Tidal Wave on the Earth's Rotation. 293 



tion round this centre be diminishing, then the earth must be 

 falling toward it; or, in other words, approaching toward the 

 moon. And if so, then the velocity of the earth's motion round 

 this centre must be increasing. Hence we arrive at the con- 

 clusion that the tidal wave produced by the sun tends to ac- 

 celerate the moon's mean motion *. 



This conclusion is apparent in another way. If we admit 

 that the tidal wave, produced by the influence of the moon, 

 affects the rotation of the earth on its axis O, then we have 

 every reason to conclude that the tidal wave produced by the 

 sun will affect the rotation of the earth on the common centre 

 of gravity 0' of the earth and moon. For the rotation of the 

 earth and moon, on their common centre, stands in exactly the 

 same relation to the sun as the diurnal rotation of the earth 

 on its own centre stands to the moon. For the earth and 

 moon may be regarded as but one body revolving on its axis 

 0' in presence of the sun. 



It was shown by Laplace that the slow r diminution which is 

 taking place in the excentricity of the earth's orbit tends to ac- 

 celerate the moon's motion. But this change, like all the other 

 great changes in celestial motion, is periodic. For when the 

 earth's orbit becomes almost a circle, and again begins to open 

 out into an ellipse, a retarding influence on the moon's motion 

 will have commenced. The reason why all such motions are 

 periodic is this ; there is no real loss of force : there is merely 

 a transference of force from one part of the system to another. 

 The elements of ultimate restoration consequently still remain. 

 But when the vis viva of celestial motion becomes transformed 

 into heat, things never can be brought back to their former po- 

 sition ; for a portion of this heat is always radiated into space 

 and lost for ever. 



Now, if the vis viva of the earth's motion on its centres 

 and 0' is being transformed into heat by the action of the tidal 

 wave, the diurnal motion of our globe will, in the long run, not 

 only be totally destroyed, but the earth and moon will ulti- 

 mately fall together and revolve round the sun as one planet. 



* Since the above was written, I have been informed by Prof. William 

 Thomson that he has arrived at results somewhat similar. He finds, 

 however, that the influence of the tidal wave is to cause the moon in the 

 first instance to recede from the earth. But the ultimate tendency is to 

 bring the sun, moon, and earth together, and cause them to rotate as one 

 rigid body on its axis. The conclusion arrived at by this able physicist 

 will, however, be shortly laid before the public. 



