812 



SCIENCE. 



[!Sr. S. Vol. VIII. No. 206. 



once be found to be exceedingly difficult, if 

 not intractable, though the problem is still 

 much simpler than that presented to us by 

 Nature. 



The depths being everywhere less than 

 thirteen miles, the wave will at no point be 

 able to keep pace with the Moon. The ap- 

 parent rate of progress of the Moon over 

 the Earth's surface is about seventeen miles 

 per minute. The rate of progress of the 

 wave will be about fifteen miles per minute 

 where the depth is ten miles, and less than 

 five miles per minute where the depth is 

 not greater than one mile. 



Let an attempt be made to trace a tidal 

 wave westward, starting from the 180th 

 meridian in the Pacific. The northern por- 

 tion of the wave will be confronted by the 

 full width of both Asia and Europe ; the 

 middle portion will have deep water across 

 the Indian Ocean, but will be obliged to 

 cross submerged Africa before reaehing the 

 Atlantic ; while the southern portion will 

 have unobstructed deep water to and be- 

 yond the Cape of Good Hope. This south- 

 ern portion, rounding the Cape of Good 

 Hope, will necessarily be propagated north- 

 ward up the Atlantic, as well as westward, 

 for the middle portion, travelling iu shal- 

 lower water, will not yet have reached the 

 Atlantic. The middle and northern portions 

 of the wave will have acquired an irregular 

 front on account of the various depths 

 traversed by different portions. This Cape 

 wave, as it progressed northward up the At- 

 lantic valley, would combine at an angle in 

 some complex fashion with the irregular 

 wave emerging gradually from the shoals of 

 Africa., and finally from Europe. In short, 

 even with the conditions so far imposed, it 

 would be exceedinglj' difBcult, if not impos- 

 sible, with our present knowledge, to com- 

 pute the wave to be found in the Atlantic, to 

 say nothing of the additional complexity 

 produced when this already complicated 

 wave crossed the submerged Americas. 



Still we are dealing with a problem very 

 much simpler than that of Nature. In the 

 actual case the Moon would outstrip the 

 wave in its westward progress, and then 

 the direct effect of its attraction would be 

 to tend to tear down the old wave and 

 build up a new one in advance of it. This 

 action would bring about radical modifica- 

 tions in the wave, even within one trip 

 around the globe. 



Moreover, the variations in depth pro- 

 duce other effects upon the wave fully as 

 important as the one just considered. The 

 increased friction in small depths tends to 

 reduce the height of the wave. On the 

 other hand, when a wave passes from deep 

 to shallow water there is a tendency for the 

 wave to attain a much greater height than 

 before, since nearly the same amount of 

 kinetic energy must be concentrated in a 

 much smaller amount of water. So a tidal 

 wave continually varies between wide 

 limits in amplitude, as well as in its rate of 

 propagation, in a way that is exceedingly 

 difficult, to say the least, to compute. 

 These variations in range produce obvious 

 difficulties in such a case as that just sug- 

 gested, in which waves from different 

 regions coalesce. 



As one more step in making our assumed 

 problem approach the actual problem, let 

 the water surface, which has been supposed 

 to be at the level of the summit of Mt. 

 Everest, subside to its present actual posi- 

 tion. One-fourth of the earth's surface be- 

 comes dry land. There is now in the prob- 

 lem all the previous intricacies, and in ad- 

 dition a new set of difficulties, arising from 

 the fact that the oceans are bounded by 

 irregular shores, from which the tidal wave 

 is reflected to a greater or less extent at every 

 point of contact. The actual tidal waves 

 may as properly be compared to a choppy 

 sea, such as may be seen along the docks of 

 a crowded port, as to a regularly progres- 

 sive wave passing to westward around the 



