Dr. J. R. Mayer on Celestial Dynamic's. 403 



VIII. The Tidal Wave. 



In almost every case the forces and motions on the surface 

 of the earth may be traced back to the rays of the sun. Some 

 processes, however, form a remarkable exception. 



One of these is the tides. Beautiful, and in some respects 

 exhaustive researches on this phenomenon have been made by 

 Newton, Laplace, and others. The tides are caused by the 

 attraction exercised by the sun and the moon on the moveable 

 parts of the earth's surface, and by the axial rotation of our 

 globe. 



The alternate rising and falling of the level of the sea may be 

 compared to the ascent and descent of a pendulum oscillating 

 under the influence of the earth's attraction. 



The continual resistance, however weak it may be, which an 

 instrument of this nature (a physical pendulum) suffers, con- 

 stantly shortens the amplitude of the oscillations which it per- 

 forms ; and if the pendulum be required to continue in uniform 

 motion, it must receive a constant supply of vis viva correspond- 

 ing to the resistance it has to overcome. 



Clocks regulated by a pendulum obtain such a supply, either 

 from a raised weight or a bent spring. The power consumed 

 in raising the weight or in bending the spring, which power is 

 represented by the raised weight or the bent spring, overcomes 

 for a time the resistance, and thus secures the uniform motion 

 of the pendulum and clock. In doing so, the weight sinks 

 down or the spring uncoils, and therefore force must be expended 

 in winding the clock up again, or it would stop moving. 



Essentially the same holds good for the tidal wave. The 

 moving waters rub against each other, against the shore, and 

 against the atmosphere, and thus, meeting constantly with re- 

 sistance, would soon come to rest if a vis viva did not exist com- 

 petent to overcome these obstacles. This vis viva is the rotation 

 of the earth on its axis, and the diminution and final exhaustion 

 thereof will be a consequence of such an action. 



The tidal wave causes a diminution of the velocity of the rota- 

 Hon of the earth. 



This important conclusion can be proved in different ways. 



The attraction of the sun and the moon disturbs the equi- 

 librium of the moveable parts of the earth's surface, so as to 

 move the waters of the sea towards the point or meridian above 

 and below which the moon culminates. If the waters could 

 move without resistance, the elevated parts of the tidal wave 

 would exactly coincide with the moon's meridian, and under 

 such conditions no consumption of vis viva could take place. 

 In reality, however, the moving waters experience resistance, in 



