TIDES 741 outstanding, which is always very small in amount. A further cause of variation in the height of the tides is the variation of the dis- tances of the sun and moon, b> reason of the lipticity of their orbits. The efficacy of a leavenly body in raising tides is shown by "leory to be inversely proportional to the cube the distance. Hence the efficacy of the sun nil fluctuate between the extremes 19 and 21, iking 20 for its mean value, and that of the >on between 43 and 59. Taking into account cause of difference, the highest spring tide all be to the lowest neap as 59 + 21 to 4319, as 80 to 24, or 10 to 3 ; leaving out of con- leration the local circumstances of access and )th, which greatly modify these proportions, the North Atlantic the highest tides are observed a day and a half or two days after ~ e syzygies. At New York, the high water rhich we observe about 8 o'clock in the even- on the days of full or change are those lue to the meridian transit of the moon (and ) on the preceding day, and the highest ide will not occur until the evening of the blowing day. At Boston this delay, which called the retard, or age of the tide, is near- 36 hours. It is the same at Brest, and the ide wave occupies 10 hours in travelling from jt up the English channel and Thames to mdon, making the age of the tide at the jr place 46 hours. This delay, which even the cape of Good Hope amounts to 14 hours, is still the subject of investigation, and is robably mainly due to friction. The inter- nal between the moon's passage over the me- lian of a place and the time of high water, rhich we have referred to as the establish- lent of the port, is also called the luni-tidal iterval. This interval is constant for each )lace so far as the lunar tide wave is con- srned ; but as the actual high water depends ipon the combination of the lunar and solar "les, it is subject to a variation which is lown as the half-monthly inequality in time. )n the day after the spring tides the top of solar tide wave will be nearly an hour in advance of that of the lunar tide wave, and the two waves will combine to make high water earlier than the moon's alone would bring it; hence the luni-tidal interval is shorter. It will continue to shorten until the moon's transit is later by three hours than when the tide is greatest ; it then increases again, passes its mean value when the moon has fallen be- hind six hours, attains its maximum when it is nine hours later, and again decreases until at the next spring tides it reaches its mean value. The mean of all the luni-tidal inter- vals for half a month at a port is called its mean or corrected establishment, to distinguish it from the vulgar establishment, which is the luni-tidal interval at full and change. The former is now generally used for finding the time of high water on any given day, and tables are constructed from observations at the principal ports for finding the correction for semi-monthly inequality due to the moon's age.^ Thus for New York the corrected es- tablishment or mean luni-tidal interval is 8h. 13m., and its least and greatest values are 7h. 52 m. and ah. 35m. On the Atlantic coast of the United States the range of this inequality is about three fourths of an hour; on the coasts of France and Great Britain it often exceeds an hour and a half. This difference of the half-monthly inequality in time at dif- ferent places is analogous to the variation in the proportion of spring and neap tides above noticed, and is due to the same causes. The motion of the water in the tide wave is to- tally unlike that in an ordinary surface wave, such as the wind produces. "When a Barrow wave of the latter kind, or a succession of such waves of equal breadths and heights, is formed in deep water, a light floating body, as a cork, revolves either in a vertical circle or an ellipse not very different from one, having the longer axis vertical. But in the tide wave the move- ment of each particle may be regarded as per- formed in an excessively elongated ellipse, the shorter axis of which is vertical. The breadth of the tide wave from crest to crest, supposing all the earth covered, would be half the earth's circumference, or 12,500 miles, in comparison with which the depth of the sea is insignifi- cant; and the slightest consideration suffices to show that, as all the water which goes to form the elevated portion must be brought from that depressed, this can only take place by a lateral approach of the vertical sections of the sea when the water is rising, and their recess from each other when falling (i. e., over a quadrant of the globe in either case, which is only another way of expressing an alterna- ting backward and forward horizontal current at any given place), with this peculiarity, that these currents (the flow and ebb current) run most rapidly at the moments of high and low water ; the instants of most rapid rise and fall being those of slack water or no current one way or the other. In fact, it is obvious that the surface must be rising most rapidly when the water is setting in equally both ways to, and sinking most rapidly when setting out equally both ways from the place ; in neither of which cases can there be any current at the place. The tide wave -differs also from a wind wave in another very remarkable point. It affects the whole depth of the ocean equal- ly, from the bottom to the surface, while the wind waves, even in the most violent storms, agitate it to a very trifling depth; for the force which acts to produce the former is exerted equally in every portion of the vertical ex- tent of the water, while those producing the latter are strictly confined' to the surface. A tide wave of 4 ft. in total height (between high and low water), which is that of the tide at the atolls of the Indian ocean, advancing over a sea 30,000 ft. deep, implies in each par- ticle an alternate advance and recess of 2,800 ft. in its total extent ; but this movement, being
