24. AGAIN the tides have some farther varieties from the situation of the places where they happen northward or southward. Let _p_ P (in fig. 115.) represent the axis, on which the earth daily revolves, let _h_ _p_ H P represent the figure of the water, and let _n_ B N D be a globe inscribed within this figure. Suppose the moon to be advanced from the equator toward the north pole, so that _h_ H the axis of the figure of the water _p_ A H P E _h_ shall decline towards the north pole N; take any place G nearer to the north pole than to the south, and from the center of the earth C draw C G F; then will G F denote the altitude to which the water is raised by the tide, when the moon is above the horizon: in the space of twelve hours, the earth having turned half round its axis, the place G will be removed to _g_; but the axis _h_ H will have kept its place preserving its situation in respect of the moon, at least will have moved no more than the moon has done in that time, which it is not necessary here to take into consideration. Now in this case the height of the water will be equal to _g_ _f_, which is not so great as G F. But whereas G F is the altitude at high water, when the moon is above the horizon, _g_ _f_ will be the altitude of the same, when the moon is under the horizon. The contrary happens toward the south pole, for K L is less than _k_ _l_. Hence is proved, that when the moon declines from the equator, in those places, which are on the same side of the equator as the moon, the tides are greater, when the moon is above the horizon, than when under it; and the contrary happens on the other side of the equator. 25. NOW from these principles may be explained all the known appearances in the tides; only by the assistance of this additional remark, that the fluctuating motion, which the water has in flowing and ebbing, is of a durable nature, and would continue for some time, though the action of the luminaries should cease; for this prevents the difference between the tide when the moon is above the horizon, and the tide when the moon is below it from being so great, as the rule laid down requires. This likewise makes the greatest tides not exactly upon the new and full moon, but to be a tide or two after; as at Bristol and Plymouth they are found the third after. 26. THIS doctrine farther shews us, why not only the spring tides fall out about the new and full moon, and the neap tides about the quarters; but likewise how it comes to pass, that the greatest spring tides happen about the equinoxes; because the luminaries are then one of them over the equator, and the other not far from it. It appears too, why the neap tides, which accompany these, are the least of all, for the sun still continuing over the equator continues to have the greatest power of lessening the moon’s action, and the moon in the quarters being far removed toward one of the poles, has its power thereby weakned.