PEEFACE. iii 



rectangular section of small depth can be extended to that of 

 non- rectangular section, and made to meet the cases of seiches. 

 With a shght modification, the investigation can be extended to 

 a wave motion in a canal, whose line of symmetry is not 

 necessarily straight. When the mean Tine is curved, the wave 

 will also participate in its course in nearly the same curvature. 

 The amplitude of oscillation is always affected by a factor 

 (breadth)"- x (depth)"^", showing how the height of the wave is 

 changed by the contour of the boundary and the deptJi of 

 water. The presence of the said factor shows that the effect 

 of a narrow basin is more conspicuous than its shallowness, 

 inasmuch as the elevation varies as the inverse square root of 

 the breadth, while the depth affects it inversely as the fourth 

 root. As a good illustration of tlie presence of this factor, we 

 may cite the extraordinary elevation of the destructive waves, 

 when the inlet gradually tapers like a wedge. The profile of 

 the wave is however difficult of calculation. On the coasts 

 bordering on the ocean, the term affecting the height is only 

 the deptli, so that the effect is not so ominous as in bays 

 and inlets ; consequently on calm days, the secondary oscil- 

 lations are not so pronounced. In fact, cases have often been 

 observed in which the boats far out at sea did not in the least 

 encounter the swell of the waves, although these caused great 

 disaster on the shore. These considerations led me to the con- 

 clusion that the mode of vibration of destructive sea waves is 

 of the nature of oscillations in a canal of variable depth and 

 breadth. If the vibration is stationary, and the length between 

 the node and loop /, then the period is 4/ — -7=^-, where /^ is the 



depth, g the acceleration due to gravity and s the length 

 measured along the median line. Further it appeared to me 



