Chapter VIII: Part I: I (6)

"If we agree that the tides are occasioned by the attraction of sun and moon, more particularly the latter, we can readily understand their dependence on some known and determinate laws. Our almanacs published long in advance give the exact time of high water at any prominent port in the United States on the morning and afternoon for every day in the year; and seafaring men can tell you when the tide will be high or low, notwithstanding the fact that these movements are not fixed. They know from experience that the time of ebb and flow varies about three quarters of an hour each day.

"The first person who clearly pointed out the accepted cause of the tides and showed its agreement with the effects, was Sir Isaac Newton. He discovered a relationship between the moon and the tides, and by the application of his new principles of geometry, the attraction was made clear.

"The ocean, it is well known, covers more than one half the globe; and this large body of water is found to be in continual motion, ebbing and flowing alternately, without the least intermission. For instance, if the tide is now at high water mark, in any port or harbour which lies open to the ocean, it will presently subside, and flow regularly back for about six hours, when it will be found at low water mark. After this it will again gradually advance for six hours; and then recede in the same time to its former situation, rising and falling alternately twice a day, or in the space of about twenty-four hours. The interval between its ebb and flow is not precisely six hours, for there is a little difference in each tide; so that the time of high water does not always happen at the same hour, but is about three quarters of an hour later each day, for about thirty days, when it again recurs as before. For example, it is high water to-day at noon, it will be low water at eleven minutes after six in the evening; and, consequently, after two changes more, the time of high water the next day will be at about three quarters of an hour after noon; the day following it will be at about half an hour after one, the day following that at a quarter past two, and so on for thirty days; when it will again be found to be high water at noon, as on the day the observation was first made. This exactly answers to the motion of the moon which rises every day about three quarters of an hour later than upon the preceding one, and by moving in this manner round the earth, completes her revolution in about thirty days, and then begins to rise again at the same time as before.

"To make the matter still plainer; suppose, at a certain place, it is high water at three o'clock in the afternoon, upon the day of the new moon; the following day it will be high water at three quarters of an hour after three; the day after that at half an hour past four; and so on till the next new moon, when it will again be high water exactly at three o'clock, as before. By observing the tides continually at the same place, they will always be found to follow the same rule; the time of high water, upon the day of every new moon, being exactly at the same hour, and three-quarters of an hour later every succeeding day.

"The change of the tides is in such exact conformity with the motion of the moon that, independently of mathematical calculations, a thoughtful person would certainly be induced to look to her as their cause.

"The waters at Z, on the side of the earth, A, B, C, D, E, F, G, H, next the moon M, (Fig. 68) are more attracted by the moon than the central parts of the earth, O, and the central parts are more attracted by her than the waters on the opposite side of the earth at _n_; and therefore the distance between the earth's centre and the waters on its surface under and opposite to the moon will be increased. Let there be three bodies at H, O, and D; if they are all equally attracted by the body M, they will all move equally fast toward it, their mutual distance from each other continuing the same. If the attraction of M is unequal, then that body which is most strongly attracted will move most quickly and will increase its distance from the other body. M will attract H more strongly than does O, by which the distance between H and O will be increased, and a spectator on O will perceive H rising higher toward Z. In like manner, O being more strongly attracted than D, it will move farther toward M than D does; consequently the distance between O and D will be increased; and a spectator on O, not perceiving his own motion, will see D receding farther from him towards N; all effects and appearances being the same, whether D recedes from O, or O from D.

"Suppose now there is a number of bodies, as A, B, C, E, F, G, H, placed round O, so as to form a flexible or fluid ring; then, as the whole is attracted toward M, the parts at H and D will have their distance from O increased; whilst the parts at B and F being nearly at the same distance from M as O is, these parts will not recede from one another; but rather by the oblique attraction of M, they will approach near to O. Hence, the fluid ring will form itself into an ellipse Z, _n_, L, N, whose longer axis _n_, O, Z, produced will pass through M, and its shorter axis B, O, F, will terminate in B and F. Let the ring be filled with fluid particles, so as to form a sphere round O; then, as the whole moves toward M, the fluid sphere being lengthened at Z and _n_ will assume an oblong or oval form. If M is the moon, O the earth's centre, A, B, C, D, E, F, G, H, the sea covering the earth's surface, it is evident, by the above reasoning, that whilst the earth by its gravity falls toward the moon, the water directly below at B will swell and rise gradually toward her; also the water at D will recede from the centre, (strictly speaking, the centre recedes from D) and rise on the opposite side of the earth; whilst the water at B and F is depressed, and falls below the former level. Hence as the earth turns round its axis from the moon to the moon again in 24-3/4 hours, there will be two tides of flood and two of ebb in that time, as we find by experience.

"That this doctrine may be still more clearly understood, let it be considered that, although the earth's diameter bears a considerable proportion to the distance of the earth from the moon, yet this diameter is almost nothing when compared to the distance of the earth from the sun. The difference of the sun's attraction, therefore, on the sides of the earth under and opposite to him, will be much less than the difference of the moon's attraction on the sides of the earth under and opposite to her; and, for this reason, the moon must raise the tides much higher than they can be raised by the sun. The effect of the sun's influence, in this case, is nearly three times less than that of the moon. The action of the sun alone would, therefore, be sufficient to produce a flow and ebb of the sea; but the elevations and depressions caused by this means would be about three times less than those produced by the moon.

"The tides, then, are not the sole production of the moon, but of the joint forces of the sun and moon together. Or, properly speaking, there are two tides, a solar one and a lunar one, which have a joint or opposite effect, according to the situation of the bodies which produce them. When the actions of the sun and moon conspire together, as at the time of new and full moon, the flow and ebb become more considerable; and these are then called the spring tides. But when one tends to elevate the waters while the other depresses them, as at the moon's first and third quarters, the effect will be exactly the contrary: the flow and ebb, instead of being augmented, as before, will now be diminished; and these are called the neap tides.

"To explain this more completely, let Fig. 69 represent the sun, Z, H, R, the earth, and F and C the moon at her full and change. Then, because the sun S, and the new moon C, are nearly in the same right line with the centre of the earth O, their actions will conspire together, and raise the water above the zenith Z, or the point immediately under them, to a greater height than if only one of these forces acted alone. But it has been shown that when the ocean is elevated to the zenith Z, it is also elevated to the opposite point, or nadir, at the same time; and therefore in this situation of the sun and moon, the tides will be augmented. And again, whilst the full moon F raises the waters at N and Z, directly under and opposite to her, the sun S, acting in the same right line, will also raise the waters at the same point Z and N, directly under and opposite to him. Therefore, in this situation also, the tides will be augmented; their joint effect being nearly the same at the change as at the full; and in both cases they occasion what are called the spring tides.

"On this theory, the tides ought to be highest directly under and opposite to the moon; that is, when the moon is due north and south; but we find that in open seas, where the water flows freely, the moon is generally past the north and south meridian of the place where it is high water. The reason is obvious; for though the moon's attraction were to cease altogether when she was past the meridian, the motion of ascent communicated to the water before that time would make it continue to rise for some time after; much more must it do so when the attraction is only diminished. A little impulse given to a moving ball will cause it still to move farther than otherwise it could have done; and experience shows that the day is hotter about three in the afternoon than when the sun is on the meridian, because of the increase made to the heat already imparted.

"Tides do not always answer to the same distance of the moon from the meridian at the same place, but are variously affected by the action of the sun, which brings them on sooner when the moon is in her first and second quarters, and keeps them back later when she is in her third and fourth; because, in the former case, the tide raised by the sun alone would be earlier than the tides raised by the moon; and in the latter case, later.

"The sea, being put in motion, would continue to ebb and flow for several times, even though the sun and moon were annihilated, and their influences at an end, on the same principle that if a basin of water is once agitated, the water will continue to move for some time after the basin is left to stand still. A pendulum, put in motion by the hand, continues to make several vibrations without any new impulse. When the moon is at the equator, the tides are equally high in both parts of the lunar day, or time of the moon's revolving from the meridian to the meridian again, which is 24 hours 50 minutes. But as the moon declines from the equator toward either pole, the tides are alternately higher and lower at places having north or south latitude. One of the highest elevations, which is that under the moon, follows her toward the pole to which she is nearest, and the other declines toward the opposite pole; each elevation describing parallels as far distant from the equator, on opposite sides, as the moon declines from it to either side; and consequently the parallels described by those elevations of the water are twice as many degrees from one another as the moon is from the equator; then increase their distance as the moon increases her declination, till it is at the greatest, when these parallels are, at a mean state, 47 degrees from one another; and on that day the tides are most unequal in their heights. As the moon returns toward the equator, the parallels described by the opposite elevations approach toward each other, until the moon comes to the equator, and then they coincide. As the moon declines toward the opposite pole, at equal distances, each elevation describes the same parallel in the other part of the lunar day which its opposite elevation described before. Whilst the moon has north declination, the great tides in the northern hemisphere are when she is above the horizon; and the reverse whilst her declination is south.

"In open seas, the tides rise to very small heights in proportion to what they do in wide-mouthed rivers, opening in the direction of the stream of tide. In channels growing narrower gradually, the water is accumulated by the opposition of the contracting bank--like a gentle wind, little felt on an open plain, but stronger and brisk in a street; especially if the wider end of the street is next the plain, and in the way of the wind.

"The tides are so retarded in their passage through different shoals and channels, and otherwise so variously affected by striking against capes and headlands, that in different places they happen at all distances of the moon from the meridian, consequently at all hours of the lunar day.

"There are no tides in lakes because they are generally so small that when the moon is vertical she attracts every part of them alike; and, therefore, by rendering all the waters equally light, no part of them can be raised higher than another. The Mediterranean and Baltic Seas suffer very small elevations, because the inlets by which they communicate with the ocean are so narrow that they cannot, in so short a time, receive or discharge enough to raise or sink their surface sensibly.

"Air being lighter than water and the surface of the atmosphere being nearer to the moon than the surface of the sea, it cannot be doubted that the moon raises much higher tides in the air than in the sea. Therefore many have wondered why the mercury does not sink in the barometer when the moon's action on the particles of air makes them lighter as she passes over the meridian. But we must consider, that as these particles are rendered lighter, a greater number of them are accumulated, until the deficiency of gravity is made up by the height of the column; and then there is an equilibrium, consequently an equal pressure upon the mercury as before; so that it cannot be affected by the aerial tides. It is probable, however, that stars seen through an aerial tide of this kind will have their light more refracted than those which are seen through the common depth of the atmosphere; and this may account for the supposed refractions of the lunar atmosphere that have been sometimes observed.

"You see now how the tides are caused; while there may be some influences at work other than those exerted by the sun and moon, the latter are the chief ones, so I will not attempt to explain any other.

"Here, on the Passaic River, we do not have excessive tides, as the highest on the coast near us seldom rise over ten or twelve feet. As a rule, tides rise highest and strongest in those places that are narrowest. In the Black Sea and the Mediterranean, the tides are scarcely perceptible, while at the mouth of the Indus, in the Bay of Fundy, and other places, they rise thirty or more feet at times. The general rise, however, in mid-ocean, is from eleven to twelve feet.

"The diameter of our moon is nearly 2,200 miles, and her distance from the earth is about 240,000 miles; so you see it is not her size, but her proximity to the earth that gives her so much influence over the tides; for the sun, which is many times larger than the earth and moon combined, because of its being some ninety-three millions of miles away, exerts only one sixth of the attraction on the earth that the moon does.

"These facts, children, should be remembered, as you may often be called upon to make use of them.

"Oh, papa!" said Jessie "how many wonderful things there are in this world."

"But I have not told you all, my dear. There is much more to learn, but I hope the knowledge you have now acquired will act as an incentive, and cause you to pursue this study further."

Next morning Fred asked his father to enlighten himself and George regarding the making of a few simple meters, such as barometer, hygrometer, and a thermometer. He also wished to know if it would be possible for him to make a boomerang. Mr. Gregg told him he would be pleased to help him, and that there would be no difficulty in making a boomerang if he went to work at it earnestly.

On the arrival of his father that evening, the subject was again introduced, and Mr. Gregg using the blackboard, laid out the following drawing and wrote the accompanying instructions.

"The best hygrometer of absorption is (according to Deschanel) that of De Saussure, consisting of a hair deprived of grease, which by its contractions moves a needle. When the hair relaxes, the needle is caused to move in the opposite direction by a weight which serves to keep the hair always tight as seen in the illustration, Fig. 70. The hair contracts as the humidity increases. In the accompanying illustration A A and B B represent the frame; e f, the scale; a, screw for tightening the hair; b, the hair; O, weight; H, thermometer.

"A neater hygrometer, and one on the same principle, may be made by taking an old tooth powder box (as deep a one as possible, since the longer the string, the more sensitive it is), and boring a hole through the centre of the top and bottom. Paste a kind of dial in paper on the top of the box; take a piece of catgut, or small fiddle string, and push it up through the hole in the bottom and out at the one in the lid. Glue the bottom end immovably, and let the top end move freely: make a small index of a strip of whalebone (Fig. 71); bore a hole in the centre, and fix it on the catgut with glue. Wet the catgut, see which way it turns, and mark 'wet' and 'dry', accordingly on the dial.

"So much for the hygrometer. Now about that curious thing, the boomerang. If the following directions are closely adhered to, and the proper shape followed, a regular Australian boomerang will result. It is not difficult to make. Take a piece of hard wood, the natural shape of one of the segments of an ordinary wheel felloe, or bend in the wood; let it be 1/4 inch thick, shaped as at Fig. 72, to be held in the right hand at A, which shows the way the edges of the side facing the left hand must be bevelled off. It requires a slight curve on the flat side; so that, if on a table, each end would turn about 1/8 inch. It is then a part of a very fine pitch screw, in motion similar to a piece of slate jerked into the air, the sole difference being due to the slight curve in the back, which gives the screw motion, in conjunction with the forward and rotatory motion given by the hand. Sheet-iron would not do, as there would not be thickness to show the bevelled edge. The boomerang was made in the form of a cross, with four legs of equal length, bevelled, but it does not work as well as the regular form. You must be careful in throwing it as it may strike you on return."

George asked his father to describe one and to explain its uses. Mr. Gregg told the boys that a boomerang, as used by the aborigines of Australia for a weapon or missile of war or in the chase, consisted of a flat piece of hard wood bent or curved in its own plane, and from 16 inches to 2 feet long. Generally, but not always, it is flatter on one side than on the other. In some cases the curve from end to end is nearly an arc of a circle; in others it is rather an obtuse angle than a curve, and in a few specimens there is a reverse curve toward each end. In the hand of a skilful thrower, the boomerang can be projected to a great distance, and made to ricochet almost at will. It can be thrown in a curved path, somewhat as a ball can be "screwed" or "twisted," and it can be made to return to the thrower, striking the ground behind him. It is capable of inflicting serious wounds.

"It is very good of you, father," said Fred, "to tell and show us all these things; I'd like very much to have a very common, every-day matter explained: the theory of the pump." The following questions also were asked by one or another on the same line: What is the greatest distance or height a pump of any type can be placed away from the water? Is there any limit to the length of the delivery pipe to the tank? What is the difference between a lift and a plunger or force pump? Is it the sucker of the pump that draws the water up, or does it flow because the air being drawn out of the pump barrel and forced on the water outside, causes it to flow into the pump?

Mr. Gregg started in at once to give them the facts desired: "Theoretically, the greatest height a pump can be fixed above the water level depends on certain conditions: the atmospheric temperature, and the altitude the pump is to be fixed above the sea-water level. The higher the temperature, and the greater the altitude, the less distance the height of the pump can be above the water. The height to which water can be drawn from the source to the top of the bucket, or under side of a piston or plunger, when at the top of the stroke, or what is termed the 'height of suction,' cannot reach more than about 33 feet when the pump is at the sea level. If a tube about 34 feet long is immersed in a well, and the air is extracted by means of an air pump at the upper so that a vacuum is formed, the water will not rise in the tube until the air is expelled, when it will not rise more than 33 feet, even though there is a complete vacuum formed in the upper end of the tube. The reason why the water will not rise in the tube higher than this, is that the height of the water counterbalances the pressure of the atmosphere. This height is the theoretically greatest height that water will rise in a suction pipe. For the pump to discharge water, it is necessary for the water to be in motion, and to set and keep it in motion a portion of the water will rise, due to the atmospheric pressure. The shorter the suction pipe, the more certain the pump is of being completely filled at every stroke of the pump handle.

"The action of the pump is as follows: The bucket on moving upward attracts the air, so that the atmospheric pressure on the surface of the water in the well causes the water to follow the bucket up the suction pipe, through the suction valve, into the working barrel. On the return stroke, the suction valve will close, the valve in the bucket will open, and the water which before was under the bucket will pass through it to the top side. When the bucket is again raised, the water will be lifted through the delivery valve into the delivery pipe. There is practically no limit to the height of lift, which may be any height consistent with the strength of the pump and the available power. The ordinary pump used for raising water to the level of the top of the bucket, is termed a lift pump; for raising water above this, a force pump or a plunger pump must be used, when the water is displaced by a solid plunger on its downward stroke, when the quantity of water raised will be equal to the volume of the plunger. This system may be repeated when water is to be lifted more than ordinary heights."

X

WALL MAKING AND PLUMBING

A few evenings later, Mr. Gregg and his little family were gathered together on the river's bank, watching the movements of a number of pleasure boats and launches, when a good-sized tugboat came along and made quite a "wash" as she steamed past the Gregg domain. Mr. Gregg noticed that this had actually carried down a portion of the bank near the new pier, and he called Fred's attention to it. The two, followed by George, walked to the pier, and, to their alarm, found that quite a piece of the bank had been carried away by the current, the tides, and the frequent wash of passing steamers.

"This will never do," said Mr. Gregg. "We must protect the bank at this point, or the water will soon undermine and demolish our pier, for you see it is only near the landing where the bank shows signs of injury, and it is as badly damaged on one side as the other. This is caused by projection of the pier into the river, which prevents the water from flowing in its regular course, and causes it to rush into the angle formed by the junction of the pier with the bank, thus cutting away the latter."

"Perhaps it will be best to build a sort of retaining wall against the bank for ten or twelve feet each side of the pier to prevent this rush of water from cutting away the earth. If we had field stones enough on the ground, it would be cheaper to use them, though they would not make as good a 'job' as either cut stones or concrete; since we haven't the stones, we'll build it of concrete, as you have some knowledge of that material, and I will engage Nick to help you."

The next day Mr. Gregg ordered Portland cement and all the other materials required to build the wall, and engaged Nick, who promised to come the following morning. In the evening, Mr. Gregg had the boys in his den, and explained to them how to go about constructing the wall. He decided to have it built of concrete blocks about 12 × 24 × 12 inches, to be faced with good, strong, cement mortar on the face and ends, which would give the exposed wall a nice, smooth appearance. Mr. Gregg explained that there must be a foundation of stone under the concrete, formed by large bowlders or "fielders," laid as closely together as possible, the joints filled in with smaller stones and, when possible, cement mortar, to bind the whole into a solid mass--as shown by dotted lines in the illustration which he made on the blackboard. The blocks for the work were to be cast in wooden moulds or forms, which Fred and George could easily make out of boards taken from the dismantled barn. At the points where the wall was wanted, the bank was about 8 feet high from the bottom of the river, and it was determined to make the wall 8 feet high, 2 feet wide at the top and 3 feet at the bottom, with the batter on the water side, the weight of the wall being 140 pounds per cubic foot. It is always best to have the inclined surface on the side of the wall where the water will be. The water at high tide rises to a level of 6 feet above the base C D.

"In designing such a retaining wall," said the father, "for water one side, and earth the other, or determining its stability, the principles generally followed may easily be worked out by Fred, or even by George.

"Taking the earth side first, as shown in diagram Fig. 72_a_, W C X, angle of repose of earth to be retained--30 degrees; G C, the line of rupture; G C A, the wedge of earth at 112 pounds per cubic foot to be accounted for, the weight of which equals--

(GA × AC)/2 × 112 lb. = (4' 7" × 8')/2 × 112 lb. = 2,053 lb.

"This will act at a point one-third the height of the wall H. From H erect a perpendicular H I equal to 2,053 lb. Set out the angle H I J equal to angle of repose, 30 degrees. From H erect a perpendicular to A C, cutting I J in J. Then J H equals the direction and magnitude of the weight of the earth acting on the wall.

"Produce J H through the wall toward the water side. Find centre of gravity of wall in K and the weight of the wall, which in this illustration equals--

(AB + CD)/2 × AC × 140 lb. = (2 + 3)/2 × 8/1 × 140 lb. = 2,800 lb.

"From where J H produced meets a vertical line drawn through the centre of gravity, K, in L set of L N equal to 2,800 lb.; make L M equal to J H; complete parallelogram L M O N, when L O equals resultant of earth and wall.

"The magnitude and direction of P R can be found as in the first part of this article. Produce R P through the wall, and from where it cuts the resultant L O in S make S T equal R P. Let the diagonal L O now be produced so as to make S V equal to L O. Complete the parallelogram S T U V, when the resultant S U equals the combined resultant of earth, water, and wall, and as it passes within the middle third it can be considered safe.

"Now, boys," said Mr. Gregg, "I have not only told you how to build a retaining wall, I have also told you how to make all the necessary calculations for designing it, as the same figuring and diagraming, on this principle, will answer for any sea wall requiring like conditions.

"I know you both understand figures and geometry enough to make such calculations, if you are ever called upon to do so."

The next morning, before the boys had finished their breakfast, Nick was on hand ready to go to work, equipped with a pair of hip rubber boots which would enable him to wade in water two feet deep and remain dry.

Fred and George were soon ready and Mr. Gregg went out to tell them the proper way to commence. The foundation was the first consideration, so an examination of the site and was made, the length of the proposed walls measured off. While waiting for the tide to ebb to its lowest point, Nick and the boys busied themselves gathering up stones for the foundation and wheeling them to the point nearest where they were to be used.

After gathering all the stones thought necessary, the question of making the moulds for the concrete blocks was considered, and, as the greatest bulk of the blocks would be simply blocks with square ends and square faces, the moulds for these would be a box having inside dimensions of 12 inches deep, 12 inches wide, and 24 inches long. These dimensions would then allow of blocks being made in the moulds that will contain exactly 2 cubic feet. The mixed concrete was dropped gently in the mould and lightly tamped so as to make it solid. The mixture consisted of not less than 3 of cement, 5 of sand, and 7 of very fine gravel or broken stone, no piece being larger than a white bean. It was mixed in the same manner and in accordance with the rules given for making concrete for the sidewalk in