SECT. XIII. INFLUENCE OF SUN AND MOON. 97 



cube of the parallax or apparent diameter of the body producing 

 it, for the greater the apparent diameter the nearer the body 

 and the more intense its action upon the sea ; hence the spring 

 tides are much increased when the moon is in perigee, for then 

 she is nearest to the earth. 



The second phenomenon in the tides is the augmentation 

 occurring at the time of the equinoxes, when the sun's declina- 

 tion is zero (N. 159), which happens twice in every year. The 

 spring tides which take place at that time are often much in- 

 creased by the equinoctial gales, and,- on the hypothesis of the 

 whole earth covered by the ocean, would be the greatest possible 

 if the line of the moon's nodes coincided with that of her perigee, 

 for then the whole action of the luminaries would be in the plane 

 of the equator. But since the Antarctic Ocean is the source of 

 the tides, it is evident that the spring tide must be greatest 

 when the moon is in perigee, and when both luminaries havo 

 their highest southern declination, for then they act most directly 

 upon the great circuit of the south polar seas. 



The sun and moon are continually making the circuit of the 

 heavens at different distances from the plane of the equator, on 

 account of the obliquity of the ecliptic and the inclination of the 

 lunar orbit. The moon takes about 29i days to vary through all 

 her declinations, which sometimes extend 281 on each side of 

 the equator, while the sun requires nearly 365J days to accom- 

 plish his motions through 23 on each side of the same plane, 

 so that their combined action causes great variations in the tides. 

 Both the height and time of high water are perpetually changing, 

 and, although the problem does not admit of a general solution, 

 it is necessary to analyse the phenomena which ought to arise 

 from the attraction of the sun and moon, but the result must 

 be corrected in each particular case for local circumstances, so 

 that the theory of the tides in each port becomes really a matter 

 of experiment, and can only be determined by means of a vast 

 number of observations, including many revolutions of the 

 moon's nodes. 



The mean height of the tides will be increased by a very small 

 quantity for ages to come, in consequence of the decrease in the 

 mean distance of the moon from the earth ; the contrary effect 

 will take place after that period has elapsed, and the moon's 

 mean distance begins to increase again, which it will continue to 



F 



