256 THE OCEAN. [Book X. 



force of astral gravitation is equal to the square of 

 velocity, then the resistance of astral gravitation is as 

 the square of 8 on each side ; but immediately the 

 top moves downwards from that position — say with 

 the velocity of 4 in a downward direction — then the 

 particles on the side d ah, with this motion added to 

 them, have their velocity increased ; and that velocity 

 of 4 added to the velocity of 8 makes the velocity of 

 12, whereas the velocity on the side h c d\& reduced 

 to 4 ; so that the resistance of astral gravitation on 

 one side is the square of 4, or say 16, whereas the 

 force on the other side is 144, say the square of 12 ; 

 so that the force of astral gravitation on the side 

 d ah IB 144 drawing upwards and 16 on the side 

 h c d drawing downwards. Thus there is a difference 

 of 128, representing an excess in the force of astral 

 gravitation drawing upwards; and, unless the earth's 

 power of gravitation drawing it downwards is equal 

 to that difference of 128, the top cannot fall ; it is 

 then supported, and it is only when the top's rotation 

 becomes so slow that the earth's power of gravitation 

 dragging it down is greater than the difference be- 

 tween those two forces of astral gravitation, that the 

 top can fall. 



The tangential action of the force at a, which 

 supports the top (constantly lifting that side whilst 

 the side c falls) carries the top round with the motion 

 of revolution in the direction e f g h. 



A force of astral gravitation at the point h then 



