superiority over the equilibrium theory, is still but an imperfect 

 representation of the real circumstances of the actual ocean. 

 Accordingly Laplace again attacked the problem from another side. 



The law of the rise and fall of the sea may be broadly 

 stated as follows. If we suppose a circle traced on a dock 

 wall, so that the lower extremity of its vertical diameter may coincide 

 with low water mark, and the upper extremity with high water mark, 

 and if we divide its circumference between these points into six equal 

 parts, representing each one hour, then tlie tide will, as it rises, just cover 

 one of these divisions each hour, and similarly uncover one for each 

 hour that it falls. A rule founded on this is in practical use among 

 seamen for finding the alteration produced by the tide in the soundings 

 marked on the chart. This motion of the v.-ater is what is termed a 

 simple harmonic motion. 



Let us suppose that, as the minute hand of a clock travels round 

 the face, a point moves along the vertical diameter, so as always to 

 keep on the same level as the extremity of the hand. This point then 

 will have a simple harmonic motion. Let us suppose the hand and 

 the point to start from the figure VL of the dial : at first, then, the 

 upward motion of the point will be very slow ; as the hand gets nearer 

 to IX. the point will move faster, attaining its greatest speed when the 

 hand is at IX. ; its speed will then decrease as the hand goes towards 

 XII. Thus we see that the velocity of a simple harmonic motion is 

 continually varying : thus— though the water will cover equal arcs of 

 the circle on the dock wall in equal lines, its vertical rise in the same 

 time will vary greatly. 



Now just as the absolute motion in space of a man on board a 

 ship is compounded of his motion relative to the ship, of the ship's 

 motion relative to the earth, and of the earth's motion in space, so we 

 may conceive a motion compounded of several simple harmonic 

 motions. 



Owing to the varying distances and positions of the sun and moon, 

 the tide-producing forces which they exert are always varying in 

 intensity ; for example, the varying distance of the moon from the 

 earth produces one variation in her tide-producing force, her varying 

 distance from the equator produces another. Now, Laplace was led 

 to conclude, from his mathematical results, that each such periodical 

 variation in the tide-producing forces causes a corresponding variation 



