108 Dr. J. R. Mayer on Celestial Dynamics', 



traded towards the east. The upper tidal elevation is not only 

 more powerfully attracted because it is nearer to the moon, but 

 also because the angle under which it is pulled aside is more 

 favourable for lateral deflection than in the case of the opposite 

 protuberance. The pressure from east to west of the upper 

 elevation preponderates therefore over the pressure from west to 

 east of the opposite mountain ; according to calculation, these 

 quantities stand to each other nearly as 14 to 13. From the 

 relative position of these two tidal protuberances and the moon, 

 or the unchangeable position of the major axis of the earth- 

 spheroid towards the centre of gravity of the moon, a pressure 

 results, which preponderates from east to west, and offers an 

 obstacle to the earth's rotation. 



If gravitation were to be compared with magnetic attraction, 

 the earth might be considered to be a large magnet, one pole of 

 which, being more powerfully attracted, would represent the 

 upper, and the other pole the lower tidal elevation. As the: 

 tipper tidal wave tends to move towards the moon, the earth 

 would act like a galvanometer, w T hose needle has been deflected 

 from the magnetic meridian, and which, whilst tending to 

 return thereto, exerts a constant lateral pressure. • 



The foregoing discussion may suffice to demonstrate the in- 

 fluence of the moon on the earth's rotation. The retarding 

 pressure of the tidal wave may quantitatively be determined in 

 the same manner as that employed in computing the precession 

 of the equinoxes and the nutation of the earth's axis. The 

 varied distribution of land and water, the unequal and unknown 

 depth of the ocean, and the as yet imperfectly ascertained 

 mean difference between the time of the moon's culmination 

 and that of high water in the open sea, enter, however, as 

 elements into such a calculation, and render the desired result 

 an uncertain quantity. 



■ t In the mean time this retarding pressure, if imagined to act 

 at the equator, cannot be assumed to be less than 1000 millions 

 of kilogrammes. In order to start with a definite conception, 

 we may be allowed to use this round number as a basis for the 

 following calculations. 



The rotatory velocity of the earth at the equator is 464 

 metres, and the consumption of mechanical work, therefore, 

 for the maintenance of the tides 464,000 millions of Km, or 6000 

 millions of horse-powers per second. The effect of the tides may 

 consequently be estimated at -^~th of the effect received by the 

 earth from the sun. 



The rotatory effect which the earth at present possesses, may 

 be calculated from its mass, volume, and velocity of rotation. 

 The volume of the earth is 2,650,686,000 cubic miles, and 



