106 SPRING AND NEAP TIDES. [SECT. xiri. 



happens near the equinoxes, while the moon is in perigee. 

 The inclination of the moon's orbit to the ecliptic is 5 8' 

 47"'9 ; hence in the equinoxes the action of the moon would 

 be increased if her node were to coincide with her perigee ; 

 for it is clear that the action of the sun and moon on the 

 ocean is most direct and intense when they are in the plane 

 of the equator, and in the same meridian, and when the moon 

 in conjunction or opposition is at her least distance from the 

 earth. The spring tides which happen under all these fa- 

 vourable circumstances must be the greatest possible. The 

 equinoctial gales often raise them to a great height. Besides 

 these remarkable variations, there are others arising from the 

 declination or angular distance of the sun and moon from the 

 plane of the equator, which have a great influence on the 

 ebb and flow of the waters. The sun and moon are con- 

 tinually making the circuit of the heavens at different dis- 

 tances 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 twenty-nine days and a half to vary 

 through all her declinations, which sometimes extend 28| 

 degrees on each side of the equator, while the sun requires 

 nearly 365^ days to accomplish his motion from tropic to tropic 

 through about 23^ degrees ; so that their combined motion 

 causes great irregularities, and at times their attractive forces 

 counteract each other's effects to a certain extent ; but on 

 an average the mean monthly range of the moon's declina- 

 tion is nearly the same as the annual range of the declina- 

 tion of the sun : consequently the highest tides take place 

 within the tropics, and the lowest towards the poles. The 

 declination of the moon likewise causes the two tides of the 

 same day to rise to unequal heights ; this diurnal inequality 

 of course vanishes when the moon is in- the equator. 



Both the height and time of high water are thus per- 

 petually changing ; therefore in solving the problem it is 

 required to determine the heights to which the tides rise, the 

 times at which they happen, and the daily variations. 



