212 THE TIDES. 



course, separated from each other by half the circumference of the globe. 

 As the globe revolves with its diurnal motion upon its axis, every part of its 

 surface passes successively under these tidal waves ; and at all such parts as 

 they pass under them, there is the phenomenon of high water. Hence it is 

 that in all places there are two tides daily, having an interval of about twelve 

 hours between them. Now if the common notion of the cause of the tides 

 were well founded, there would be only one tide daily ; viz., that which would 

 take place when the moon is at or near the meridian. 



That the moon's attraction upon the earth simply considered would not ex- 

 plain the tides, is easily shown. Let us suppose that the whole mass of mat- 

 ter on the earth, including the waters which partially cover it, were attracted 

 equally by the moon ; they would then be equally drawn toward that body, and 

 no reason would exist why they should be heaped up under the moon ; for if they 

 were drawn with the same force as that with which the solid globe of the earth 

 under them is drawn, there would be no reason for supposing that the waters 

 would have a greater tendency to collect toward the moon than the solid bot- 

 tom of the ocean on which they rest. In short, the whole mass of the earth, 

 solid and fluid, being drawn with the same force, would equally tend toward 

 the moon ; and its parts, whether solid or fluid, would preserve among them- 

 selves the same relative position as if they were not attracted at all. 



When we dbserve, however, in a mass composed of various particles of mat- 

 ter, that the relative arrangement of these particles is disturbed, some being 

 driven in certain directions more than others, the inference is, that the compo- 

 nent parts of such a mass must be placed under the operation of different 

 forces ; those which tend more than others in a certain direction being driven 

 with a proportionally greater force. Such is, in fact, the case with the earth, 

 placed under the attraction of the moon. NEWTON showed that the law of 

 gravitation is such, that its attraction increases as the distance of the attracted 

 object diminishes, and diminishes as the distance of the attracted object in- 

 creases. The exact proportion of this change of energy of the attractive 

 force, is technically expressed by stating that it is the inverse proportion of the 

 square of the distance ; the meaning of which is, that the attraction which any 

 body like the moon would exercise at any proposed distance, is four times that 

 which it would exercise at twice the distance ; nine times that which it would 

 exert at three times the distance ; one fourth of that which it would exercise 

 at half the distance, and one ninth of that which it would exercise at one third 

 the distance, and so on. Thus we have an arithmetical rule, by which we can 

 with certainty and precision say how the attraction of the moon will vary with any 

 change of its distance from the attracted object. Let us see how this will be 

 brought to bear upon the explanation of the effect of the moon's attraction upon 

 the earth. 



Let A, B, C, D, E, F, G, H, represent the globe of the earth, and, to simplify 

 the explanation, let us first suppose the entire surface of the globe to be covered 

 with water. Let M, the moon, be placed at the distance K L from the nearest point 

 of the surface of the earth. Now it will be very apparent that the various points 

 of the earth's surface are at different distances from the moon, M. A and G are 

 more remote than H ; B F still more remote ; C and E more distant again, 

 and D more remote than all. The attraction which the moon exercises at H 

 is, therefore, greater than that which it exercises at A and G, and still greater 

 than that which it produces Rt B and F ; and the attraction which it exercises 

 at D is least of all. Now this attraction equally afffects matter in every state 

 and condition. It affects the particles of fluid as well as solid matter, but there 

 is this difference between these effects ; that where it acts upon solid matter, 

 the component parts of which are at different distances from it, and therefore I 



