ON THE TIDES. 447 



according to the place of the moon's nodes, which allows her declination to 

 be greater or less, and this difference is most observable in high latitudes, 

 for instance, in Iceland ; since, in the neighbourhood of the poles, the tides 

 depend almost entirely on the declination. 



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 mag- 

 nitude 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 12 

 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 falls ; 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 displace- 

 ment 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 distance below the surface, so as to be beyond the reach of super- 

 ficial agitations, and having within it a float, carrying a wire, and indicating 

 the height of the water on a scale properly divided. 



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

 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, 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 resulting 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 breadths are as 29 to 30, be supposed to pass in the same direction 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 at the times of conjunction and oppo- 

 sition, or of the new and full moon, and opposed at the quadratures, or first 

 and last quarters. The high tides at the times of the equinoxes are pro- 

 duced by the joint operation of the sun and moon, when both of them are 

 so situated as to act more powerfully than elsewhere. 



The lunar tide being much larger than the solar tide, it must always 

 determine the time of high and low water, which, in the spring and neap 

 tides, remains unaltered by the effect of the sun ; so that in the neap tides, 

 the actual time of low water is that of the solar high water ; but at the 

 intermediate times, the lunar high water is more or less accelerated or 



