442 LECTURE XLVII. 



Aristotle mentions the tides of the northern seas, and remarks that they" 

 vary with the moon, and are less conspicuous in small seas than in the 

 ocean : Caesar, Strabo, Pliny, Seneca, and Macrobius give also tolerably 

 accurate accounts of them. 



There are in the tides three orders of phenomena which are separately 

 distinguishable ; the first kind occurs twice a day, the second twice a 

 month, and the third twice a year. Every day, about the time of the 

 moon's passing over the meridian, or a certain number of hours later, the 

 sea becomes elevated above its mean height, and at this time it is said to 

 be high water. The elevation subsides by degrees, and in about six hours 

 it is low water, the sea having attained its greatest depression ; after this 

 it rises again when the moon passes the meridian below the horizon, so 

 that the ebb and flood occur twice a day, but become daily later and later 

 by about 50 minutes, which is the excess of a lunar day above a solar one, 

 since 28 lunar days are nearly equal to 29| solar ones. 



The second phenomenon is, that the tides are sensibly increased at the 

 time of the new and full moon ; this increase and diminution constitute 

 the spring and neap tides; the augmentation becomes also still more 

 observable when the moon is in its perigee or nearest the earth. The 

 lowest as well as the highest water is at the time of the spring tides ; the 

 neap tides neither rise so high nor fall so low. 



The third phenomenon of the tides is the augmentation which occurs at 

 the time of the equinoxes ; so that the greatest tides are when a new or 

 full moon happens near the equinox, while the moon is in its perigee. The 

 effects of these tides are often still more increased by the equinoctial winds, 

 which are sometimes so powerful as to produce a greater tide before or 

 after the equinox, than that which happens in the usual course, at the time 

 of the equinox itself. 



These simple facts are amply sufficient to establish the dependence of the 

 tides on the moon ; they were first correctly explained by Newton as the 

 necessary consequences of the laws of gravitation, but the theory has been 

 still further improved by the labours of later mathematicians. The 

 whole of the investigations has been considered as the most difficult of all 

 astronomical problems ; some of the circumstances depend on causes 

 which must probably remain for ever unknown to us; and unless we 

 could every where measure the depth of the sea, it would be impossible to 

 apply a theory, even if absolutely perfect, to the solution of every difficulty 

 that might occur. A very injudicious attempt has been made to refer the 

 phenomena of the tides to causes totally different from these, and depending 

 on the annual melting of the polar ice ; the respectability of its author is 

 the only claim which it possesses even to be mentioned ; and a serious 

 confutation of so groundless an opinion would be perfectly superfluous. 



A detached portion of a fluid would naturally assume, by its mutual 

 gravitation, a spherical form, but if it gravitate towards another body at 

 a distance, it will become an oblong spheroid of which the axis will 

 point to the attracting body ; for the difference of the attraction of this 

 body on its different parts will tend to separate them from each other in 

 the greatest part of the sphere, that is, at all places within the angular 



