

WAVKS AND TIDES. 



WAVES AND TIDES. 



77C 



The definition above given of the " Establishment " U only appruxi- 

 tuatively true: it is observed by I'r. Ul,,well, in the ' Essay,' that it 

 would be correct if the high-tide always occurred when the moon'i 

 hour-circle makes equal angle* with the meridian ; but in fact the hour 

 of tide on any day ia reckoned from the time that the aun ia on the 

 meridian ; and as the moon change* her right ascension every day by 

 about forty-eight minutes (the observed hour of the tide being given 

 on the day of new or full moon), the moon's hour angle may differ 

 according to the time of the day when the conjunction or opposition 

 takes place, compared with the time of clay when the high tide is 

 observed. Therefore an observation of the hour of the tide <>n tin- 

 day of new or full moon may leave an uncertainty of about Ih. 8m. in 

 the time of the " Establishment," unless account is taken whether the 

 morning or afternoon tide was observed, and at what hour the syrygy 

 took place. 



The subjoined cut, which shows the principal cotidal lines in the 

 Indian and Atlantic ocean*, is from Dr. Whewi 11'* chart above men- 

 tioned, and contains the modifications introduced in that which ia 

 given by Mr. Airy, in his Essay on ' Tides and Waves/ in the ' Encyclo- 

 pedia Metropolitan*.' 



;n c;o SO 40 SO JO 10 x 10 20 SO 40 50 00 JO 80 90 

 



70 60 50 40 SO 20 10 10 20 30 40 50 60 70 80 80 

 I In investigations relating to the tides, it is required to determine 

 the form assumed by the surface of the water when the particles are 

 subject to the actions of disturbing forces; and for this purpose it is 

 convenient to assume that if no such forces existed, the earth would 

 consist of a solid spherical nucleus within a body of water whose 

 exterior surface is that of a sphere concentric with the nucleus. Let 

 the circle cJ represent the nucleus, and the circumference alt the sur- 

 face of the surrounding water in a plane passing through the centre of 

 the earth, and the sun or moon at u : then, in the theory indicated by 

 Newton, the attraction of the celestial body will draw the particles of 

 water towards it so that the surface ab will assume the form a'b' ; at 

 the same time the attraction exercised on the solid part ed will cause 

 the latter to take the position tfd'. Thus at the same instant the sur- 



face of the water at a' and V is farther removed from the centre of the 

 earth than it would bo if there were no perturbation ; while at < and 

 fA a nearer the centre. If the celestial body were constantly in the 

 plane of the equator, the summit of the elevated water would also be 

 in that plane, and exactly or nearly under the body. A section of the 

 pheroid of water passing through the poles of the equator and the 

 summit jurt ii-nti-,n.<l would bo an ellipse, and its periphery would 

 coincide with the direction of a terrestrial meridian. liy the diurnal 

 rotation this tide-wave, as it may be called, would appear to move 

 about the earth from cut to west at the rate of above 1000 miles per 

 hour at the equator ; and iU positions at the end of every hour would 

 contitute a series of cotidal lines Hence, if a email island at the 

 terrestrial equator were to project above the surface of the water it 

 would arrive successively at the points a', <, t,',f, a ' t *, that in the time 

 of a rotation of the earth on its axis with respect to the cclcntial 1 U 

 there would occur at the island two states of high-water and two of 



I low-water. The arrival of the island at the summit a', v h. i. 

 if X were the moon, take place at the end of every 24 h. 60 m. nearly, 

 is called the diurnal tide ; and that which Uke place when the island 

 arrives at the summit 6', that is 12 h. 25 m. after the former, is called 

 the semidiurnal tide. By this theory there ought to be scarcely any 

 tides near the poles, the water being always drawn from them towards 

 the tropical regions ; and the attractions at a' under the celestial body 

 being greater than the attractions at 6', it should follow that the 

 diurnal tide is greater than the semidiurnal tide, neither of which cir- 

 cumstances, however, is conformable to observ . 



If nn island having a great extent from the equator towards the 

 north and south were to intercept the tide-wave, the elevated 

 passing round the extremities of the island, would on it* westci 

 form two waves, which would advance towards, and meet one another 

 at the equator, making, at different places on the coast, high 

 successively later, in th directions of their motions. And it is easy to 

 conceive that the tide- wave of a great ocean will send brand > 

 any seas which it mny approach in its movement about the earth : such 

 are called derived tides. 



The combined actions of the sun and moon, when those luminaries 

 ore in conjunction or opposition, that is, at new or full moon, may be 

 readily conceived to produce what are called spring-tides; and the 

 diminution of each other's attractions when in quadratures, to produce 

 the neap-tides. It may further be understood that, as the distances of 

 the sun and moon from the earth vary by the cllipticity of the orbits, 

 at the times when either of the celestial bodies is in perigee, its attr.ir- 

 tive power being greater than at other times, the tide-wave raised by 

 it will attain a greater elevation than usual ; on the other hand, when 

 in apogee, the high-water elevation must be the least. 



The tides are greatly modified at any station or port by the position 

 of the latter with respect to the equator, and by the declination of the 

 sun and moon. The two summits of the great tide-wave are, at the 

 same instant, diametrically opposite to one another; and if the latitude 

 of the station were equal to the moon's declination on a given day, 

 both moon and station being for example north of the equator* the 

 summit of the wave would on that day be at the station when the 

 moon is in or near the zenith ; but about twelve hours afterwards, 

 the station, having described half the circumference of a circle about 

 the earth's axis by the diurnal rotation, will be on the opposite of 

 the meridian ; and the summit of the wave, being on the southern 

 side of the equator, will be at a distance from the station equal t 

 twice the moon's declination ; consequently the height of this tide will 

 be much less than that of the former tide. The contrary phenomenon 

 occurs when the moon and the station are on opposite sides of the 

 equator. 



Among the tide-waves with which we are best acquainted are thoso 

 of the Indian and Atlantic oceans ; and from the known times of high- 

 water at different places, it is ascertained that the summit of a wave 

 advances from the seas to the south of Australia into the Bay of 

 Bengal, and towards the Persian Gulf, causing the hour of high-water 

 to be successively later at the ports from Ceylon northwards, on both 

 sides of the western peninsula of India, The summit of a single 

 seems to extend from the mouth of the Red Sea, along the eastern 

 coast of Africa, to the Cape of Oood Hope, where it joins the tide-waves 

 of the Atlantic. These advancing northwards, cause the time of high- 

 water to be successively later at the different ports on the western 

 coast of Africa and Europe, and on the whole eastern coast of Smith 

 and North America ; so that the wave which at a certain instant ia at 

 the Cape, in 15 hours from that time is at the mouth of the English 

 Channel and on the western coast of Ireland. This wave, bein^ 

 rently checked in its progress by the British Isles, divides itself into 

 two principal branches, of which one Hows up the Channel, and passing 

 through the Straits of Dover, is off the mouth of the Thames in S 

 hours from the time that it was at Brest. A small branch advance! 

 up St. George's Channel ; but the second principal branch of the wave 

 flowing round the northern extremity of Scotland, proceeds slowly 

 down the North Sea, and meets the first branch off the mouth of the 

 Thames in 20 hours from the time that it was at the entrance of th 

 Channel. 



From Rio Janeiro to the Falkland Islands a wave summit seems to 

 advance directly from east to west ; and from the form of the con- 

 tinent of South America, the high tide occurs successively later in 

 ;oing southward from Cape Frio, as if the wave came from the n 

 The wave from the southern ocean sets northward, from Tierra del 

 r*uego and the Falkland Islands to the coast of Patagonia, and at Port 

 St. Elena on that coast it occurs \'l hours later than at tho.se islands. 

 3n the western coast of America the tide travels from north to south, 

 Between Acapulco and the Straits of Magflhaens ; while from the 

 'ortner place it travels northwards. In the Pacific Ocean the g< 

 direction of the tide wave in from east to west ; but the heights > i 

 ,idcs are small, not exceeding 2 feet at the islands of the Sum 

 It ia observed however by Dr. Whewcll (' Phil. Trans.,' 1833), that this 

 nust not be understood to be the tide which would be raised if the 

 whole earth were covered with water, on account of the modifications 

 irmleeed by the form of the continent of South Am most 



part of New South Wales between 2J and 30" S. lat., has the 

 li.'li t.ilc earlier than points which ore situated towards the north or 

 outh of that tract. 



