represents the facts of the case, for high water is not only produced on the side of the Earth immediately under the Moon, but also on the opposite side at the same time. The coincident tides are therefore separated from each other by 180°, or by half the circumference of the globe. Since the diurnal rotation of the Earth causes every portion of its surface to pass successively under the tidal waves in about 24h, it follows that there are everywhere 2 tides daily, with an interval of about 12h between each; whereas, if the common supposition were correct, there would be only one.

The

Such being the observed facts, and it being admitted that the attraction of the Moon gives rise to the upper tide, some further explanation must be sought to account for the lower one. solution is extremely simple as an elementary conception: it is only necessary to bear in mind that not only does the Moon attract the upper mass of water, but also the solid globe itself, which is consequently compelled to recede from the waters beneath, leaving them behind, and in a sense heaped together.

Besides the influence of the Moon in elevating the waters of the ocean, that of the Sun is to some extent concerned, but it is much more feeble than that of the former, on account of the much greater distance of the solar globe. The mean distance of the Sun from the Earth is 309.144 times that of the Moon; its attractive power is consequently (309·144)2, or 95,570 times less; but inasmuch as the mass of the Sun exceeds that of the Moon in the ratio of 25,916,280 to 1, which is much greater than 95,570 to 1, it will naturally be said that surely the attraction exercised by the Sun exceeds that of the Moon in the same proportion that 25,916,280 exceeds 95,570. This, however, is not the case, for a reason which will now be stated. It must be borne in mind that the tides are due solely to the inequality of the attraction in operation on different sides of the Earth, and that the greater that inequality is the greater will be the resulting tide, and vice versa. The mean distance of the Sun from

b To avoid complicating the obviously crude argument in the text certain things are left out of consideration.

the Earth is 11,720 diameters of the latter, and consequently the difference between its distance from the one side of the Earth and from the other will be only 110 of the whole distance, while in the case of the Moon, whose mean distance is only 30 terrestrial diameters, the difference between the distances from one side and from the other, reckoned from the Moon, will be 3 of the whole distance. The inequality of the attraction (upon which the height of the tidal wave depends) is therefore much greater in the case of the Moon than of the Sun; the ratio, according to Newton, being 58:23, or about 21 : 1.

We thus see that there are 2 kinds of tides, lunar and solar. When therefore the Sun, Moon, and Earth are in the same straight line with each other, that is to say, when it is either New or Full Moon, the attractions of the two former bodies act in the same line, and we have the highest possible tidal elevations, and what are known as "Spring tides;" but when the Moon is in quadrature, or 90° from the Sun, its attraction acts along a line which is perpendicular to that along which the attraction of the Sun acts, the two tidal elevations are 90° apart, and we have the tides which are called "Neap."

It may be convenient to state here a few general facts relating to the tides:-

1. On the day of New Moon, the Sun and Moon cross the meridian at the same time, i. e. at noon, and at an interval after their passage (varying according to the place of observation, but unchangeable or nearly so for each place) high water occurs. The water, having reached its maximum height, begins to fall, and after a period of 6h 12m attains a maximum depression; it then rises for 6h 12m, and reaches a second maximum; falls for another interval of 6h 12m, and rises again during a 4th interval of 6h 12m. It has therefore 2 maxima and 2 minima in a period of 24h 48m, which is called a Tidal Day.

с

2. On the day of Full Moon, the Moon crosses the meridian

Practically this is somewhat incorrectly expressed, for it is found that the intermediate low water does not take

place at the mean moment between the two tides, the waters usually taking a shorter time to rise than they do to fall.

12h after the Sun, i. e. at midnight, and the tidal phenomena are the same as in (1).

3. As time is reckoned by the apparent motion of the Sun, the solar tide always happens at the same hour at the same place, but the lunar tide, which is the greater, and thereby gives a character to the whole, happens 48m 44 later every day; it therefore separates Eastwards from the solar tide, at that rate, and gradually becomes later and later, till at the periods of the 1st and 3rd quarters of the Moon it happens at the same time as the low water of the solar tide: then the elevation of the high, and the depression of the low water, will be the difference of the solar and the lunar tides, and the tide will be neap.

4. The difference in height between the high and low water is called the Range of the tide.

5. The spring tides are highest, especially those which happen 36h after the New, or Full Moon.

6. The neap tides are the lowest, especially those which happen 36h after the Moon is in quadrature.

7. The interval of time from Noon to the time of high water at any particular place is the same on the days both of New and Full Moon. This interval is technically known as the "Establishment of the port."

The reason why an interval of time elapses between the Moon's meridian passage and the time of high water is, that the waters of the ocean have to overcome a certain peculiar effect of friction, which cannot immediately be accomplished; it thus happens that the lunar tidal wave is not found immediately under the Moon, but follows it at some distance. Similar results ensue in the case of the solar wave. The tidal wave is also affected in another way, by the continued action of both these luminaries, and at certain periods of the lunar month is either accelerated or retarded in a way which will now be described: "In the 1st and 3rd quarters of the Moon, the solar tide is Westward of the lunar one; and conscquently the actual high water (which is the result of the combination of the 2 waves) will be to the Westward of the place it would have been at if the Moon had acted

alone, and the time of high water will therefore be accelerated. In the 2nd and 4th quarters, the general effect of the Sun is, for a similar reason, to produce a retardation in the time of high water. This effect, produced by the Sun and Moon combined, is called the Priming and Lagging of the tides. The highest spring tides occur when the Moon passes the meridian about 11h after the Sun; for then the maximum effect of the 2 bodies coincides." The "priming" and "lagging" effect deranges the average retardation, which from a mean value of 48m may be augmented to 60m or be reduced to 36m.

The 2 tides following one another are also subject to a variation, called the Diurnal Inequality, depending on the daily change in declination of the Sun and Moon; the laws which govern it are, however, very imperfectly known.

Guillemin writes:-"The height of the tides again varies with the declinations of the Moon and Sun; it is by so much greater as the two bodies are nearer the equator. Twice a year, towards March 21 and Sept. 22, the Sun is actually in the equator. If, at the same time, the Moon is near the same plane the tides which occur then are the highest of all. These are the Equinoctial Spring Tides, because the Earth is then at the vernal or autumnal equinox. On the other hand, the smallest tides take place towards the solstices, if the Moon attains its smallest or its greatest meridional height at the same time as the Sun. Lastly, the distances of the Moon and Sun from the Earth have also their influence on the height of the tides. Other things being equal, the height of a tide is greater or less, according as the attracting bodies are nearer to or farther from the Earth. Thus the tides of the winter solstice are higher than those of the summer one"

a The Heavens. Eng. ed., p. 461.

CHAPTER II.

LOCAL TIDAL PHENOMENA.

Local disturbing influences.-Table of Tidal ranges.-Influence of the Wind.Experiment of Smeaton.-The Tides in the Severn at Chepstow.-Tidal phenomena in the Pacific Ocean. -Remarks by Beechey.-Velocity of the great Terrestrial Tidal wave. Its course round the Earth, sketched by Johnston.— Effects of Tides at Bristol.-Instinct of animals.—Tides extinguished in rivers. -Instances of abnormal Tidal Phenomena.-The "Mascaret" on the Seine.— Historical notices.

W

E have hitherto been considering the tidal wave, on the supposition of the Earth being a perfect sphere covered with water to a uniform depth; but inasmuch as this is not the case, it follows that the actual phenomena of the tides are widely different and of a much more complicated character, owing to the irregular outline of the land, the uneven surface of the ocean bed, the action of winds, currents, friction, &c. The effects of these disturbing influences are rendered especially manifest in the difference of the range of the tide at different places on the Earth's surface. If the surface of our globe were entirely covered with water, the height of a solar tide would be Ift 11in, and of a lunar tide 4ft oin; but the differences in the level of the water of the ocean brought about by tidal influences are often far in excess of these figures. For instance, in deep estuaries or creeks, open in the direction of the tidal