The Sewerage of Sea Coast Towns

by Henry Charles Adams

Considered from the point of view of a person on the earth, this primary tidal wave constantly travels round the Southern Ocean at a speed of 13,500 miles in 24 hr. 52 min, thus having a velocity of 543 miles per hour, and measuring a length of 13,500/2 = 6,750 miles from crest to crest. If a map of the world be examined it will be noticed that there are three large oceans branching off the Southern Ocean, namely, the Atlantic, Pacific, and Indian Oceans; and although there is the same tendency for the formation of tides in these oceans, they are too restricted for any very material tidal action to take place. As the crest of the primary tidal wave in its journey round the world passes these oceans, the surface of the water is raised in them, which results in secondary or derivative tidal waves being sent through each ocean to the furthermost parts of the globe; and as the trough of the primary wave passes the same points the surface of the water is lowered, and a reverse action takes place, so that the derivative waves oscillate backwards and forwards in the branch oceans, the complete cycle occupying on the average 12 hr. 26 min Every variation of the tides in the Southern Ocean is accurately reproduced in every sea connected with it.

Wave motion consists only in a vertical movement of the particles of water by which a crest and trough is formed alternately, the crest being as much above the normal horizontal line as the trough is below it; and in the tidal waves this motion extends through the whole depth of the water from the surface to the bottom, but there is no horizontal movement except of form. The late Mr. J. Scott Russell described it as the transference of motion without the transference of matter; of form without the substance; of force without the agent.

The action produced by the sun and moon jointly is practically the resultant of the effects which each would produce separately, and as the net tide-producing effect of the moon is to raise a crest of water 1.4 ft above the trough, and that of the sun is 0.6 ft (being in the proportion of I to 0.445), when the two forces are acting in conjunction a wave 1.4 + 0.6 = 2 ft high is produced in the Southern Ocean, and when acting in opposition a wave 1.4 - 0.6 = 0.8 ft high is formed. As the derivative wave, consisting of the large mass of water set in motion by the comparatively small rise and fall of the primary wave, is propagated through the branch oceans, it is affected by many circumstances, such as the continual variation in width between the opposite shores, the alterations in the depth of the channels, and the irregularity of the coast line. When obstruction occurs, as, for example, in the Bristol Channel, where there is a gradually rising bed with a converging channel, the velocity, and/or the amount of rise and fall of the derivative wave is increased to an enormous extent; in other places where the oceans widen out, the rise and/or velocity is diminished, and similarly where a narrow channel occurs between two pieces of land an increase in the velocity of the wave will take place, forming a race in that locality.

Although the laws governing the production of tides are well understood, the irregularities in the depths of the oceans and the outlines of the coast, the geographical distribution of the water over the face of the globe and the position and declivity of the shores greatly modify the movements of the tides and give rise to so many complications that no general formulae can be used to give the time or height of the tides at any place by calculation alone. The average rate of travel and the course of the flood tide of the derivative waves around the shores of Great Britain are as follows:—150 miles per hour from Land's End to Lundy Island; 90 miles per hour from Lundy to St. David's Head; 22 miles per hour from St. David's Head to Holy head; 45-1/2 miles per hour from Holyhead to Solway Firth; 194 miles per hour from the North of Ireland to the North of Scotland; 52 miles per hour from the North of Scotland to the Wash; 20 miles per hour from the Wash to Yarmouth; 10 miles per hour from Yarmouth to Harwich. Along the south coast from Land's End to Beachy Head the average velocity is 40 miles per hour, the rate reducing as the wave approaches Dover, in the vicinity of which the tidal waves from the two different directions meet, one arriving approximately twelve hours later than the other, thus forming tides which are a result of the amalgamation of the two waves. On the ebb tide the direction of the waves is reversed.

The mobility of the water around the earth causes it to be very sensitive to the varying attraction of the sun and moon, due to the alterations from time to time in the relative positions of the three bodies. Fig. [Footnote: Plate I] shows diagrammatically the condition of the water in the Southern Ocean when the sun and moon are in the positions occupied at the time of new moon. The tide at A is due to the sum of the attractions of the sun and moon less the effect due to the excess of the centripetal force over centrifugal force. The tide at C is due to the excess of the centrifugal force over the centripetal force. These tides are known as "spring" tides. Fig. 2 [Footnote: Plate I] shows the positions occupied at the time of full moon. The tide at A is due to the attraction of the sun plus the effect due to the excess of the centrifugal force over the centripetal force. The tide at C is due to the attraction of the moon less the effect due to the excess of the centripetal force over centrifugal force. These tides are also known as "spring" tides. Fig. 3 [Footnote: Plate I] shows the positions occupied when the moon is in the first quarter; the position at the third quarter being similar, except that the moon would then be on the side of the earth nearest to B, The tide at A is compounded of high water of the solar tide superimposed upon low water of the lunar tide, so that the sea is at a higher level than in the case of the low water of spring tides. The tide at D is due to the attraction of the moon less the excess of centripetal force over centrifugal force, and the tide at B is due to the excess of centrifugal force over centripetal force. These are known as "neap" tides, and, as the sun is acting in opposition to the moon, the height of high water is considerably less than at the time of spring tides. The tides are continually varying between these extremes according to the alterations in the attracting forces, but the joint high tide lies nearer to the crest of the lunar than of the solar tide. It is obvious that, if the attracting force of the sun and moon were equal, the height of spring tides would be double that due to each body separately, and that there would be no variation in the height of the sea at the time of neap tides.

It will now be of interest to consider the minor movements of the sun and moon, as they also affect the tides by reason of the alterations they cause in the attractive force. During the revolution of the earth round the sun the successive positions of the point on the earth which is nearest to the sun will form a diagonal line across the equator. At the vernal equinox (March 20) the equator is vertically under the sun, which then declines to the south until the summer solstice (June 21), when it reaches its maximum south declination. It then moves northwards, passing vertically over the equator again at the autumnal equinox (September 21), and reaches its maximum northern declination on the winter solstice (December 21). The declination varies from about 24 degrees above to 24 degrees below the equator. The sun is nearest to the Southern Ocean, where the tides are generated, when it is in its southern declination, and furthest away when in the north, but the sun is actually nearest to the earth on December 31 (perihelion) and furthest away on July I (aphelion), the difference between the maximum and minimum distance being one-thirtieth of the whole.

The moon travels in a similar diagonal direction around the earth, varying between 18-1/2 degrees and 28-1/2 degreed above and below the equator. The change from north to south declination takes place every fourteen days, but these changes do not necessarily take place at the change in the phases of the moon. When the moon is south of the equator, she is nearer to the Southern Ocean, where the tides are generated. The new moon is nearest to the sun, and crosses the meridian at midday, while the full moon crosses it at midnight.

The height of the afternoon tide varies from that of the morning tide; sometimes one is the higher and sometimes the other, according to the declination of the sun and moon. This is called the "diurnal inequality." The average difference between the night and morning tides is about 5 in on the east coast and about 8in on the west coast. When there is a considerable difference in the height of high water of two consecutive tides, the ebb which follows the higher tide is lower than that following the lower high water, and as a general rule the higher the tide rises the lower it will fall. The height of spring tides varies throughout the year, being at a maximum when the sun is over the equator at the equinoxes and at a minimum in June at the summer solstice when the sun is furthest away from the equator. In the Southern Ocean high water of spring tides occurs at mid-day on the meridian of Greenwich and at midnight on the 180° meridian, and is later on the coasts of other seas in proportion to the time taken for the derivative waves to reach them, the tide being about three- fourths of a day later at Land's End and one day and a half later at the mouth of the Thames. The spring tides around the coast of England are four inches higher on the average at the time of new moon than at full moon, the average rise being about 15 ft, while the average rise at neaps is 11 ft 6 in.

The height from high to low water of spring tides is approximately double that of neap tides, while the maximum height to which spring tides rise is about 33 per cent. more than neaps, taking mean low water of spring tides as the datum. Extraordinarily high tides may be expected when the moon is new or full, and in her position nearest to the earth at the same time as her declination is near the equator, and they will be still further augmented if a strong gale has been blowing for some time in the same direction as the flood tide in the open sea, and then changes when the tide starts to rise, so as to blow straight on to the shore. The pressure of the air also affects the height of tides in so far as an increase will tend to depress the water in one place, and a reduction of pressure will facilitate its rising elsewhere, so that if there is a steep gradient in the barometrical pressure falling in the same direction as the flood tide the tides will be higher. As exemplifying the effect of violent gales in the Atlantic on the tides of the Bristol Channel, the following extract from "The Surveyor, Engineer, and Architect" of 1840, dealing with observations taken on Mr. Bunt's self-registering tide gauge at Hotwell House, Clifton, may be of interest.

Date: Times of High Water. Difference in Jan 1840. Tide Gauge. Tide Table. Tide Table. H.M. H.M. 27th, p.m……. 0. 8 ……. 0. 7 ….. 1 min earlier. 28th, a.m……. 0.47 ……. 0.34 ….. 13 min earlier. 28th, p.m……. 11.41 ……. 1. 7 ….. 86 min later. 29th, a.m……. 1.29 ……. 1.47 ….. 18 min later. 29th, p.m……. 2.32 ……. 2.30 ….. 2 min earlier.