THE TIDES. 275 



readily driven in opposite directions by these opposite forces. If the 

 earth were entirely solid, then there could be no sucli bulging out of 

 any of its matter, and therefore no tides. 



A few words here in regard to the law of gravitation are in place. 

 Every body of matter attracts every other body of matter, and with 

 a force equal to the amount of matter each body contains ; and this 

 force diminishes as the square of the distance increases. Two bodies of 

 equal mass approach each other equally ; but, if one body contains 

 four times as much matter as another, the smaller approaches the 

 larger with a velocity four times as great as the larger does the 

 smaller. Suppose two such bodies, beiug separated at a distance of 

 100,000 miles, attract each other \vith a certain known force : if this 

 distance be increased to 200,000 miles, the force of attraction between 

 these two bodies will be only one-fourth as great. In like manner, 

 the earth, at the point farthest from the sun, feels a smaller degree 

 of attraction than the matter at the centre. And, as the centrifugal 

 force is also greater at this point than at the centre, there is here an 

 excess of centrifugal over centripetal force, and sufficient, as can be 

 ascertained by exact mathematical calculation, to produce a solar 

 tide. And at that part of the earth's surface which is nearest the 

 sun, or facing it, there is, according to the same law of gravity, an 

 excess of centi*ipetal over centrifugal force. Hence we have also a 

 solar tide at this part of the surface of the earth. 



I give one more illustration. Suppose the earth, at E (F\g. 1), is 

 moving in a straight line toward E^ and with a velocity of 68,000 

 miles an hour; and suppose when she reaches E' she comes under the 



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attractive influence of the sun. She will then be deflected from her 

 rectilineal course and move in a curvilineal orbit around the sun. 

 That part of her surface turned away from the sun will be 8,000 miles 

 farther from the attractive influence of the central orb than that part 

 of her surface facing the sun. Hence this remote part will have a 

 greater tendency to continue moving on in a straight line than any 

 other part ; and this tendency will show itself in the motion of its 

 waters, by producing a tide. The waters will have a tendency to 

 move in a line tangent to the orbit of the earth. The part of the 



