﻿224 On the Secular Effects of Tidal Action, 



This is the loss of terrestrial momentum in the instant of time 

 dt ; and the loss must fall on the water alone if its movements 

 were wholly unimpeded by friction. It thus appears that the 

 waste of motive force is sixty times as great to the earth as to 

 the moon, as may be seen by comparing the last formula with 

 equation (9) after multiplying the latter by m. The same con- 

 formity to the law for the preservation of areas may be shown 

 for zones of water parallel to the equator in every latitude. 



While the enlargement of the moon's orbit through tidal in- 

 fluence converts her apparent gain into an actual loss of velocity, 

 a corresponding result of indirect action would be exhibited in 

 our liquid domain if no friction retarded its movements. Were 

 the terrestrial waters confined to regular channels ranging with 

 the equator or the parallels of latitude, the constant loss of mo- 

 tion would serve to increase the gravity and the pressure of the 

 fluid. But if an ocean of uniform depth covered the entire 

 earth, and if its bottom were perfectly smooth, its waters, though 

 losing some velocity by tidal movements, would have their velo- 

 city of rotation increased by retiring towards the polar regions 

 as the centrifugal force declined. In the aqueous envelope of 

 the earth there would accordingly be a gain of momentum, while 

 a loss occurred to the moon on a corresponding scale and from 

 the same cause. But the result is much modified by friction, 

 which makes the oceanic waters partake of the velocity of our 

 planet, and occasions a consumption of motion proportional to 

 the calorific energy of the tides. 



The effects of the impediments to the great movement of our 

 seas may be readily understood from what is known to attend 

 the collision of imperfectly elastic bodies. If a large meteorite 

 moving from west to east directly over the equator, and having 

 a circular orbit coincident with the verge of our atmosphere, 

 were to have its planetary career arrested by striking a very high 

 mountain, the collision would occasion no loss of momentum ; 

 for whatever the body parted with must be gained by the earth ; 

 but the sum of the living forces which the earth and the me- 

 teorite possess, and which are measured by the masses multiplied 

 by the square of the velocities, would be diminished in proportion 

 to the amount of heat developed as the meteorite struck the 

 mountain or incorporated with our planet in any other way. 

 There is a similar destruction of living force and a corresponding 

 development of heat from the rolling of the vast bodies of water 

 over the asperities in the bed of the ocean ; and motion is ever 

 annihilated in giving birth to calorific energy. Yet nothwith* 

 standing the effects of friction, much of the velocity which the 

 moon gives the liquid domain is retained for some time and ex- 

 hibited in the production of oceanic currents; but as the force 



