416 THE MATHEMATICAL PRINCIPLES [BOOK in diate time that aproaches nearer to the third hour of the moon than tc that of the sun. And, therefore, while the moon is passing from the syzy gies to the quadratures, during which time the 3d hour of the sun precedes the 3d hour of the moon, the greatest height of the waters will also precede the 3d hour of the moon, and that, by the greatest interval, a little after the octants of the moon; and, by like intervals, the greatest tide will fol low the 3d lunar hour, while the moon is passing from the quadratures to the syzygies. Thus it happens in the open sea : for in the mouths of rivers the greater tides come liter to their heiirht. o O But the effects of the luminaries depend upon their distances from the earth ; for when they are less distant, their effects are greater, and when more distant, their effects are less, and that in the triplicate proportion of their apparent diameter. Therefore it is that the sun, in the winter time, being then in its perigee, has a greater effect, and makes the tides in the syzygies something greater, and those in the quadratures something less than in the summer season ; and every month the moon, while in the peri gee, raises greater tides than at the distance of 15 days before or after, when it is in its apogee. Whence it comes to pass that two highest tides do not follow one the other in two immediately succeeding syzygies. The effect of either luminary doth likewise depend upon its declination or distance from the equator ; for if the luminary was placed at the pole, it would constantly attract all the parts of the waters without any inten sion or remission of its action, and could cause no reciprocation of motion. And, therefore, as the luminaries decline from the equator towards either pole, they will, by degrees, lose their force, and on this account will excite lesser tides in the solstitial than in the equinoctial syzygies. But in the solstitial quadratures they will raise greater tides than in the quadratures about the equinoxes ; because the force of the moon, then situated in the equator, most exceeds the force of the sun. Therefore the greatest tides fall out in those syzygies, and the least in those quadratures, which happen about the time of both equinoxes : and the greatest tide in the syzy gies is always succeeded by the least tide in the quadratures, as we find by experience. But, because the sun is less distant from the earth in winter than in summer, it comes to pass that the greatest and least tides more frequently appear before than after the vernal equinox, and more frequently after than before the autumnal. Moreover, the effects of the lumi naries depend upon the latitudes of places. Let AjoEP represent the earth covered with deep waters ; C its centre; P, p its poles; AE the equator ; F any place without the equator ; F/ the parallel of the place ; /F~ M ^ Drl the correspondent parallel on the K 1ST