OP TIDES. 325 



In all these cases, the law of the elevation and depression of each 

 tide may be derived, like that of the vibrations of a pendulum 

 and of a balance, from the uniform motion of a point in a circle. 

 Thus, if we conceive a circle to be placed in a vertical plane, having 

 its diameter equal to the whole magnitude of the tide, and touching 

 the surface of the sea at low water, the point, in which the surface 

 meets the circumference of the circle, will advance with a uniform 

 motion, so that if the circle be divided into twelve parts, the point 

 will pass over each of these parts in a lunar hour. It sometimes 

 happens, however, in confined situations, that the rise and fall of the 

 water deviates considerably from this law, and the tide rises some- 

 what more rapidly than it fulls; and in rivers, for example in the 

 Severn, the tide frequently advances suddenly with a head of several 

 feet in height. These deviations probably depend on the magnitude 

 of the actual displacement of the water, which in such cases bears 

 a considerable proportion to the velocity of the tide, while in the 

 open ocean a very minute progressive motion is sufficient to produce 

 the whole elevation. The actual progress of the tides may be most 

 conveniently observed, by means of a pipe descending to some dis. 

 tance below the surface, so as to be beyond the reach of superficial 

 agitations, and having within it a floajt, carrying a wire, and indi- 

 cating the height of the water on a scale properly divided. 



We have hitherto considered the tides so far only as they are oc- 

 casioned by the moon ; but in fact the tides, as they actually exist, 

 depend also on the action of the sun, which produces a series of 

 effects precisely similar to those of the moon v although much less 

 conspicuous, on account of the greater distance of the sun, the solar 

 tide being only about two-fifths of the lunar. These tides take place 

 independently of each other, nearly in the same degree as if both 

 were single ; and the combination resuUiug from them is alternately 

 increased and diminished, accordingly as they agree or disagree, 

 with respect to the time of high water at a given place ; in the same 

 manner as if two series of waves, equal among themselves, of which 

 the breadth* are as 29 to 30, be supposed to pass in the same direc- 

 tion over the surface of a fluid, or if two sounds similarly related be 

 heard at the same time, a periodical increase and diminution of the 

 joint effect will in either case be produced. Hence are derived the 

 spring and neap tides, the effects of the sun and moon being united 

 Stl the times of conjunction and opposition, or of the new and full 



