298 CELESTIAL DYNAMICS. 



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 unchange- 

 able 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 attrac- 

 tion, the earth might be considered to be a large magnet, one 

 pole of which, being more powerfully attracted, would repre- 

 sent the upper, and the other pole the lower tidal elevation. 

 As the upper tidal wave tends to move towards the moon, the 

 earth would act like a- galvanometer, whose needle has been 

 deflected from the magnetic meridian, and which, while tend- 

 ing to return thereto, exerts a constant lateral pressure. 



The foregoing discussion may suffice to demonstrate the 

 influence 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 pre- 

 cession 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 ascer- 

 tained mean difference between the time of the moon's cul- 

 mination and that of high water in the open sea, enter, how- 

 ever, as elements into such a calculation, and render the de- 

 sired result an uncertain quantity. 



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 



