progressive waves of long wave-length, irrespective 
of their periods, are sufficient to cause a disastrous effect on 
the coast; for by Green's law of amplitudes, long waves con- 
siderably increase their amplitude the nearer they approach a 
shallow shore. Thus it is that the report on actually de- 
structive sea-waves almost always speaks of high wave-fronts 
