TIDAL OBSERVATIONS. 295 



" 805. The rise and fall of water at any point of the earth's surface we may 

 now imagine to be produced by making these two disturbing bodies (moon and 

 anti-moon, as we may call them for brevity) revolve round the earth's axis 

 once in the lunar twenty-four hours, with the line joining them always in- 

 clined to the earth's equator at an angle equal to the moon's declination. If 

 we assume that at each moment the condition of hydrostatic equilibrium is 

 fulfilled, that is, that the free liquid surface is perpendicular to the resultant 

 force, we have what is called the ' equilibrium theory of the tides.' 



" 806. But even on this equilibrium theory, the rise and fall at any place 

 would be most falsely estimated if we were to take it, as we believe it is 

 generally taken, as the rise and fall of the spheroidal surface that would bound 

 the water were there no dry land (uncovered solid). To illustrate this state- 

 ment, let us imagine the ocean to consist of two circular lakes A and B, with 

 their centres 90° asunder, on the equator, communicating with one another by 

 a narrow channel. In the course of the lunar twelve hours the level of lake A 

 would rise and fall, and that of lake B would simultaneously fall and rise to 

 maximum deviations from the mean level. If the areas of the two lakes were 

 equal, their tides would be equal, and would amount in each to about i of 

 a foot above and below the mean level ; but not so if the areas were unequal. 

 Thus, if the diameter of the greater be but a small part of the earth's qua- 

 drant, not more, let us say, than 20°, the amounts of the rise and fall in the 

 two lakes will be inversely as their areas to a close degree of approximation. 

 For instance, if the diameter of B be only -^ of the diameter of A, the rise 

 and fall in A will be scarcely sensible ; while the level of B will rise and fall 

 by about 1| feet above and below its mean ; just as the rise and fall of level 

 in the open cistern of an ordinary barometer is but small in comparison with 

 fall and rise in the tube. Or, if there be two large lakes. A, A', at opposite 

 extremities of an equatorial diameter, two small ones, B, B', at two ends of the 

 equatorial diameter perpendicular to that one, and two small lakes, C, C, at 

 two ends of the polar axis, the largest of these being, however, stiU supposed 

 to extend over only a small portion of the earth's curvature, and all the six 

 lakes communicate with one another freely by canals or underground tunnels : 

 there will be no sensible tides in the lakes A and A' ; in B and B' there will 

 be high water of 1^ feet above mean level when the moon or anti-moon is 

 in the zenith, and low water of If feet below mean when the moon is rising 

 or setting ; and at C and C there will be tides rising and falling -^ of a foot 

 above and below the mean, the time of low water being when the moon or 

 anti-moon is in the meridian of A, and of high water when they are on the 

 horizon of A. The simplest way of viewing the case for the extreme circum- 

 stances we have now supposed is, first, to consider the spheroidal surface that 

 would bound the water at any moment if there were no dry land, and then 

 to imagine this whole surface lowered or elevated all round by the amount 

 required to keep the height at A and A' invariable. Or, if there be a large 

 lake A in any part of the earth, communicating by canals with small lakes 

 over various parts of the surface, having in all but a small area of water in 

 comparison with that of A, the tides in any of these will be found by drawing 

 a spheroidal surface of If feet difference between greatest and least radius, 

 and, without disturbing its centre, adding or subtracting from each radius 

 such a length, the same for all, as shall do away with rise or fall at A. 



" 807. It is, however, only on the extreme supposition we have made, cf 

 one water area much larger than all the others taken together, but yet itself 

 covering only a small part of the earth's curvature, that the rise and fall can. 

 be done away with nearly altogether in one place, and doubled in another 



