Art. IX.—The Tides, Currents, and the Moon.
[Read before the Auckland Institute, 2nd August, 1897.]
Some three years ago I read a modern book, the subject of which was the moon, the tides, and ocean currents. I came to the conclusion that the reasons given for the various phenomena were in some cases obscure, and in others doubtful affirmatives were made. However, I let the subject drop, until not long ago I took it up again, and perused some other books on the subject, in which I found the same reasons were given, but on this occasion I made notes, which gradually extended into the material which makes up this paper.
I will begin my remarks by taking the following as a sound basis to start from—that is, that the globe revolves on its axis, and that its path is round the sun. I will also suppose that we begin our inquiry without any water on the globe or any moon in the heavens. Under those conditions it would revolve on its axis, the axis would be through its centre of gravity, and there would be five forces exerted in the combined process of revolution—namely, (1) The force which is required to keep it revolving upon its axis; (2) the centrifugal force which is generated by this the rotary motion; (3) the force which carries it on its path round the sun; (4) the force of gravity which is exerted by the sun to hold the globe in its path; (5) the centrifugal force which is generated by the force which causes the globe to go round its orbit and the gravity force which holds it in its circular path round the sun. The two first-named forces are so active on our globe that the fifth is almost latent, and each of those five forces has some influence in governing its motion round the sun.
Under the conditions from which we have started everything on the globe would be solid and rigid. There would be no life, no moonlight, no tides, and no atmosphere such as we have. Everything would be perfectly still, so beautifully poised; without any disturbing influence it would perform its annual, aimless, and silent journey round the sun.
I will now suppose that we had the water in such a position that it could be launched on to the globe, and that we did do so. Well, it would not remain at the place on which it was put. We would find that the rotary and centrifugal forces would take control of the fluid and distribute it over the earth's surface. Then gradually evaporation would take place. The rains would fall, and the hollows would be filled up. The same oceans would be formed. The same rivers would flow. So that in a short time the whole would be in equilibrium, just as it is at present. All this would take place without disturbing in the slightest degree the globe's centre of gravity.
Suppose, again, that we had put a mass of rock on to one side of the globe instead of the water, but equal in weight to it. The effect would be entirely different. We would find under those conditions the globe would have to shift its axis so as to run on its centre of gravity. In this supposition, of course, I am assuming the globe to be dense enough to resist any yielding of its mass.
From this I wish to establish the principle that the globe's centre of gravity is through its solid parts, and that the water has no influence whatever in fixing it.
We will now take into consideration the ocean currents, and in doing this we are still supposed to be without the moon; but, as she has very little to do with those currents, we will proceed without her.
The instability of water is so apparent that some philosopher converted this peculiarity into a proverb: “Unstable as water.” This instability and want of cohesion is nowhere more apparent than it is on the huge volume of water on the surface of the globe. As the globe revolves the water is too unstable to be able to resist the centrifugal force generated by the revolving mass, so that at the speed at which it now revolves some of the water is turned away from the direction of the poles to the equator, causing it to bulge out there. This action must cause some amount of current to flow from the direction of the poles to the equator, where it is heaped up or bulged out; the water there being furthest away from the influence of gravity, and the revolving speed being greatest at that place, the water is unable to travel quite so fast as the solid parts of the earth. If the globe revolved once in twenty-three hours, then there would be a greater flow from the poles to the equator, and the water there would bulge out further, and would also be left further behind. A still greater speed would cause a greater flow from the direction of the poles to the equator, a greater bulging-out would take place,
and it would be left still further behind. Now, this would continue until at a certain speed the water would fly off in the opposite direction to that in which the globe revolves. At this speed no water would remain on it, and all this would occur while the solid portions of the earth would have sufficient cohesion to hold together. From this it is reasonable to suppose that there is a slight centrifugal current to the equator, and that from the time the revolving speed of the globe causes the water to bulge out at the equator gravity begins to lose control, so that at the same time that the water on the equator begins to bulge out it also begins to lag behind, which is equivalent to a current in the opposite direction to that in which the globe is travelling. The centrifugal current and the water which lags behind on the equator join, and this is the cause of the Gulf Stream, the source of which would be somewhere in the vicinity of the north-west of the South American Continent, on the equator; thence to the Galapagos Islands the bulged-out water on the equator is gradually left behind, and as it goes west it increases in volume and speed all through the Pacific Ocean until it is broken up by the islands between the Malay Peninsula and the Continent of Australia. However, a large body of this current must pass through into the Indian Ocean, and goes on increasing and accumulating all through the Indian Ocean, until it is met by the advancing Continent of Africa, which meets the current like a float of a huge paddle-wheel, and the only way in which it can escape is down the coast of Africa, through the Mozambique Channel, thence down to the Cape of Good Hope. Here it would be impossible to follow it; there will be too many eddies, surface- and under-currents, which must take place with such a large body of water working its way round the Cape. Much of it, no doubt, will be deflected in directions different from what we might expect. However, some of it no doubt does get round the Cape into the Atlantic Ocean. Its course would be chiefly to the north, to replace the water flowing down the South American east coast; subsequently joining the heaped-up water at the equator, which is also getting left behind in the Atlantic Ocean, and which is forming another westerly current. Those two currents combine, and are afterwards met by the advancing South American Continent. The stream then runs down the slanting northern part of South America from Pernambuco into the Mexican Gulf, and from the gulf onward to the north. This stream is so vast, and its temperature so high, that as it travels north it changes the climate from the north-west of Europe to Iceland. It is over fifty miles in width, and different in colour to the Atlantic Ocean. Its channel through this ocean is almost as clearly defined as
the channel of a river flowing over a continent, and in some places it attains a speed of four knots per hour. As it flows north towards Newfoundland it is divided — one branch crosses the Atlantic towards the British Islands, and this current flows into the seas, channels, and inlets surrounding those islands, complicating the high- and low-water gravity tides.
From this it will be seen that the whole of the Gulf Stream is collected on and near to the equator, and this accounts for its very high temperature. In the same way a large portion of the water which is left behind on the equator is met by the South American Continent, and the only way for it to escape is by flowing down the coast from Pernambuco to Cape Horn, and, after getting round the cape, it travels north to the place from where we started; so that there must be a continuous circulating current, and also equilibrium circulation.
When a mass of water is set in motion any attempt to follow its course must be very problematical. Even in rivers, where the mass of water is descending, there are also currents ascending; but in the oceans there are other influences, causing circulation which would lead to greater complication. However, my object is to determine the cause which sets the Gulf Stream in motion; its course in any case would be the same.
I am informed that the equatorial wind theory has been demonstrated by actual experiment. The model is described as follows: A glass trough is filled with water, then wind is blown along the surface of the water, and the result is a current similar to the Gulf Stream. But the same current would take place if the trough is moved forward at a uniform speed. Both these experiments would be futile, because in each case both the gravity and centrifugal forces are ignored. To make the gravity effect clear I will give the following illustration: Water will fly off a grindstone when driven at a moderate speed, but if a power existed in the centre of the grindstone which held the water to it, then it would require to be driven at a greater speed to cause it to fly off. So it is with the trough experiment: gravity exerts its power over both the trough and the water, but the trough has no gravity power over the water. Just imagine the effect of moving the troughful of water at a speed of fifty miles an hour, and consider that on the equator the speed is a thousand miles an hour. Then the centrifugal force acts on the particles of water furthest away from the centre, where the speed is greatest, so that the tendency would be to skim the tropical surface-water on to the equator. This centrifugal force also counteracts gravity, especially on the equator, where the
speed is greatest. This would also assist in causing the surface-water on the equator to lag behind. No doubt the moderate equatorial winds may have some influence; but it is inconceivable that those moderate winds could be the cause of setting in motion such a mighty mass of water as the Gulf Stream.
We will now suppose the moon to be in her place, where she will effect some changes upon the water which is on the surface of our globe, but before we proceed with this we will take a short time with the moon herself. It is supposed that at one time the moon revolved on her axis, and had oceans and tides on her surface. At that time she would be governed by the same five forces previously mentioned as governing the motion of our planet; but now we find the rotary motion has ceased, and with it the centrifugal force generated by the rotary; so that now there are only three of the five forces controlling the moon's motion—viz., gravity, holding her in her place; the force which carries her round her orbit; and the centrifugal force generated by the other two. This centrifugal force has come into great prominence since the rotary ceased, and it now controls the water on the moon. If any water now exists on the moon it must be on the hemisphere furthest away from the earth, because, it being a fluid, the centrifugal force would cause it to get as far away from the axis as possible, and the axis of the moon moving round her orbit is the earth. In the same way, if the globe ceased to revolve, then the same forces would cause the waters upon it to recede to the hemisphere furthest away from the sun, and the other one would always be presented to it, precisely the same as what takes place with the earth and the moon.
I think it is the opinion of scientific men that there is water on the moon, and when we take into consideration the fact that the rotary motion has ceased this helps to confirm this opinion, for without water upon it there would be nothing to retard its rotary motion, so that it would have continued to revolve; but with water on its surface the tides would be excessive, because the attraction of the moon's mass would have little control of the fluid, while the globe's attraction holding the moon in her place would have a great disturbing-power over the water, and consequently would have an effective retarding influence. The water, which we will suppose to be on the moon, and which is forced furthest away from the axis by the centrifugal force, would act (in keeping the moon's face to the earth) much the same as the piece of lead on the bottom of the ship's compass, which keeps its face
always upwards; and, for the same reason, if one hemisphere is denser than the other, it also would get furthest away from the axis.
The moon's influence in causing high- and low-water gravity tides preponderates over all other causes, so that it will be better to comment only on the moon's tides. When referring to the tides it is generally considered that it is the attraction of the moon which causes them. This is not quite correct, as it is the attraction of the earth which does so; it attracts the moon, and compels her to keep in her present path. From this we find that the moon is held in her orbit by the earth's attraction, and the strain of holding is always exerted on every square inch of land and water on the hemisphere which is under her. This strain of holding is just as real as if we could see attachments to the moon from every square inch of surface on this hemisphere. Now, the solid earth holds without yielding to the strain; but when the strain comes on the surface which is covered with water, then the water yields, and is gathered up under the moon, forming a tide; but a second tide occurs at the same time on the opposite side of the globe, and the water which forms that tide is furthest away from the moon, therefore least under her influence. This is an equilibrium tide. The truth of the above rests on the affirmation that the globe's centre of gravity is through its solid mass, and that it revolves on its axis independent of the unstable fluid on its surface. A solid body of whatever shape or size revolving in space must revolve on its centre of gravity; and if by any chance such a revolving body met with sufficient obstruction to disturb its centre of gravity, then, so soon as the disturbing influence became expended, it would have the power to immediately adjust itself so as to again revolve on its centre of gravity, demonstrating the fact that matter has an inherent power to revolve on its centre of gravity.
Now, suppose the globe to be travelling exactly the same as it is doing at present, but without water upon it, and that it rained all over the Northern Hemisphere, until there was as much water on its surface as there is on the globe at present. This water would not remain on the North Hemisphere, or, if it did, the globe would have to shift its centre of gravity, as the whole mass must revolve in poise. The shifting of the globe's centre of gravity is inconceivable, therefore the water would be distributed over the globe by the spinning motion it is subject to, causing it also to have the power of independent adjustment. From this reasoning it appears clear that the proportion of the slippery and unstable fluid on the surface
of the globe is too insufficient in proportion to the enormous weight and mass of the solid globe; and when we consider the speed at which it revolves, combined with the momentum it has acquired, the unstable fluid on its surface could not be a factor in determining its centre of gravity.
In order to get a better idea of the relative proportion which the globe and the oceans have to each other, I will suppose we have a globe 14 in. in diameter, which in round numbers would be 3 ft. 6 in. in circumference. The specific gravity of this globe is more than twice that of granite and five times greater than water. On such a globe the depth of the oceans would be represented by a thick sheet of paper. How could a globe of this density, while spinning round, have its centre of gravity influenced by such an insignificant amount of light fluid which is free to move in any direction? I am desirous of making this as clear as possible, as several statements herein may depend upon this fact.
In conclusion, we have the fact that the globe does revolve on its axis, and its axis is through its centre of gravity, so that when a tide occurs under the moon a derangement of the centre of gravity takes place, which must be adjusted in some way, and the mode of adjustment is very simple. It is accomplished by the tide which occurs at the same time on the opposite hemisphere.
From what has been said it is apparent that the tide opposite to the one raised by the moon is what I call an equilibrium tide to counterbalance the tide produced by the moon, and is governed by the same law or power which makes it compulsory for all revolving bodies to revolve on their centre of gravity, and which has also the power to adjust the equilibrium of the water when it is disturbed. This disturbance and adjustment being independent of the solid mass, consequently, for an absolute certainty, there is an equal quantity of water on the Northern and Southern Hemispheres, and, as there is a greater area of water on the southern oceans, the northern oceans must be deeper.
It is generally supposed mathematically correct that the moon has greater power to draw the water away from the earth immediately under her, but this is not correct, for it is just the opposite which takes place. To illustrate: Let us suppose the water under the moon to be on the surface of a level plain instead of being on a globe; then in that case there would be no tide of any kind, because the water would hold without yielding to the strain of holding the moon, just the same as the land holds. Under those conditions a tide would mean that the water would have to be drawn away from the earth, which is impossible; but on a globe it is quite different, as the moon does not draw the water up im-
mediately under her. The tide on the equator is only an accumulation, which cannot be very high, as the moon's influence passes too rapidly for any great rise and fall to take place immediately under her; so that it will be seen the greatest rise and fall of the tide must be on the horizon of the globe as seen from the moon.
From this reasoning I would expect — first, that the British Isles, being near to where the rise and fall of the tide is greatest, combined with the formation of the bays, seas, and inlets, together with the Gulf Stream flowing into them, would cause the water surrounding those islands to have the most complicated tides of any in the world; second, that the tides in the Hauraki Gulf would have the greatest rise and fall of any place on the Southern Hemisphere within the 40th degree of latitude, because the formation of the land in the gulf gives easy facility for the water to be drawn away by the strain of holding the moon, and the water so drawn away is not so readily replaced, and the angle is greater than it would be nearer the equator. As the distance extends the leverage increases so as to draw the water down the semicircle, and just in the same ratio the speed on the surface of the globe decreases, so that there is a longer time of exposure to the strain of holding from the minimum to the maximum. This is not quite correct, but the effect is just the same, because the speed of the globe at the equator spreads the strain of holding over a greater surface, which is equivalent to a longer exposure to the strain of holding, so that those two factors act on the water so as to produce a greater and gradually increasing rise and fall of the tide. From this reasoning we may discard Australia and all the Pacific islands as not likely to have anything like the same rise and fall that there is in the Hauraki Gulf. Then, on the Continent of South America there is no formation of the land which suggests facility of withdrawal and obstruction to immediate partial replacement; therefore I think it is reasonable to expect the greatest rise and fall of the tide within the prescribed latitude to be in the Hauraki Gulf. On the same line of reasoning I would expect that the greatest rise and fall of the tides on the Southern Hemisphere would be in some of the estuaries near Magellan Straits, because those estuaries are at the maximum land-angle, and the speed on the surface of the globe is slowest; consequently the leverage would be greatest, and the strain of holding would be longer on one place.
In the beginning of this paper I say there are five forces which govern the motion of the earth round the sun, but it should have been six. This sixth force is that which causes all revolving bodies to revolve on their centre of gravity; but
under ordinary circumstances it is apt to be overlooked as a force, because all revolving planets revolve on their centre of gravity; but in the earth and moon system we have this sixth force illustrated by the equilibrium tide. This daily tide requires an enormous force to produce it, and the force so expended must be for adjusting the equilibrium of the whole mass at the least expenditure of energy. Without this tide the globe would revolve as an excentric, and the law of motion abhors such a form of rotation; therefore the very existence of this tide proves all I have said in regard to the purpose it serves.
I will remark, in conclusion, that when we consider the enormous amount of water on the surface of the globe, and the number of influences which affect this unstable fluid, such as tides, currents, gravity, storms, the configuration of the land on the surface and under water, &c., deflecting it into unknown channels—these causes will always render it impossible to tell by any method of calculation the time and height of high water at any given place on the globe.