SECONDARY UNDULATIONS OF OCEANIC TIDES. 69 



normal to the line of the length, and then taking the length as 

 abscissa and plotting corresponding breadth as ordinates, we 

 o-et a breadth- diagram. Draw mean breadth line, at a distance 

 eqnal to tlie whole snrface of the bay divided by the length. 

 Taking now this line as the new axis of co-ordinates, we can 

 easily draw the diagram for ^ b cos — — ; whence by mechanical 



integration, we get 0,113 as the value of— M 6 cos -1— dr. Pro- 



ceeding in a similar way for the sectional area, the value of 



— j J S co-i ^-- (Ix is found to be 0.002. Applying these values 



of corrections to 97.5'", we finally get 100'" as the period of the 

 lateral oscillation of the bay, in good accordance with the ob- 

 served value 10o"\ In this case, the correction due to the mouth 

 is of course unnecessary. 



As for the longer period, the calculation of the period as a 

 rectangular bay gives 213'"; the correction due to the variation 

 of the section, as calculated in the manner above described, is 

 24.8'". The correction due to the mouth is 46.5"\ so that the 

 corrected value for the period of longitudinal oscillation is 284™, 

 which fairly accords with the observed value. 



(b) Bay of Ofunato. 



The simple calculation of the period of fundamental oscil- 

 lation on the assumption that the bay is a rectangular tank, 

 whose depth is 19.0 m. and whose length is 8.1 km., gives 39.5™. 

 The corrections due to the variation of the section and due to 

 mouth are respectively -10.7'" and +8.6'"; tlie corrected value is 

 therefore 36.4'". In this case, the correction of the section and 

 that of the mouth have opposite signs, tiie former a little over- 

 weighing the latter. 



