OK THE TIDES. 583 



Such are the general outlines of the lunar tides; they are, however, liable 

 to a great variety of modifications, besides their combination with the tides 

 produced by the sun. When the moon is exactly over the equator, the 

 highest part of the remoter, or inferior, as well as of the nearer or superior 

 tides, passes also over the equator, and the effect of the tide in various lati- 

 tudes decreases gradually from the equator to the pole, where it vanishes ; 

 but when the moon has north or south declination, the two opposite summits 

 of the spheroid describe parallels of latitude, remaining always diametrically 

 opposite to each other. Hence the two successive tides must be unequal at 

 every place except the equator, the greater tide happening when the nearer 

 elevation passes its meridian : and the mean between both is somewhat smaller 

 than the equal tides which happen when the moon passes the equator. This 

 inequality is, however, much less considerable than it would be if the sea 

 assumed at once the form of the spheroid of equilibrium; and the most 

 probable reasons for this circumstance, are, first, that our tides are partly de- 

 rived from the equatorial seas; secondly, that the effects of a preceding tide 

 are in some measure continued so as to influence the height of a succeeding 

 one ; and, thirdly, that the tides of a narrow sea are less affected by its lati- 

 tude than those of a wide ocean. The height of the sea at low water is the 

 same whatever the moon's declination may be. There is also a slight differ- 

 ence in the tides, 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 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 I'i parts, the point will 

 pass over each of these parts in a lunar hour. It sometimes happens, how- 

 ever, in confined situations, that the rise and fall of the water deviates con- 

 siderably from this law, and the tide rises somewhat more rapidly than it 

 falls; and in rivers, for example in the Severn, the tide frequently advances 



