December 9, 1898.] 



SCIENCE. 



811 



tions we will deal explicitly with the lunar 

 tides only. 



We may start with the problem of de- 

 termining the shape of the free ocean sur- 

 face on the supposition that the Earth con- 

 sists of a rigid nucleus completely covered 

 with a great and uniform depth of water 

 and upon the supposition that the Moon 

 moves in a circular orbit in the plane of 

 the Earth's equator at such a rate that one 

 face of the Earth is always presented to the 

 Moon, just as the Moon now always pre- 

 sents the same face to us. Eoughly speak- 

 ing, the ocean in this case would become an 

 ellipsoid with its major axis in the line join- 

 ing the centers of the Earth and Moon, and 

 this tide, if we may call it so, is the so- 

 called static or equilibrium tide. This 

 problem has been completely solved. 



As a next step toward the actual prob- 

 lem, let the Moon be supposed to remain in 

 a circular orbit in the plane of the Earth's 

 equator, but let its period in that orbit be 

 twenty-seven days, as at present it is. The 

 Earth now presents different parts to the 

 Moon in rapid succession . as the Earth 

 rotates once on its axis in each solar day. 

 At once the problem becomes much more 

 diflBcult than before ; for the effects of vis- 

 cosity of the water, of its inertia and of 

 friction against the ocean bottom combine 

 to reduce the height of the wave, to modify 

 the shape of the wave, to cause its crest to 

 lag behind the Moon. The problem is now 

 that of dealing with a forced wave — a much 

 more diflBcult one than the static problem 

 just outlined, and more difficult than that 

 of dealing with a free wave. But it is still 

 a problem which has been so thoroughly in- 

 vestigated that there is comparatively little 

 hope for a new worker to extend our knowl- 

 edge much along this line. 



The introduction of the actual Moon with 

 its rapid changes in declination and dis- 

 tance, and its variable motion in right as- 

 cension, in the place of the fictitious Moon 



we have been considering, makes the prob- 

 lem heavier, but not essentially much more 

 difficult. 



From the theory of wave motions in 

 liquids it has been shown that for a wave, 

 such as the tidal wave, of which the length 

 from crest to crest is great in comparison 

 with the depth of the water, the rate of 

 progress of the wave is connected with the 

 depth by the law V — \/gh, in which Fis 

 the velocity of progress of the wave, g the 

 acceleration due to gravity and h the depth 

 of the water. According to this law a free 

 tidal wave would succeed in keeping pace 

 with the Moon in its apparent progress 

 around the Earth only in case the assumed 

 uniform depth of the water is greater than 

 thirteen miles. If the uniform depth be as- 

 sumed less than thirteen miles the old wave 

 will, in effect, be continually being lost in 

 the race and a new wave be continually 

 being built up in front of it. The tide of 

 our previous problem will be still further 

 reduced in range and modified in shape 

 and will lag still further behind the Moon, 

 which produces it. The problem is still 

 tractable, though exceedingly difficult, and 

 still falls in the category of thoroughly in- 

 vestigated problems. 



Now let the problem become nearer like 

 that of Nature by supposing the shape of 

 the surface of the solid portion of the Earth 

 to be just what it is in fact, an irregular 

 succession of great continental elevated 

 areas, great oceanic basins, mountain 

 ranges, broad valleys, great plateaus, etc. 

 Let the problem still differ from that of Na- 

 ture by supposing that the water level is 

 just high enough to cover the summit of 

 Mt. Everest, so that the whole Earth is 

 covered with depths varying from zero, at 

 Mt. Everest, to ten miles, on a few small 

 areas at the deepest portions of the oceans. 

 If, under these conditions, an attempt is 

 made to follow the history of the wave in 

 its westward progress, the problem will at 



