Secondary Undulations of Oceanic Tides. Ill 
§6. Method and Results of Determining the Period 
of Oscillation by Calculation. 
In the calculation of the period of oscillation in a bay by the 
simplest formula, it was necessary to estimate the length and 
the mean depth of the bay from the charts ; the charts used 
were those published by the hydrographical section of the 
Xaval Department. As the mean depth, we took the ratio of 
the total volume of the water in a bay to the area of the 
surface. The length of the bay was measured along a line 
drawn lengthwise and perpendicular to the contour-lines of 
the bed of the bay. 
To find the mean depth of a bay, we began by drawing- 
contours on the chart, where the depths at a number of points 
referring to low- water springs are given. After dra wing- 
as many contours as the case requires, we measure with a 
planimeter the areas between them. These areas multiplied 
by the corresponding depths, increased if necessar}^ by the 
half range, give the partial volumes of water. Dividing the 
sum of these partial volumes by the area of the free surface, 
we get the mean depth. 
We calculated by formula (1) the periods for all observed 
bays. For several typical bays we also calculated the cor- 
rection due to the change of the section, as well as that due 
to the mouth, and compared the corrected values with the 
observed. 
The calculation of the correction due to the variation of 
the section was carried out in the following way. We drew 
on the chart several lines at suitable positions normal to the 
line of length, and then taking the length as abscissa and 
the corresponding breadth as ordinate, we got a breadth- 
diagram. We next drew the mean breadth-line at a distance 
equal to the whole surface of the bay divided by the length. 
Taking now this line as the new axis of coordinates, we could 
easily draw the diagram for &b cos — y— ; whence by mechan- 
J2 7rv 
Ah cos —j- dx. Pro- 
ceeding in a similar way for the sectional area, we got the 
value of I AS cos — y— dx. From these two the required 
correction was obtained by simple operations. 
