34 THE OCEAN WORLD. 
traversed in the same time, the force, directed towards the sun, which 
must be exerted to effect the necessary bending, is greater the larger 
the orbit. This is proved in all treatises on mechanics. Hence a 
greater force in the direction Ds is required at D to keep that part 
of the earth in its orbit than the force acting upon the central parts 
at o, a, and c; and a less force is sufficient at B. Now, the sun does 
not supply a force which varies in this way ; on the contrary, the sun’s 
attraction is least at D and greatest at B, since the attraction of the 
sun is a force which decreases with distance. Hence the sun exerts 
more than a sufficient attraction at B, and less than a sufficient 
attraction at D, z.¢, more and less than would keep those parts of the 
earth in the orbits which they actually pursue. Hence, at B there is 
a small surplus of solar attraction, which is not employed in keeping 
that part of the earth in its path ; and as it acts there in the opposite 
direction to the attraction ef the earth, it makes bodies at B less 
heavy than they would otherwise be. And, again, at D a force some- 
what more powerful than the sun’s attraction is required to keep this 
part of the earth in its orbit, and therefore a portion of the force of 
gravity, z.¢, of the attraction towards the centre of the earth, has to 
assist in this situation and supply the deficiency. This diminishes 
the weight of bodies at p. The upshot, then, is that at B and p bodies 
are a little less heavy than they would be in other situations, as at 
aorc. This defect of weight is very slight, amounting at B and p, 
where it is greatest, to a loss of not more than one twenty-five- 
millionth of the whole gravity, but, small as it is, it produces the 
solar tide. For, keeping still to the supposition of an earth without 
~daily rotation, and supposing further that our imaginary earth is 
covered everywhere with an ocean, it is evident that water being 
slightly lighter at B and D than at a and c, there will be an exceed- 
ingly feeble tendency to flow from a and c towards B and D, so as to 
raise protuberances there, The distance from a to B is about 6,200 
miles, and as soon as the water has risen about twenty-three inches 
higher at B and p than at a and c, the tendency to slip back caused 
by the protuberance is enough to balance the feeble force with which 
we have to deal. Hence the sun would cause two excessively broad 
and flat protuberances of the height of twenty-three inches on our 
imaginary earth. 
Let us now take into account the further circumstance that the 
earth rotates daily on its axis in the direction aBcp. This rotation 
will carry the protuberance at B towards c. When it is removed 
from 8 it will tend to return to its natural station at B, and will take 
np its position in some situation such as 2, where its own tendency 
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