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4. To reduce a Decimal of any Compound Quantity to suc cessive lower Denominations.

For instance, suppose it be required to reduce £3.21875 to pounds, shillings, and pence.

This is the reverse process to that already explained in Art. 2.
21875 x 20
shil. 437500
= 4.375 shil.
100000

Now £21875

=

Li

21875 100000

=

375 shil. shillings

1606

=

100050

375 x 12 1000 5×4 farthings=1= 2 farthings. 10 Hence, £3.21875 = £3 4s. 41d.

pence 1888 = 4.5 pence.

natural divisions of the earth's surface, we have given two maps, one of the Atlantic Ocean and the other of the Pacific Ocean, which will be found useful in showing on a larger scale than that on which our Map of the World was drawn, the shores of the countries that are washed by these great bodies of water, and their mutual position with regard to each other. These maps are arranged in such a manner that the student may ascertain the longitude East or West from Greenwich or Washington of any place that is marked in them. In the map of the Atlantic Ocean the meridians are marked according to their position east and west from Greenwich along the top, and from Washington along the bottom. In the map of the Pacific Ocean the distance of each meridian from Greenwich is marked along the bottom of An examination of the above will sufficiently explain the fol the map, and from Washington along the top. A representation lowing method of arranging the work:of by far the greater part of the surface of the globe between the Arctic and Antarctic Circles is given in these maps. part which does not appear in them is that portion of the Indian Ocean which washes the southern coast of Asia and the eastern shore of Africa, with the whole of Central and Western Asia and the east part of Africa.

The

LESSONS IN ARITHMETIC.-XXX. DECIMALS IN CONNECTION WITH COMPOUND QUANTITIES -REDUCTION OF DECIMALS.

1. To reduce any given Compound Quantity to the Decimal of another given Compound Quantity of the same kind.

This is the name given to the process of finding, in the form of a decimal, what fraction the one quantity is of the other; or, in other words, of expressing the ratio of the two quantities as a decimal fraction.

Hence, clearly, all we have to do is to find the ratio of the two quantities expressed as a vulgar fraction, and then to reduce

that fraction to a decimal.

Thus 4s. is £, and } = 2.

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And 5 pence 1% pence =

£3.21875

20

4:37500

12

4.500 (leaving out unnecessary ciphers.)

2.0 £3 4s. 4}d.-Answer.

Notice that the decimal part only of each line is multiplied.

5. Hence we get the following tion in successive lower Denominations. Rule for finding the Value of a Decimal of any one Denomina

Multiply the decimal part by the number of units of the next lower denomination which makes one of the denomination in which the decimal is expressed, and cut off from the result a number of decimal places equal to the number in the multiplicand. The integral part in this result will express the number of units of the lower denomination. Proceed to reduce the remaining decimal part to the next lowest denomination exactly in the same way, and continue the process until the lowest required denomination is arrived at.

6.-EXAMPLE.-Reduce 4258 days to hours, minutes, etc.

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Here, in multiplying we are obliged to take in additional figures of the recurring period, in order to obtain the recurring period after the multiplication correctly; and this might give rise to considerable trouble if the number of figures in the recurring period were large. It will be often better, therefore, in such cases, to reduce the recurring decimal to a vulgar fraction, and proceed to perform the operation as follows:

=

£2173

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533 x 20

2475

shillings

=

£2173-21

9900

shillings

172 × 12

pence =

495

28 x 4

165

=

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215 shillings

405

L.

=

4133 shillings.

pence pence = 4 pence.

=

farthings 13 farthings.

165) 112.000 (678

990

1300

1155

1450

1320

130

Hence £2173 = 4s. 4d. and '678 farthings.

EXERCISE 49.-EXAMPLES IN REDUCTION OF DECIMALS.
Reduce-

1. 4s. 9d. to the decimal of £1.

2. 10s. 9d. to the decimal of £1.

3. 17s. 7d. to the decimal of £1.

4. 6d. to the decimal of a shilling.

5. 2 furlongs 2 rods to the decimal of a mile.

6. 3 hours 3 minutes to the decimal of a day.

7. 5 lbs. 4 oz. to the decimal of a cwt.

8. 15 minutes 30 seconds to the decimal of an hour.

9. 7 ounces 8 drachms to the decimal of a pound.

10. 1 guinea to the decimal of a moidore, and 2s. 6d. to that of 1 guinea. Deduce from your results what decimal 2s. 6d. is of a moidore.

11. 2 roods 10 perches to the decimal of an acre.
12. 18s. 10d to the decimal of a guinea.

13. What decimal is a day of a year, and 3s. 74d. of 18s. 23d. ?
14. What decimal is a pound of a cwt., and 2s. 94d. of 13s. 101d.?
15. Express of 3 lbs. 8 oz. as a decimal of 2 qrs. 15 lbs. 7 oz.

16. Reduce 43 of £2 17s. 6d. to the decimal of £5 15s.

Find the value of—

17. £725 in shillings, etc.

18. £1325 in shillings, etc.

19. 8258. in pence, etc.

20. 435 lbs. in ounces and drachms.

21. 275 miles in rods, yards, etc.

22. 4258 days in hours, etc.

23. 845 hours in minutes, etc.

24. Reduce 4s. 74d. to the decimal of '01 of £1.

25. Find 3 of a pound in shillings, pence, etc.

26. Reduce 1 + * + 1° of £1 to the decimal of a guinea.

1+ 3 + 4

Find the value of→

27. 890625 of £1 in shillings, pence, etc.

which overhangs towns, it dissolves sulphurous acid gas and ammonia, but of these only the slightest trace.

When rain-water percolates through the earth, it dissolves various salts which it finds in its course. These are most usually calcium carbonate, CaCO, (chalk); common salt, NaCl. (sodium chloride); calcium sulphate, CaSO4; magnesium sulphate and carbonate, MgSO, and MgCO,. The water in the neighbourhood of London contains about eighteen grains of chalk in each gallon. Mineral Waters are waters impregnated with a large propor tion of any one of these salts. Generally their temperature is higher than the surface of the earth where they make their appearance, and most usually they occur in volcanic neighbourhoods.

Chalybeate springs contain iron, which they deposit on their channel, making the water-course red with iron-rust. The Cheltenham springs are of this kind, but they are of frequent occurrence in the neighbourhood of iron beds.

Seltzer water, and those of a kindred nature, owe their effervescence to the escape of carbonic acid gas, of which they contain large quantities.

Harrogate water owes its offensive smell to the presence of sulphuretted hydrogen gas.

Saline springs, such as those at Epsom, abound in magnesium sulphate. The Cheltenham springs also contain saline mattersodium sulphate, Na,SO-and common salt.

The presence of these salts may be readily detected by the tests given under the various substances.

Most of these waters are medicinal, but none of their contents are pernicious. This is, however, not the case with organic matter, which some "surface" waters contain. We shall take London as an instance. The city is built on gravel, below which is a bed of clay, known as the "London clay." The rain percolates through this gravel, and is arrested by the clay; a well which is sunk down to the clay is soon filled with this water. The liquid is bright, sparkling, very refreshing, and in about the same proportion as its apparent good qualities recommend it, so are its contents deleterious. Animal and vegetable matters as they decompose give rise to the formation of nitrates, which are readily soluble, and the water becomes impregnated with these salts, and it also holds some of the animal matter in solution. These impurities are classed under the name of "organic matter." To the use of such water the origin of the malignant epidemics which sometimes scourge our towns is frequently traced. Water containing organic matter, when evaporated to dryness, leaves a brown residuum, which chars when sufficiently heated. It may, also, be tested for by permanganate of potash. If a dilute solution of this salt be added to distilled water which has been acidulated with a few drops of sulphuric acid, and then raised to 60° Cent. for half an hour, it will be found to retain its pink colour; but if water containing organic matter be used, the solution is rendered colourless in a few minutes. The water with which the companies supply London is got from the

28. 27 xi of 28. 9 d., and reduce the result to the decimal of a chalk which lies beneath the clay. pound to 4 places.

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The reader must have frequently noticed that it is a disagreeable and indeed difficult matter to wash in some waters. These are termed "hard waters." Their peculiarity arises from the fact that they contain salts whose bases are lime and magnesia. When soap is dissolved in them, these mineral salts and the soap act upon each other, or, in chemical language, undergo a double decomposition, the result of which is the formation of insoluble compounds of the fatty acids of the soap (oleic and stearic) and the bases of the salts. These oleates and stearates of lime and magnesia, being insoluble, are, of course, precipitated, but they are of a stringy nature, and adhere to any kind of textile fabric, rendering it difficult to wash clothes in such waters.

Various ways have been proposed to "soften" water, the object of which will be at once comprehended when we state that these salts are not by nature soluble in water, but are rendered so by the presence of carbonic acid gas. If, for instance, some powdered chalk be shaken up in a bottle of water, the liquid will become milky, but if the experiment be repeated with a bottle of "soda-water" freshly opened, the chalk will dissolve, and the water retain its transparency. If by any means the carbonic acid gas can be driven out of the hard water, its salts will be precipitated, and it will become soft. This may partially be effected by boiling; hence the explanation of the calcareous deposit found at the bottom of boilers. This fact may be rec exhibited by boiling a flask of hard water; after some m

will become milky, owing to the precipitation of the salts. A similar effect may be produced by adding a little lime-water; the lime appropriates the carbonic acid, and consequently the salts originally in the water and the newly-made carbonate of lime are precipitated together.

The formation of stalagmites and stalactites in caverns, and likewise the petrifaction of bodies placed in the water of many wells-for example, the "Dropping Well," at Knaresborough, in Yorkshire is due to this suspension of calcium carbonate by carbonic acid gas. When the water is distributed over the surface of the body undergoing petrifaction, or as it drips from the roof of the cavern, the carbonic acid gas escapes, and the calcium carbonate, being no longer capable of existing in solution, is deposited.

When water is required for delicate experiments, for photographic purposes, or for making solutions for laboratory use, distilled water must be used.

To distil water, the glass tube in Liebig's condenser should be replaced by a metal one lined with block tin; and to be quite sure that the water in the retort is not acid, it is safer to add a little carbonate of soda. Acidulated water, after the process of distillation has been continued for some time, begins to become acid.

the atmosphere we breathe, the fish would have to pass through their gills double the quantity of water-thus entailing much greater wear and tear of life. The fact that fish require air may be shown by boiling water, which expels the air from it, allowing it to cool, and then putting some "gold and silver" fish into it. The animals will come to the surface to breathe, and endeavour to "aerate" the water by agitating it with their tails. The last form we shall notice in which water is given to the earth, is dew.

During the day, as we have seen, the sun evaporates moisture, filling the air with water-vapour-steam. When the sun sets all bodies begin to radiate off their heat into the sky. The leaves of the vegetation are good radiators of heat, and therefore the grasses, etc., soon lose their heat and become cold. But not only are they good radiators, but they are also bad conductors, and therefore they receive no further addition of heat from the earth out of which they grow; upon their cold surfaces the moisture in the air is condensed, forming dew.

No dew is found on the bare earth, because it is never cold, heat being radiated from it all night; neither do we find dew under the overspreading branches of trees, nor on a cloudy night; for the branches and the clouds throw back the heat radiated from the earth, and thus the grasses beneath them are never cold. On a windy night the vegetation is warmed by brings in contact with the blades of grass, etc., warm particles of air, and by this means their temperature is kept up.

Water should never be kept in a lead cistern; for if it contain any carbonic acid gas, a lead carbonate would be formed," convection "-that is, the disturbance of the atmosphere which renders the water poisonous.

Water is a perfectly neutral body, being capable of combining with acids and likewise with alkalies. When it enters into chemical combination with a substance it forms a hydrate, while a body which contains no water is said to be anhydrous. Crystals also contain water, which is necessary to their existence; it is called the "water of crystallisation," and when driven off by heat the crystal falls to powder. It is thus expressed in symbols

tion.

Na,O,CO, +10 HO, soda crystals;

that is, sodium carbonate and ten atoms of water of crystallisa Water is a great solvent; being capable of holding in solution, more or less, almost all bodies As a general rule, more of the boly is dissolved by hot than by cold water. When a quantity of water will not take up any more of a substance, the solution is said to be saturated." If it be warm water, then, on cooling. the dissolved substance will be deposited in crystals; if cold, the crystals will appear on evaporating. This may be interestingly shown by adding alum or salt to boiling water until the water will dissolve no more; then suspend a bunch of thread, etc., in the vessel, and set it to cool in a dark, quiet place. The greater the quantity of the solution the larger will be the crystals on the thread.

The ocean is the great reservoir of water. But sea-water holds in solution a great number of salts. The effect of this is to increase its density; hence ships can bear much greater cargoes in salt than in fresh water. As we shall find that some elements are always got from sea-water, we give an analysis of that in

the British Channel:

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Ships are now fitted with apparatus for distilling sea-water; but the fresh water thus procured is insipid; if, however, it be filtered through charcoal it is "aërated," and assumes the refreshing taste of spring water.

All water contains air; but the air in water has double the proportion of oxygen in it than in atmospheric air. This is one of the of aquatic plants-they give off oxygen to the require oxygen for their existence, pass the ills, which apparatus retains the gas. If me proportion in the air in the water as in

Thus, the conditions for a copious fall of dew are a hot day, a clear, still night. If the temperature be below freezing point during the deposition of the dew, the particles of water freeze, and hoar-frost is formed.

THE PEROXIDE OF HYDROGEN (H ̧0,).

It will be remembered that in procuring oxygen from the air, one method was to pass a current of air over barytes, Ba0, this Ba0. Upon raising the temperature, this peroxide of barium oxide, combined with another atom of oxygen, thus forming parted with the second atom of oxygen, assuming its original condition, BaO. But if we take this BaO,, and dissolve it in dilute hydrochloric acid, the following equation will indicate the reaction:BaO+ 2HCl = BaCl, + H2O2;

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that is, barium chloride and peroxide of hydrogen are formed The barium chloride, BaCl,, is withdrawn from the solution, by submitting it to the low temperature of a freezing mixture, at which the BaCl, cannot remain in solution, and therefore it 'crystallises out," and is thus removed. More peroxide of barium and hydrochloric acid are added to the solution, and the process repeated until we get an appreciable quantity of the peroxide of hydrogen; besides this, there will be a little barium decomposition takes place, thuschloride in the solution; by adding silver sulphate, a double

BaCl, + Ag,SO1 = 2AgCl + BaSO.;

and seeing that both the products, silver chloride and barium sulphate, are insoluble, they are precipitated. To separate the water from the peroxide of hydrogen, the mixture is placed under the receiver of an air-pump-the same arrangement as in the freezing of water by its own evaporation, given in the last chapter. The sulphuric acid absorbs the vapour formed by the rapid evaporation, and the H2O, is left in the vessel. It is a transparent syrupy liquid, possessing a peculiar odour, and decomposes at even the low temperature of 20° Cent.; at high temperatures it decomposes with explosion. By its means fibrin may be distinguished from albumen-the two great components of flesh; the former decomposes it, the latter does not. It is remarkable that finely-divided gold, platinum, or silver are capable of decomposing this body into oxygen and water, without undergoing any change themselves. Some protoxides, such as that of lead, have the same effect, but in the process they become higher oxides, whilst the oxides of the noble metals not only are capable of causing the decomposition, but at the same time lose their own oxygen, and are reduced to the metallic state.

This substance has a powerful bleaching action, and should a process for producing it at a cheap rate be discovered, it would prove a great boon, for it does not destroy the fabric it bleaches; and the result after the bleaching is accomplished being only water, the necessity of great cleansing of the bleached material is precluded.

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