The next connection likely to be observed would be that the interval between two day tides was not exactly a solar day of twenty-four hours, but a lunar day of fifty minutes longer. For by reason of the moon's monthly motion it lags behind the sun about fifty minutes a day, and the tides do the same, and so perpetually occur later and later, about fifty minutes a day later, or 12 hours and 25 minutes on the average between tide and tide.
A third and still more striking connection was also discovered by some of the ancient great navigators and philosophers—viz. that the time of high water at a given place at full moon is always the same, or very nearly so. In other words, the highest or spring tides always occur nearly at the same time of day at a given place. For instance, at Liverpool this time is noon and midnight. London is about two hours and a half later. Each port has its own time for receiving a given tide, and the time is called the "establishment" of the port. Look out a day when the moon is full, and you will find the Liverpool high tide occurs at half-past eleven, or close upon it. The same happens when the moon is new. A day after full or new moon the spring tides rise to their highest, and these extra high tides always occur in Liverpool at noon and at midnight, whatever the season of the year. About the equinoxes they are liable to be extraordinarily high. The extra low tides here are therefore at 6 a.m. and 6 p.m., and the 6 p.m. low tide is a nuisance to the river steamers. The spring tides at London are highest about half-past two.
It is, therefore, quite clear that the moon has to do with the tides. It and the sun together are, in fact, the whole cause of them; and the mode in which these bodies act by gravitative attraction was first made out and explained in remarkably full detail by Sir Isaac Newton. You will find his account of the tides in the second and third books of the Principia; and though the theory does not occupy more than a few pages of that immortal work, he succeeds not only in explaining the local tidal peculiarities, much as I have done to-night, but also in calculating the approximate height of mid-ocean solar tide; and from the observed lunar tide he shows how to determine the then quite unknown mass of the moon. This was a quite extraordinary achievement, the difficulty of which it is not easy for a person unused to similar discussions fully to appreciate. It is, indeed, but a small part of what Newton accomplished, but by itself it is sufficient to confer immortality upon any ordinary philosopher, and to place him in a front rank.
Fig. 110.—Whirling earth model.
To make intelligible Newton's theory of the tides, I must not attempt to go into too great detail. I will consider only the salient points. First, you know that every mass of matter attracts every other piece of matter; second, that the moon revolves round the earth, or rather that the earth and moon revolve round their common centre of gravity once a month; third, that the earth spins on its own axis once a day; fourth, that when a thing is whirled round, it tends to fly out from the centre and requires a force to hold it in. These are the principles involved. You can whirl a bucket full of water vertically round without spilling it. Make an elastic globe rotate, and it bulges out into an oblate or orange shape; as illustrated by the model shown in [Fig. 110]. This is exactly what the earth does, and Newton calculated the bulging of it as fourteen miles all round the equator. Make an elastic globe revolve round a fixed centre outside itself, and it gets pulled into a prolate or lemon shape; the simplest illustrative experiment is to attach a string to an elastic bag or football full of water, and whirl it round and round. Its prolateness is readily visible.
Now consider the earth and moon revolving round each other like a man whirling a child round. The child travels furthest, but the man cannot merely rotate, he leans back and thus also describes a small circle: so does the earth; it revolves round the common centre of gravity of earth and moon (cf. [p. 212]). This is a vital point in the comprehension of the tides: the earth's centre is not at rest, but is being whirled round by the moon, in a circle about 1⁄80 as big as the circle which the moon describes, because the earth weighs eighty times as much as the moon. The effect of the revolution is to make both bodies slightly protrude in the direction of the line joining them; they become slightly "prolate" as it is called—that is, lemon-shaped. Illustrating still by the man and child, the child's legs fly outwards so that he is elongated in the direction of a radius; the man's coat-tails fly out too, so that he too is similarly though less elongated. These elongations or protuberances constitute the tides.