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They then take the piece of wood, tie a string round it, weigh it by a spring-balance, and find this exactly agrees with the figures they have worked out; and it is this weighing which gives such a character of certainty to what they have been doing, which makes them take pleasure in the work. Weighing before floating it is better.
Again, knowing the measurement of the piece of wood, supposing it to be one of known dimensions, subtracting the number of solid inches under water from the whole, gives them that part of the body above the surface, and which is floating in air.
The same would be done with pieces of ash, elm, fir, etc. Also in winter, pieces of ice afford a teacher who understands the subject an opportunity of giving a useful lesson, -pointing out how water becomes solid at a particular temperature that although water freezes at this particular point, yet pieces of ice may have a temperature far below this — that a piece of ice, temperature 20°, as measured by Fahrenheit, would be of more service for cooling butter, water, etc., than one at 32°, and so on.
The teacher might ask such a question, - What is the atmospheric pressure on the surface of the water in the vessel ? making them calculate it, and showing how it varies with the barometer.
It is by repeating these questions over and over again, in a practical way, that they tell on the minds of children.
Again, take a small square, or oblong, or a box of any shape - a piece of wood hollowed out like a boat - a tin, such as tarts and bread are usually baked in: floating these, and loading them with weights until the water reaches the edge — they then see clearly that the quantity of water displaced is equal to the measure, in volume, of the vessel and the material of which it is made : and that a boat will just float, when the weight of the cargo and the weight of the boat taken together are equal to this displaced volume of the fluid in which it floats, and that any weight beyond this will sink it.
Calculating the weight of this volume of water displaced, and subtracting from it the weight of the boat, gives the extreme weight which the boat would carry without sinking.
Applying this to boats made of iron, or any other heavy metal, it is evident, that so long as the weight of the boat is less than a weight of fluid on which it is floating, the volume of which is equal to the whole size of the boat and material included, it will carry some cargo — that the limit to the thicknesss of the iron, so that the whole may float, is that which would make the weight of the boat equal to the weight of fluid of its own volume that the thinner the material (due regard to safety being had), as in all cases the less the weight of the boat itself, of a given size, the greater cargo it would carry that a boat which would sink in one fluid, would float merrily in another which was heavier, etc. ; for instance, a load which would sink in fresh, would float in salt water, and be buoyant in mercury. The teacher would naturally point out that the same boat would carry a heavier cargo on salt water than on fresh. What • would it be on oil, milk, mercury, etc.
The number of things which the principles connected with floating bodies may be called upon to illustrate is very great.
Having made them understand what is meant by the term specific gravity, and that by taking the weight of a certain volume of water as a standard, we calculate the weight of other bodies, it will be well to have a table of the specific gravities of substances in common use, metals, woods, etc., suspended on a cord in the schoolroom; and to show them by experiment how these results are arrived at. It is quite a mistake to think that boys about twelve or thirteen years of age cannot be made to understand them, and not only that they will take a great interest in them.
A short list is added, merely for the purpose of working an example or two from it. Taking water as 1.
Distilled water 1 | Copper...... 8.788 | Coal........ 1•250 Sea water is ... 1.026 | Tin.......... 7.291 | Oil......... •940 Platina........ 22.069 Iron (cast).. 7.207 Oak ........ .925 19.258 | Iron (bar).. 70788 | Ash
.845 Mereury ...... 13:586 13.586 | Zinc ........ 7100 Maple ......
•765 Standard silver 10:474 | Flint glass .. 3:329' | Elm ........ .600 Lead .......... 11.352 | Marble...... 2:700 | Fir.......... •550 Brass .......... 8.396 Ivory........ 1.825 | Cork........ .240
A simple inspection of this table may be made a useful lesson, by pointing out to them the comparative weight of those substances they are continually handling, the difference among them being much greater than they are in the habit of thinking it—that those substances the specific gravity of which is less than I will float. In this way the comparing one thing with another makes them think. Also why distilled water is a standard--that water varies in weight with the substances it holds in solution - that its boilingpoint varies with these substances.
Assuming the weight of a cubic foot of distilled water, and at the temperature of 63° Fahrenheit to be 1000 ozs. (why distilled water, and why a fixed temperature ?) let
1000 them show that the weight of a cubic inch=- , and
1728 why the divisor is 1728.
When we speak of the specific gravity of lead being 11:352 and of iron 7.788, we mean that the weight of any given volume of lead or iron will be so many times that weight of the same volume of water, and knowing the one, the other is easily calculated.
Thus a cubic foot of water weighs 1000 ozs., therefore a cubic foot of lead weighs 1000 ozs. x 11.352=11352 ozs., of iron 1000 ozs., x 7.788, or 7788 ozs., of an inch in the same way.
The specific gravity of dry oak is .925, of fir •550, of elm •600, therefore any given volume of these woods would float, being lighter than the same volume of water. A cubic foot of dry oak would be 1000 ozs. X .925, or 925 ozs.; of fir 1000 ozs. X.550, or 550 ozs., a little more than half the weight of oak.
As applied to these substances, a good deal depends on their state of dryness, sap in them, etc. · The following questions of a practical kind may suggest others :
What is the weight of a block of marble, granite, etc., of regular figure (or any other which they can measure), base of it fifteen feet six inches by five feet two inches, and four feet high.
A given number of feet of oak, elm, ash, etc.? A given mass of metal, what would be its weight? The weight of metals is exactly known from measurement, supposing them to be pure.
In this way the scholar will be easily made to calculate what horse-power, or man-power— moving power--it will take to move given masses of these materials; and would, if called upon to put it into practice, contrive accordingly strengthening their machinery, etc., adapting it to the work required to be done.
From this also may be shown, the reason why heavy bodies appear so much lighter when moved in a fluid like water--the beavier the fluid the easier they move-as when they raise a bucketful of water from a well ; its increased heaviness the moment it gets to the surface of the water-given size of the bucket how much increased in weight ? --would it be heavier if raised out of the water into a vacuum, and how much ?-moving masses of stone, as granite, under water-floating beams of timber, etc. Having given the volume and the specific gravity of the fluid in which they are moving, to calculate what they lose in weight.
Suspend a cubic foot of lead by a chain from one end of a balance; what weight would balance it at the other end, or over a single pulley? A weight equal to itself.-Now let it fall into a vessel of water: will it take the same weight to balance it as before ? No, Sir ; a weight less than itself, by the weight of a cubic foot of water. -What does a cubic foot of water weigh? 1000 ozs.--Well, I don't recollect the weight of a cubic foot of lead, but what is its specific gravity ? - look at your table, 11•352; therefore the weight of the lead in air is 11,352, and deducting 1000 ozs., the weight of a cubic foot of water, which is the weight lost by the lead, gives 10,352, the weight necessary to balance the lead when in water.
Suppose a cubic foot of lead resting on a pile under water, what force must be exerted to pull it off, supposing no resistance from friction on the pile ? About oths of its own weight.
From this to explain how it is that the sand, stone, shingle, etc., are so easily tossed about on the sea-shorehow the human body floats, etc.
Questions: A vessel full of mercury, the bottom of which is nine inches by 4:56, and the height ten inches, what is its weight?
Suppose a cistern, twelve feet long, five feet wide, and four feet six inches high, made of lead a quarter of an inch thick, what would be its weight? • What is the weight of a cylinder of iron thirty inches in diameter and six feet high? Of a block of granite in the form of a circle, four feet six inches in diameter and twenty inches thick ?
A statue of marble is placed in a vessel full of quicksilver, and causes six cubic feet to run over, what is its weight? Would it sink? Would a statue of cast iron sink ?
Why is the line of the angler more likely to break after the fish is out of water than when it is in it ?
Do you see any connection between the weight of a given mass of matter and the altitude of the barometer? and how might a dealer in any bulky commodity profit by observing that connection ? .
The specific gravity of ice is to that of water as 8 to 9, and a field of ice of uniform thickness, has 10 feet above water, how many feet below it?
A cubic foot of a metal weighs 1000 lbs. when weighed in air; the weight of a cubic inch of air being about adoth part of a cubic inch of water at a temperature of 63°, what would be the weight of the body in vacuo; also if weighed in water, and if in air of half the density,— work out the arithmetical results.
Making them reduce the fluid measures into cubic inches, feet, etc., is a good exercise. How many cubic inches in a pint ? 34•659.
in a quart?
in a gallon, etc. ? Then of course they easily calculate the weight of any of these measures filled with a fluid, the specific gravity of which is given.
In aeriform bodies, common atmospheric air is taken as a