Now, in addition to these diurnal changes of the tide, there are others, extending over longer periods, and which must be more or less familiar to everyone who has spent some time on the coast. On a certain day, for instance, we observe that the high tide flows very far up the beach, and that this is followed, a few hours later, by an unusually low ebb, exposing rocks or sand-banks that are not frequently visible. Careful observations of the motions of the water for some days after will show that this great difference between the levels of high and low-water gradually decreases until, about a week later, it is considerably reduced, the high tide not flowing so far inland and the low-water mark not extending so far seaward. Then, from this time, the difference increases again, till, after about two weeks from the commencement of our observations, we find it at the maximum again. [Illustration: FIG. 9.--SPRING TIDES AT FULL MOON] Here again we find that the changes exactly coincide with changes in the position of the moon with regard to the sun and the earth. Thus, the _spring tides_--those which rise very high and fall very low--always occur when the moon is full or new; while the less vigorous _neap tides_ occur when the moon is in her quarters and presents only one-half of her illuminated disc to the earth. And, as the moon passes through a complete cycle of changes from _new_ to _first-quarter_, _full_, _last-quarter_, and then to _new_ again in about twenty-nine days, so the tides run through four changes from spring to neap, spring, neap, and then to spring again in the same period. [Illustration: FIG. 10.--SPRING TIDES AT NEW MOON] The reason for this is not far to seek, for we have already seen that both sun and moon exert a tide-producing influence on the earth, though that of the moon is considerably greater than that of the sun; hence, if the sun, earth, and moon are in a straight line, as they are when the moon is full, at which time she and the sun are on opposite sides of the earth, and also when new, at which time she is between the earth and sun, the sun’s tide is added to the moon’s tide, thus producing the well-marked spring tides; while, when the moon is in her quarters, occupying a position at right angles from the sun as viewed from the earth, the two bodies tend to produce high tides on different parts of the earth at the same time, and thus we have the moon’s greater tides reduced by the amount of the lesser tides of the sun, with the result that the difference between high and low tides is much lessened. [Illustration: FIG. 11.--NEAP TIDES]