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Mr. James Croll on the Influence of the 



the subject, it will be necessary, for the following reasons, to 

 enter somewhat minutely into one or two points regarding the 

 cause of the tides. 



The existence of the tidal wave depends upon the action of 

 two forces, viz. centripetal and centrifugal force. In the pro- 

 duction of the lunar wave, for instance, we have to consider, first, 

 the influence of the attraction of the moon on the water of the 

 ocean ; and secondly, the influence of the centrifugal force of the 

 earth's motion round the common centre of gravity of the earth 

 and moon. Or rather, we should say, we have to consider the 

 combined effect of these two forces on the waters of the ocean. 

 Although in every mode of explaining the production of the tidal 

 wave the element of centrifugal force must be recognized, yet it 

 is not generally stated under that particular form best adapted 

 to exhibit the influence of the wave on the vis viva of the earth's 

 rotation. That clear conceptions on the relation of centrifugal 

 force to the tidal wave are necessary, is evident if we but reflect 

 that the very subject of our present inquiry is the retarding in- 

 fluence exerted by the wave on the centrifugal force of rotation. 



The earth's mass is to that of the moon's as 87*7 to 1. The 

 mean distance between their centres being 237,000 miles, the 

 centre of gravity around which they both revolve is situated 

 2702 miles from the earth's centre, or 1261 miles below its sur- 

 face on the side next the moon. Let ABCD represent the 

 earth's equator, and O ^ 



its centre or axis on 

 which it rotates ; M the 

 moon, and 0' the centre 

 of gravity of the earth 

 and moon, around which 

 they both revolve. A' B' 

 will represent the path 

 w r hich the earth's sur- 

 face at the point B op- 

 posite to the moon will 

 take as it moves round 

 the common centre of 

 gravity 0' . It is found 

 that the centrifugal force 

 occasioned by the earth's 

 rotation on its centre 0, 

 causes the waters of the 

 ocean to rise at the equa- 

 tor ABCD to the height 

 of 34,950 feet ; this being the difference between the equatorial 

 and the mean radius of the earth. Now if the rotation of the 



