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XXIII. Popular Difficulties in Tide Theory. 

 By E. Lacy Garbett*. 



HP^HE paradoxical fact that, on a rapidly rotating earth, the 

 JL places of high and low water (friction apart) are contrary 

 to those that would exist on a non-rotating earth, seems brought 

 by Professor Abbott for the first time within easy popular ap- 

 prehension 1 — which was necessary to remove a certain stigma of 

 unreality from the current elementary teaching about tides. 

 This lucid explanation seems to be such as may enable a child 

 to see that if the waters have their diurnal rotary velocity in- 

 creased and diminished in the four quadrants, according to the 

 arrows of his diagram, the result must be " low water under the 

 moon," or high water at moonrise and moonset, and earlier the 

 more friction. But the popular difficulty is now the antecedent 

 one, to make clear (what is, of course, familiar to all who have 

 considered perturbations) that those arrows do express the direc- 

 tions of tangential force, not only iu the hemisphere next the 

 moon, but in the other also. 



The only simple way to do this, appears to be by recurring to 

 the old diagram of an equilibriated earth, with its two high 

 waters, one towards or under the moon, and one away from or 

 over the moon ; where the consideration of the decrease of lunar 

 attraction from the nearer surface to the centre, and thence to the 

 further surface, makes clear that on a globe behaving to the moon 

 as the moon does to us (which Mr. Denison well calls " waltz- 

 ing"), this is the only figure the waters could maintain ; the sum- 

 mits being where, on one side, they are literally most pulled from 

 the earth, and on the other, the earth pulled from them. 



Equilibriated 

 or waltzing. 



Suddenly 

 turned 90°. 



Spinning, 

 as the earth. 



Let such a globe with its waters be supposed instantaneously 

 turned, in either direction, a quarter round. The waters, to 

 resume their figure relatively to the moon, must make hori- 

 zontal movements in the directions of the four arrows, and with 

 velocities whose maximum, at the middle of each quadrant, is 

 calculable, and may be shown, in the most elementary way, to 



* Communicated by C. Tomlinson, F.R.S. 

 1 Phil. Mag. Jan. 1870, p. 49. 



