indication that the law of gravitation was imposed upon this for many ages the surface of the earth was too hot to permit vapour, and it began to revolve round its centre of gravity, thus water to rest upon it; but when the cooling had sufficiently procollecting itself into a fire-cloud, whose outmost edge stretched ceeded to allow of this, then that vast quantity of fluid which beyond the orbit of our most distant planet. A moment's is the blood of the geological life of the world covered the thought will decide that the shape it would take would be that surface of hard bare rock from pole to pole. But for long ere of a watch, providing that the edges were somewhat thinner, this was effected, the water, in a state of condensed vapour, As this fire-cloud revolved in space, which is devoid of heat, which forms clouds, must have enwrapped the earth, and the it would rapidly cool. Obedient to the great law, as it cooled operation ascribed to the second period of creation was the it would contract and become more dense, until its outward edge making of a firmament which should divide the waters which had reached so low a temperature that it could no longer were above the earth--the clouds—from the waters which were remain in its vapour condition, when it would condense into a on the surface: meaning to say that the cooling had sufficiently liquid. proceeded to allow the water to remain on the surface, and The globe of red-hot matter thus produced has since lost all its clouds to form. heat, and forms the furthest planet of our system. So one after With the dawn of the third era began the operation of a force another the different planets condensed from the vapoury mass. which still exists, and to which we shall frequently have to As might be expected, they did so at intervals, regulated by a law, allude: the heaving up, gradual and slow, of the northern named, after its enunciator, “Bode's law." There are several hemisphere, and the consequent draining off of the waters points in our system which support this theory. The planets and towards the southern pole. The ridges, or the crests of the their moons all move in the same direction. Their orbits are com- wrinkles, which had a generally northern direction, being elevated prised in a narrow belt, which represents the thickness of the at their northern extremity, would form continents of a triangular cloud. The exterior planets are light, and have many moons shape, the point of the triangle tending southwards. This apboth which peculiarities are accounted for by the fact that the pearance is still perpetuated in North and South America, cloud would be denser near its centre, and gradually become Africa, India, etc. Å glance at the map of the world will more rare towards its outward edge, in the region where these afford many confirmations of this theory; making allowance for planets condensed. There yet remains a further confirmation: the repeated elevations and immersions of the continents, which. the existence of Saturn's ring and the asteroids. It is well would necessarily cause some alteration in their shapes. This known that matter in rotation, if it be sufficiently pliable, will theory bears out the assertion of the sacred record, that the assume one of two shapes-either a sphere or a ring. The sun was not made until the fourth day-that is, Mercury and sphere will not be perfect, but will flatten at its poles and Venus were not until then separated from the mass, and that bulge out at its equator in proportion to the rapidity of its luminary which we call the sun produced as he now appears to us. motion and the slight cohesion of its matter. The exterior From this time the various forces which are still existing date planets are so elliptical in their shape that, looking at them the commencement of their operations. The tides, the ocean through a telescope, the eye is at once struck with the fact. currents, the rivers, the streams, the rain, the atmosphere, all The earth's equatorial diameter is twenty-six miles longer began their action on the Primary rocks, wearing them down, than its polar. It has been suggested that this shape may be and redistributing their particles in homogeneous order along due to the denudation of the poles by the continued evaporation the ocean bed; here forming stratified rocks which imbedded of water in the regions of the tropics and its condensation as the organic remains of that life which the Author of all life rain at the polar regions. By this means a thickness of thirteen had so abundantly shed upon the now habitable earth. Whether, miles was gradually transported from the pales, and deposited in after years, new facts discovered will cause another theory at the equator. But if this were the case, the earth would still to supersede this, remains to be seen. As yet, this is the only possess a spherical nucleus. This, however, is disproved by supposition at all tenable. And now, leaving theory, it is our certain astronomical considerations concerning the motion of duty to describe in turn these different agents, to notice their the moon. Hence, the earth must be elliptical from its centre- present action, and to discover traces of their handiwork in the that is, its shape is due to the action of its rotation when its rocky pages of Nature's book. mass was pliable. The ring is the only other shape which fluid in revolution can assume to be in equilibrium; but it is remarkable that if a ring LESSONS IN ARITHMETIC.-XXXVI. of oil which collects round a wire shape, immersed in a spirit of the same specific gravity as the oil, be made to revolve by SIMPLE INTEREST (continued). turning the wire, when a certain speed is attained the ring 9. Another method of finding the simple interest vpon a given suddenly breaks up into innumerable globules. sum for any assigned NUMBER OF DAYS. The existence of the ring of Saturn proves that that planet Let it be required to find the interest on £300 178. 10d. for must once have been in a fluid condition. The asteroids seem 218 days, at 6 per cent. per annum. to have been a ring of much larger dimensions, which, as in the 218 days is 30of a year. instance quoted, broke up into many small planets. The view Hence the answer would be given by simplifying the exwith which they used to be regarded-namely, that they were fragments of a planet which some internal convulsion had pression. 218 shattered is now abandoned; for it can be proved that in this (L300 178. 10d.), 100 case the fragments must periodically return to the point from which they were hurled, which is not the case. X 6 365 In questions where the time given is a number of days, it is In the lapse of untold ages the various members of our manifest that the divisor 36500 will always occur. For a system condensed from this vapour-cloud, and in process of time that is 73000, is a more convenient divisor, so that we must reason which will be explained immediately, twice this number, cooled down, until , losing their heat, they ceased to be luminous, double the numerator of the fraction. and assumed the appearance with which we are familiar. The sun is the remnant of this cloud, which was the result of Now, 12 x 218 (£300 178. 10d.) = £787132 12s., so that 787132 12s. the Great Being's first command, and no doubt the conden. the result will be obtained from £ 73000 sation and contraction are still going on. But to return to our earth. After our globe had assumed the The division by 73000 may be effected as follows :liquid condition, the process of cooling would still proceed, and It will be fonnd that 1 + f + 6 + sdo the consequent contraction. The result of this would be that 3. 73000 the vast ball of molten matter would be covered with a solid crust 721333 or skin. This crust, owing to the greater contraction of liquids 2433 than solids, would wrinkle, and, seeing the earth possessed a 243 uniform motion, the wrinkles would take a uniform direction : 100010 this direction was from north to sonth. Whether water was Hence, if to any number we add a third of itself, then th of existing in the atmosphere which enveloped the earth, as that third, and again titk of this last quotient, we shall in fact highly rarefied steam or as its constituent gases, oxygen and have multiplied it by the fraction 490010. It then we further hydrogen, in an uncombined state, is a matter of little moment. divide by 100010, we shall have divided the number by 73000. 100010 cent. 0 10 15 636 num. If, instead of dividing by 100010, we divide by 100000 (which is 2. Find the compound interest upon €555 10s. for 2 years at 4. per dene at once by cutting off 5 decimal places to the right), we cent. shall obtain a result which will be very nearly correct, being, in 3. Find the difference between the simple and the compound interest upon £250 for 4 years at 6 per cent. fact, too great only by wolono of the sum divided; 4. Find the difference between the simple and the compound interest for ιοβόσο TOUCTO + 1667700766 upon £365 4s. 8 d. for 3 years at 4 per cent. Now, 10 = 9600 farthings, and to 198000 T012836666 = TOUT, 5. Find the compound interest upon £250 for 3 years at 23 per nearly. Hence, to get our result correct to the nearest farthing, we must 6. Find the compound interest upon £1040 for 3 years at 4 per cent. reject from it now of a farthing for every £10 which occurs in 7. Find the compound interest upon £625 for 2 years at 4 per cent. the original dividend. But since this dividend is 100000 times 8. The difference between the compound and simple interest of a the result, it will be the same thing if we reject 1 farthing, for sum for 3 years at 4 per cent, is 198. ; find the sum. every £10 in the result. [N. B.-Find this difference for €100, and compare it with 198.] Performing, then, this operation upon the above example 9. I buy a field for £1000, for which I receive £30 year rent, € which I invest as soon as received at 4 per cent. compound interest. 1) 787132 12 At the end of 3 years I sell it again for £1030. What have I lost or gained by buying the field instead of investing the purchase-money on to) 262377 the same terms as I did the rent? KEY TO EXERCISE 54, LESSON XXXV. (Vol. II., page 408). 1. £21. 9. £413 ls. 3}d. 17. £121 4s. 97890. 2. £43 148. 9 d. 10. £679 149. Ogd. 18. £225, 15-67433 3. £84 13s. 70. 11. £1204 Gs. 3 d. 19. 4 years (R). 12 4. €148 15s. 5 d. 12. £6812 178. 20. £1 3s. 11 d. jf. 5. £101 6s. 70. 13. 2148117. 21. 25 years. 6. 2326 ls. 2d. 22. 3}}14 per cent. 7. £100 28. 6}a. 15. 2.833 years. 23. 4 per cent. per an. *36795 8. £75 11s. 60. 16. £280. The operation gives £10 15s. 8d., and therefore, rejecting one farthing, since the result only contains £10 once, we find the resnlt correctly to a farthing to be HYDROSTATICS.-III. £10 15s. 70. LAWS OF PRESSURE-SAFETY VALVE-SOLIDS IMMERSED IN LIQUIDS-SPECIFIC GRAVITY. Obs.-It does not necessarily follow that this method will be really the most convenient when the interest is to be found for We saw in our last lesson that the pressure in any liquid dea number of days. For instance, if the days reduce to a simple pends upon the area of the surface and the depth. It is fraction of a year, it will be best to proceed by the ordinary manifest, however, that this pressure must vary with the denmethod. The artifice is explained here as being a useful exer- sity of the liquid, and it is found to be in direct proportion to cise for the student, and as an ingenions method which it may proof of this. A glass tube is bent into the shape of a U, it. The apparatus represented in Fig. 10 supplies us with a be sometimes useful to employ. except that one limb is shorter than the other. If now we take EXERCISE 55. two liquids of different densities which will not mix, and ponr Find the interest upon : one into each limb, we shall find that the level will not be the 1. £1456 10s. od. for 131 days at 5 per cent. same in each, as it would were both filled with the same 2. 1000 0 0 for 201 days at 6 per cent. liquid. Suppose, for instance, that mercury is poured into the 3. 1698 14 8 for 189 days at 5 per cent. bend of the tube till it rises a little way in each limb. Now 4. 1476 8 6 for 20 days at 2) per cent. pour water into B until it stands 13 inches above the surface of 847 12 6 from July 8 to Dec. 26, at 5 per cent. 6. 987 18 9 the mercury, we shall find that then the level of the mercury in A from April 21 to Sept. 24, at 5 per cent. 7. 7597 10 8 from May 6 to Aug. 21, at 5 will be only 1 inch higher than in B. The 131 inches of water are, then, balanced by the 1 inch of mercury. If a layer, PO (Fig. 10), COMPOUND INTEREST. of the mercury be supposed to become solid, 10. Where compound interest is reckoned, at the end of one the pressure on each side of it must be equal, Fear the interest is added to the principal. This amount be since the fluid is at rest. Now the pressure comes the principal for the second year, and the interest upon it on the side towards B is equal to the weight of for the second year must be calculated and then added to its the mercury on that side, and of 134 inches of principal, and so on. The difference between the final amount water, while that on the other side is equal at the end of a number of years, and the original principal, is to the same amount of mercury, and a column the compound interest. 1 inch high in addition. EXAMPLE.—To find the compound interest for 3 years on If the column of mercury, instead of being 2100 at 5 per cent. 1 inch high, were made as long as that of At the end of the 1st year the amount is €105 the water, or 134 inches, the pressure would The interest of this for the 2nd year is be 131 times as great. At the end of the 2nd year the amount is We see, then, that the pressure on any Fig. 10. The interest on this for the 3rd year is. 5 10 body immersed in mercury is 13 times as great as on the same body immersed to the same depth in water. At the end of the 3rd year the amount is . £115 15 Hence the compound interest gained in 3 years is £15 15s. 3d. But the density of mercury is 13); the pressure, then, varies as the density. Hence, when two different liquids are placed in In finding the compound interest upon any sum, this is the vessels communicating with each other, the heights at which process which must be followed. It will therefore readily be seen they stand will be in inverse proportion to their densities. that, when the number of years is large, and the principal and We have now seen the most important facts concerning the mate per cent. complicated, the operation will be very laborious. pressure of liquids; but before passing on, we may just notice the 411 questions of compound interest are very much facilitated by construction of the safety-valve, which involves some of these the use of Logarithms, of which, however, we cannot treat here. principles. In an hydraulic press, the boiler of an engine, and Tables of the compound interest upon £1, at different rates other similar machines, there is a danger of the pressure beet sent., and for different numbers of years, are constructed coming greater than the strength of the materials can overfor practical use. come, in which case the cylinder will burst. To guard as much EXERCISE 56. as possible against this, a safety-valve is introduced, the object EXAMPLES IN COMPOUND INTEREST. of which is to relieve or remove the pressure when it is becoming :. Find the compound interest upon £850 for 3 years at 5 per dangerous. In a convenient part of the surface which is exposed to the per cent. B . . 0 5 5 £110 5 . 0 3 pressure, a conical hole (A, Fig. 11) is drilled, and a valve or equal to its own. If, then, it weighs only half as much as an equal plug is made to fit accurately into it. This plug is fixed to a bulk of water, it will only be immersed to half its depth. Wo lever, C D, which turns on a hinge at c, and at the other extre- thus see that a body will float, remain suspended, or sink, mity carries a weight, w. This weight can be fixed at any part according as its weight is less, equal to, or greater than that of the lever, and thus the pressure exerted by it can be altered; of an equal bulk of water. Thus any solid, however heavy, it is usually so adjusted that, before the pressure inside the may be made to float, provided it be flattened out and shaped boiler begins to be dangerons, it overcomes the weight, and, so as to displace a bulk of water weighing more than itself. In opening the valve, relieves the pressure by allowing the steam this way, though iron is seven times heavier than water, ships to escape. Suppose, for instance, that a safety-valve has to be are made of it, which, even when loaded with a heavy cargo, fitted to a boiler so as to limit the pressure to 40 lb. per are perfectly safe. square inch. Let the plug, A, have an area of half a square The human body, in its ordinary condition, is lighter than inch, and be attached to the lever at a distance of 2 inches water, and hence will float with a small portion above the sur from the fulcrum, also let the weight face. The art of swimming, therefore, is keep the body in be 24 lb. Since the plug has an such a position that the nose and mouth may be above, so that area of half a square inch, it must breathing may not be interrupted. Fear, however, causes the yield when a force of 20 lb. is ap- chest to be contracted, and thus a less bulk of water is dis plied to it, and must therefore be placed, and the body sinks deeper. The same principle accounts Fig. 11, pressed down with this force. The for the fact which every swimmer must have noticed, that it is weight is one-eighth of this, and hence easier to swim in salt water than in fresh. A volume of sea it must act at a leverage 8 times as great—that is, it must be water weighs more than an equal volume of fresh; hence a fixed 16 inches from c. If, then, the weight be adjusted thus, smaller balk is displaced by his body, and accordingly he is the boiler is perfectly safe, for when the pressure exceeds lifted higher out of it, and has a smaller quantity to displace 40 lb. to the inch, the valve will open and allow some of the as he moves through it. In the same way a ship is always steam to escape. These valves are sometimes made with a found to draw less water in the sea than in a river; hence, spiral spring instead of a lever, but they act in the same way. a vessel in a river may be loaded till she is immersed too far In practice it is common to have two; one is so placed that it below the water-line to be able to stand rough weather, but on cannot be touched or altered, and this is adjusted to the greatest reaching the sea she rises sometimes three or four inches. pressure that can with safety be applied ; the other is under the We may state, then, generally that a body in any liquid loses control of the engineer, who adjusts it according to the pressure as much of its weight as is equal to that of the liquid it dishe requires. The sides of the valve are always made to slope places. There is one simple experiment which furnishes an considerably, as otherwise it might become rusted in, and thus elegant proof of this. Let a cylinder of brass be procured, and cause an explosion. also a case which it fits into and exactly fills. Place the cylinder We now pass on to notice the effects produced on solids by and case in one pan of a pair of scales and carefully balance it. their immersion in liquid. Of course, we only deal now with Now take the cylinder from the case, and by a fine thread or the mechanical or physical effects, and therefore speak only of hair suspend it under the pan, and so arrange the apparatus that substances that are insoluble in water. Some bodies are dis- it may dip into a jar of water. The scale will at once rise, solved, and others are chemically altered by immersion in liquid; showing that the cylinder has lost weight by immersion; but if but it is the province of chemistry to examine these changes. we pour water into the case till it is filled, we shall find that the The main effects produced by the immersion of a solid in a scales balance as at first. We have thus a conclusive proof of liquid are the following: the proposition, the water in the case being clearly exactly 1. It displaces a volume of fluid equal in bulk to itself. equal in bulk to the cylinder. 2. It is buoyed up with a force exactly equal to the weight of This principle is said to have been discovered by Archimedes an equal bulk of the fluid, and therefore loses a portion of its in the following manner :-Hiero, the King of Syracuse, had some weight equal to this. gold which he wished made into a crown; so, having weighed it, 3. The upward pressure of the surrounding liquid acts ver- he handed it to a jeweller of the day for tically through the centre of gravity of the displaced liquid. that purpose. When it was returned he If we dip our hands into a heavy liquid we feel this found the weight was correct, but had a buoyancy; or if, when bathing, we lift a large stone, we shall suspicion that some of the gold had been find that it is easier to carry it when it is under water than kept back and its place supplied by baser when above. A more conclusive proof is to suspend a heavy metal. He accordingly requested Archibody from a spring balance, and having observed the weight, medes to try and discover whether or not Fig. 12 dip the body into water and observe again how much it weighs. it was so. For a long time he puzzled his We shall find that its weight is apparently less than it was. brain, trying to devise some plan for solving the problem. At When a solid is thus immersed, it is clear that it must dis- last, when taking a bath, he noticed that his body displaced place a quantity of water equal in bulk to itself. Two sub a bulk of the water, and was buoyed up by its pressure. From stances cannot occupy the same space at the same time—the this the idea struck him, and he rushed out exclaiming, “I solid, therefore, takes the place of an equal volume of the have found it! I have found it!" liquid; and if before immersion we completely fill the vessel SPECIFIC GRAVITY with water, and carefully catch all that runs over when the solid is dipped into it, we shall have an experimental proof of The principle we have been examining is of great use in the the fact. In this way the bulk of a solid of irregular shape determination of the density, or "specific gravity,” as it is may easily be ascertained. We have only to plunge it into a termed, of different bodies. vessel brim-full of water and measure the amount that runs over, It is a well-known fact that different substances contain difand this will give us the bulk of the solid. ferent quantities of matter in the same bulk. If we take a Now the loss of weight in the solid is exactly equal to that of number of 1 inch cubes of various bodies, as, for example, cork, this bulk of water. Let it have the shape of A (Fig. 12), and let oak, iron, stone, etc., and carefully weigh them, we shall find a portion of the water in the vessel having the same bulk and shape that they differ very greatly in their weight. The cork will be supposed to become solid; it will remain in equilibrium, the weigh about 60 grains, the oak about 190, while the iron will forces acting upon it being its own weight acting downwards weigh nearly 41 ounces. But though there is this difference through its centre of gravity, and the upward pressure of the between different substances, we shall find that a cubic inch of surrounding water which is exactly equal and opposite to this. any one substance always weighs nearly the same. If, then, we Now let tho solid take the place of this, and it will be buoyed up could procure equal blocks of all substances, and note their to exactly the same extent, sinco no change is made in the water weights, we could form a table of densities. The advantages around. The strain on the cord will be equal to the weight of of this would be very great. Sometimes we have a large A, less the weight of the equal bulk of liquid. A, therefore, block of known size, and we wish to know the weight, or we loses this portion of its weight. Just the same reasoning will may want to know how much space a given weight of any apply if the solid, instead of being wholly immersed, floats on substance would occupy, and all such questions could be solved the surface. The weight of the water it displaces will be exactly from this table. It is, however, impossible to procuro such EXAMPLES. blocks of many substances on account of their shape or physical and, as before, we first find the weight of water required to fill properties, and many other bodies are too small or too valuable. it to a certain mark, and then the weight of the liquid we are We cannot, then, compare their densities in this way, but we operating upon. may take some substance as a standard, and compare the The details of an actual experiment will make this clearer. weights of all others with this. A sample of nitric acid was taken, of which it was desired to Now any substance might be chosen for this purpose, the ascertain the specific gravity. The main requisites being that it shall be easily procurable in a small bottle was first put in the state of purity, and easy of manipulation. Water has been scales and found to weigh 80 grains. chosen as this standard, and is found to answer well. When, On being filled with the acid it therefore, we speak of the specific gravity of any body, we weighed 159 grains. The acid was mean' this, the proportion which exists between its weight next emptied out, the bottle rinsed, and that of an equal bulk of distilled water at a temperature and filled to the same height with of 60" water, the weight being then 136 The reason why we thus fix on a certain temperature is that grains. B water expands by heat, and therefore a cubic inch of hot water Now, since the bottle weighed weighs less than an equal bulk of cold. The temperature of 80 grains, we subtract this amount 60° is chosen merely as a matter of convenience, that being from its weight when filled with about the average, and therefore involving less trouble. When, the different liquids, and thus see Fig. 13. then, we say the specific gravity of mercury is 13-6, we mean that the water in the bottle weighed that any amount of mercury weighs 13.6 times as much as an 56 grains, while the weight of the same bulk of acid was 79 equal bulk of distilled water at 60°. Now, as we have seen, grains. We have, then, the following equation by which we the weight of a cubic inch of distilled water is 252-5 grains; a can determine the specific gravity of the liquid :cabio inch of mercury therefore weighs 252-5 grains X 136, As 56 : 79 :: 1:1'41. or 3,434 grains, which is nearly 8 oz. We can in this way, if we know the specific gravity of a body, tell the weight of any This, then, is the specific gravity of the acid, and from this we bulk of it. Questions like the following frequently occur, and can form an idea of its strength. In our next lesson we shall can thus be solved :- What is the weight of a block of coal see how to proceed in the case of solids. 3 feet x 5 x 4, the specific gravity of coal being 1.270 ? Since the specific gravity of the coal is 1.270, the weight of 1. A cubic foot of glass weighs 166 pounds; what is its specific a cabio foot is 1.270 times that of an equal bulk of water. But a gravity ? cubic foot of water weighs about 1,000 oz.; a cubic foot of coal 2. A flask holds 8 ounces of water and 10% of another liquid; what must then weigh 1,270 ounces. Now the total bulk of the coal is the specific gravity of the latter? is 3 x 5 x 4 = 60 cubic feet. Its weight, therefore, is 3. A small flask weighs when empty 150 grains, when full of an oil 60 X 1,270 ounces=76,200 ounces, or 42 cwt. 2 qr. 24 lb. Again, 290 grains, and when full of water 315 grains; what is the specific strong oil of vitriol has a specific gravity of 1.850; how much gravity of the oil ? 4. A rectangular block of timber measures 14 in. x 14 x 10. Its will 6 lb. measure ? A fluid ounce of water, it must be re- specific gravity is -850. If it floats with its largest surface horizontal, membered, weighs one ounce avoirdupois; 6 lb. of water, how deep will it be immersed? Also, how deep if it be vertical? then, would measure 96 oz.: but since oil of vitriol is heavier 5. A block of chalk 3 feet 30" x 30" X 2'6" is suspended in water. than it in the proportion of 1,850 to 1,000, it will measure pro- Taking its specific gravity as 2.660, what is the strain on the rope portionately less. Hence the following proportion will give us supporting it? the bulk :As 1,850 : 1,000 :: 96 : the required volume.. ANSWERS TO EXAMPLES IN LESSON II. (Vol. II., page 398). On working this out, we shall find that the vitriol will measure tion of the squares of their diameters, the larger has 144 times the 1. Since the areas of the pistons are to one another in the propor51.89 oz., or nearly 34 ordinary pints. area of the smaller. There is also a gain of 6 by the lever. Thus the We see thus the importance of knowing the specific gravity advantage gained is 144 x 6 or 864. If we divide 20 tons by this, we of any substance, and there are several modes of ascertaining find the required pressure is 51.85 pounds. it, one or other of which is more applicable according to the 2. The area of the sides is together 144 feet, and the mean depth circumstances of the case. If, however, we bear in mind 24 feet. The total pressure on them is thus equal to the weight of This is nearly 324,000 ounces, or exactly what it is we wish to know, we shall find little difficulty 144* 2 or 324 cubic feet of water. in remembering which way to proceed. 9 tons and 90 pounds. The pressure on the bottom is 6x10x 44*1,000 We will consider, first, how to proceed in the case of a liquid. onnces, or 7 tons 10 cwt, 2 qrs. 19 lb. 3. Rather more than 19 tous. Procure a thin glass flask (Fig. 13, A) provided with an accurately 4. The area of the large piston is 38] square inches. The required fitting stopper. Instead, however, of this being solid, let it be pressure is therefore nearly 40 pounds. drawn out, as shown at B, into a long tubular neck, so that when 5. Just over 15 tons. it is put in its place any excess of liquid may escape through it. 6. The additional pressure will be that of a column of water having The task is best made of such a size as to hold 1,000 grains up an area of 6 square inches, and a height of 3 feet. This will be of to the mark o in the neck. Now procure a small piece of metal, a cubic foot, and therefore weigh 7 lb. 13 oz. The total pressure is and file or grind it till it exactly balances the flask and stopper therefore 10 lb. 13 oz. when empty. If the flask, filled with distilled water to the level o, be put in one pan of a balance and the counterpoise or LESSONS IN GREEK.—XIV. weight in the other, we must add just 1,000 grains to balance the water. Empty this out, and fill it with the liquid whose REVIEW OF THE THREE DECLENSIONS. specific gravity we want to know-say, for instance, the strongest With the nouns of the first and second declension, the student, alcohol- and weigh again; we shall now find that only 792 if he has thoroughly mastered the foregoing lessons, will find no grains are required to balance it. The weight, then, of any difficulty in any attempt he may make to construe classical volume of alcohol is to that of an equal bulk of water in the Greek. It is somewhat different with nouns of the third deproportion of 792 to 1,000; or, in other words, the specific clension, the discovery of the nominative of which is necessary gravity of the alcohol is 1792. The reason why we chose a flask in order to consult a Greek lexicon with ease and effect. I containing 1,000 grains is now clear, for all trouble in calcula- therefore subjoin the following, which will enable him from the tion is thus avoided. We have only to take the weight of the genitive case to find the nominative ; in which form substanliquid in grains, and point off three figures as decimals, and we tives and adjectives appear in dictionaries. I give the genitive, have the specific gravity. because the genitive is, as it were, the key to the remaining Thus, if we fill the bottle with sea water, we shall find it oblique cases. Thus, if you meet with avopa, you know the will weigh 1,028 grains; the specific gravity is therefore 1.028. genitive must have two of these letters, namely, op; if you moet Sometimes, however, it is difficult or costly to procure a with xeluwves, you know the genitive will have the letters sufficient quantity of the liquid to fill such a large flask. We xeluwv; if you meet with weaves, you know the genitive will then use a much smaller one, usually made out of a glass tube, I have the letters melav. Now, from the genitive you may get pressure, a conical hole (A, Fig. 11) is drilled, and a valve or equal to its own. If, then, it weighs only half as much as an equal plug is made to fit accurately into it. This plug is fixed to a bulk of water, it will only be immersed to half its depth. Wo lever, CD, which turns on a hinge at c, and at the other extre- thus see that a body will float, remain suspended, or sink, mity carries a weight, w. This weight can be fixed at any part according as its weight is less, equal to, or greater than that of the lever, and thus the pressure exerted by it can be altered; of an equal bulk of water. Thus any solid, however heavy, it is usually so adjusted that, before the pressure inside the may be made to float, provided it be flattened out and shaped boiler begins to be dangerous, it overcomes the weight, and, so as to displace a bulk of water weighing more than itself. In opening the valve, relieves the pressure by allowing the steam this way, though iron is seven times heavier than water, ships to escape. Suppose, for instance, that a safety-valve has to be are made of it, which, even when loaded with a heavy cargo, fitted to a boiler so as to limit the pressure to 40 lb. per are perfectly safe. square inch. Let the plug, A, have an area of half a square The human body, in its ordinary condition, is lighter than inch, and be attached to the lever at a distance of 2 inches water, and hence will float with a small portion above the sur from the fulcrum, also let the weight face. The art of swimming, therefore, is to keep the body in be 21 lb. Since the plug has an such a position that the nose and mouth may be above, so that area of half a square inch, it must breathing may not be interrupted. Fear, however, causes the yield when a force of 20 lb. is ap- chest to be contracted, and thus a less bulk of water is dis plied to it, and must therefore be placed, and the body sinks deeper. The same principle accounts Fig. 11. pressed down with this force. The for the fact which every swimmer must have noticed, that it is weight is one-eighth of this, and hence easier to swim in salt water than in fresh. A volume of sea it must act at a leverage 8 times as great—that is, it must be water weighs more than an equal volume of fresh; hence a fixed 16 inches from c. If, then, the weight be adjusted thus, smaller bulk is displaced by his body, and accordingly he is the boiler is perfectly safe, for when the pressure exceeds lifted higher out of it, and has a smaller quantity to displace 40 lb. to the inch, the valve will open and allow some of the as he moves through it. In the same way a ship is always steam to escape. These valves are sometimes made with a found to draw less water in the sea than in a river; hence, spiral spring instead of a lever, but they act in the same way. a vessel in a river may be loaded till she is immersed too far In practice it is common to have two; one is so placed that it below the water-line to be able to stand rough weather, but on cannot be touched or altered, and this is adjusted to the greatest reaching the sea she rises sometimes three or four inches. pressure that can with safety be applied ; the other is under the We may state, then, generally that a body in any liquid loses control of the engineer, who adjusts it according to the pressure as much of its weight as is equal to that of the liquid it dishe requires. The sides of the valve are always made to slope places. There is one simple experiment which furnishes an considerably, as otherwise it might become rusted in, and thus elegant proof of this. Let a cylinder of brass be procured, and cause an explosion. also a case which it fits into and exactly fills. Place the cylinder We now pass on to notice the effects produced on solids by and onse in one pan of a pair of scales and carefully balance it. their immersion in liquid. Of course, we only deal now with Now take the cylinder from the case, and by a fine thread or the mechanical or physical effects, and therefore speak only of hair suspend it under the pan, and so arrange the apparatus that substances that are insoluble in water. Some bodies are dis. it may dip into a jar of water. The scale will at once rise, solved, and others are chemically altered by immersion in liquid; showing that the cylinder has lost weight by immersion; but if but it is the province of chemistry to examine these changes. we pour water into the case till it is filled, we shall find that the The main effects produced by the immersion of a solid in a scales balance as at first. We have thus a conclusive proof of liquid are the following: the proposition, the water in the case being clearly exactly 1. It displaces a volume of fluid equal in bulk to itself. equal in bulk to the cylinder. 2. It is buoyed up with a force exactly equal to the weight of This principle is said to have been discovered by Archimedes an equal bulk of the fluid, and therefore loses a portion of its in the following manner:-Hiero, the King of Syracuse, had some weight equal to this. gold which he wished made into a crown; so, having weighed it, 3. The upward pressure of the surrounding liquid acts ver- he handed it to a jeweller of the day for tically through the centre of gravity of the displaced liquid. that purpose. When it was returned he If we dip our hands into a heavy liquid we feel this found the weight was correct, but had a buoyancy; or if, when bathing, we lift a large stone, we shall suspicion that some of the gold had been find that it is easier to carry it when it is under water than kept back and its place supplied by baser when above. A more conclusive proof is to suspend a heavy metal. He accordingly requested Archibody from a spring balance, and having observed the weight, medes to try and discover whether or not Fig. 12. dip the body into water and observe again how much it weighs. it was so. For a long time he puzzled his We shall find that its weight is apparently less than it was. brain, trying to devise some plan for solving the problem. At When a solid is thus immersed, it is clear that it must dis- last, when taking a bath, he noticed that his body displaced place a quantity of water equal in bulk to itself. Two sub- a bulk of the water, and was buoyed up by its pressure. From stances cannot occupy the same space at the same time-the this the idea struck him, and he rushed out exclaiming, “I solid, therefore, takes the place of an equal volume of the have found it! I have found it!" liquid; and if before immersion we completely fill the vessel with water, and carefully catch all that runs over when the SPECIFIC GRAVITY. solid is dipped into it, we shall have an experimental proof of The principle we have been examining is of great use in the the fact. In this way the bulk of a solid of irregular shape determination of the density, or "specific gravity," as it is may easily be ascertained. We have only to plunge it into a termed, of different bodies. vessel brim-full of water and measure the amount that runs over, It is a well-known fact that different substances contain difand this will give us the bulk of the solid. feront quantities of matter in the same bulk. If we take a Now the loss of weight in the solid is exactly equal to that of number of 1 inch cubes of various bodies, as, for example, cork, this bulk of water. Let it have the shape of A (Fig. 12), and let oak, iron, stone, etc., and carefully weigh them, we shall find a portion of the water in the vessel having the same bulk and shape that they differ very greatly in their weight. The cork wil be supposed to become solid; it will remain in equilibrium, the weigh about 60 grains, the oak about 190, while the iron wil forces acting upon it being its own weight acting downwards weigh nearly 4 ounces. But though there is this differenc through its centre of gravity, and the upward pressure of the between different substances, we shall find that a cubic inch surrounding water which is exactly equal and opposite to this. any one substance always weighs nearly the same. If, then, w Now let the solid take the placo of this, and it will be buoyed up could procure equal blocks of all substances, and note thei to exactly the same extent, sinca no change is made in the water weights, we could form a table of densities. The advantage nround. The strain on the cord will be equal to the weight of of this would be very great. Sometimes we have a larg A, less the weight of the equal bulk of liquid. A, therefore, block of known size, and we wish to know the weight, loses this portion of its weight. Just the same reasoning will may want to know how much space a given weight of an apply if the solid, instead of being wholly immersed, floats on substance would occupy, and all such questions could be solve the surface. The weight of the water it displaces will be exactly from this table. It is, however, impossible to procuro sud |