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 d s 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, i.e., 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 of 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, i.e., 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 d. The upshot, then, is that at b and d bodies 

 are a little less heavy than they would be in other situations, as at 

 A or c. This defect of weight is very slight, amounting at b and d, 

 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 d 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 a b c D. This rotation 

 will carry the protuberance at b towards c. When it is removed 

 from B it will tend to return to its natural station at b, and wiU take 

 np its position in some situation such as 71, where its own tendency 



