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5 x 4
natural divisions of the earth's surface, we have given two maps, 4. To reduce a Decimal of any Compound Quantity to sucone of the Atlantic Ocean and the other of the Pacific Ocean, cessive lower Denominations. which will be found useful in showing on a larger scale than that For instance, suppose it be required to reduce £3-21875 to on which our Map of the World was drawn, the shores of the pounds, shillings, and pence. countries that are washed by these great bodies of water, and This is the reverse process to that already explained in Art. 2. their mutual position with regard to each other. These maps are
21875 x 20 arranged in such a manner that the student may ascertain the
100000 longitude East or West from Greenwich or Washington of any
375 x 12 place that is marked in them. In the map of the Atlantic Ocean
•375 shil. = U6 shillings
1988 = 4:5 pence. the meridians are marked according to their position east and west from Greenwich along the top, and from Washington along
And : 5 pence
Po pence = farthings 19 = 2 farthings.
10 the bottom. In the map of the Pacific Ocean the distance of
Hence, £3-21875 = £3 4s. 4 d. 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
£3.21875 the Arctic and Antarctic Circles is given in these maps. The
20 part which does not appear in them is that portion of the Indian Ocean which washes the southern coast of Asia and the eastern
4.37500 shore of Africa, with the whole of Central and Western Asia
12 and the east part of Africa.
4.500 (leaving out unnecessary
ciphers.) LESSONS IN ARITHMETIC.-XXX. DECIMALS IN CONNECTION WITH COMPOUND QUANTITIES
2:0 £3 4s. 4 d.- Answer. -REDUCTION OF DECIMALS.
Notice that the decimal part only of each line is multiplied. 1. To reduce any given Compound Quantity to the Decimal of
5. Hence we get the following another given Compound Quantity of the same kind. This is the name given to the process of finding, in the form tion in successive lower Denominations.
Rule for finding the Value of a Decimal of any one Denominaof a decimal, what fraction the one quantity is of the other; or, in other words, of expressing the ratio of the two quantities as lower denomination which makes one of the denomination in
Multiply the decimal part by the number of units of the next a decimal fraction.
which the decimal is expressed, and cut off from the result a Hence, clearly, all we have to do is to find the ratio of the number of decimal places equal to the number in the multitwo quantities expressed as a vulgar fraction, and then to reduce plicand. The integral part in this result will express the number that fraction to a decimal.
of units of the lower denomination. Proceed to reduce the Thus 4s. is £}, and } = -2. Hence 4s., reduced to the decimal of a pound, is £ 2.
remaining decimal part to the next lowest denomination exactly
in the same way, and continue the process until the lowest Again, 14s. 6d. = £20.
required denomination is arrived at. And we find, as in the margin, that 88, expressed 40) 29.000
6.-EXAMPLE.-Reduce ·4258 days to hours, minutes, etc. as a decimal, is 725. Hence, 14s. 6d., reduced to the decimal of a pound, 725
.4258 is £*725. 2. But instead of reducing the whole of the one compound
17032 quantity to the fraction of the other, and then reducing this
8516 fraction to a decimal, we can, in many cases, obtain the result more conveniently by reducing the separate portions successively
10.2192 hours. to decimals of the next higher denomination.
Thus, if it be required to reduce £3 4s. 4 d. to the decimal of a pound, we may proceed as follows:
13.1520 minutes. d.
5 of a penny. Therefore 4 d. And 4;d. of a shilling •375 of a shilling.
9.1200 seconds. Therefore 4s. 4 d. 4:375 of a shilling.
Hence :4258 days = 10 h. 13 m. 9.12 s. And 48. 410. = of a pound.
7. It is evident that, since each of the two processes we have
explained is the converse of the other, we can prove the correctHence £3 48. 4 d., reduced to the decimal of a pound, is £3.21875.
ness of our operations in any case by reducing the result to the In practice we should arrange the process thus :
original form. 4) 2:0 farthings.
Thus we showed that £3 4s. 4£d. was £3-21875, and then, 12) 4'5
by the converse process, we proved that £3-21875= £3 43.41d. pence.
8. EXAMPLE.—Reduce -2173 of a pound to shillings, pence, ets. 20 ) 4.375 shillings.
This may be performed in two ways.
2173 3.21875 pounds. Writing down the two farthings and dividing by 4, we get •5 pence, before which we place the 4d. of the given sum.
4.347 viding this again by 12, we get .375 shillings, before which
lace the 4s. of the given sum; and, similarly, dividing this ), we get .21875 pounds, before which we place the 3 pounds
4:169 e given sum. EXAMPLE.-Reduce 5 days 3 hours 36 minutes to the nal of 3 weeks.
Hence £ 2173 = 43. 4d. and .67s farthings.
Here, in multiplying we are obliged to take in additional figures
of the recurring period, in order to obtain the recurring period 7) 5:150000 days.
after the multiplication correctly; and this might give rise to
considerable trouble if the number of figures in the recurring 3) •73571428 weeks.
period were large. It will be often better, therefore, in such
cases, to reduce the recurring decimal to a vulgar fraction, and .24523809 decimal of 3 weeks.--Answer. proceed to perform the operation as follows :
which overhangs towns, it dissolves sulphurous acid gas and 9900
ammonia, but of these only the slightest trace.
When rain-water percolates through the earth, it dissolves 2475
various salts which it finds in its course. These are most usually 172 x 12 111 shillings
pence = 44 pence = 4*4's pence. calcium carbonate, CaCO3 (chalk); common salt, NaCl. (sodium 495
chloride); calcium sulphate, Caso,; magnesium sulphate and 28 x 4 les pence = farthings id farthings. 165
carbonate, MgSO, and MgCO3. The water in the neighbourhood 165 ) 112.000 ( 678
of London contains about eighteen grains of chalk in each gallon.
Mineral Waters are waters impregnated with a large propor990
tion of any one of these salts. Generally their temperature is 1300
higher than the surface of the earth where they make their appear1155
ance, and most usually they occur in volcanic neighbourhoods.
Chalybeate springs contain iron, which they deposit on their 1450
channel, making the water-course red with iron-rust. The 1320
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 effer
vescence to the escape of carbonic acid gas, of which they EXERCISE 49.--EXAMPLES IN REDUCTION OF DECIMALS. contain large quantities. Reduce
Harrogate water owes its offensive smell to the presence of 1. 48. 9d. to the decimal of £1,
sulphuretted hydrogen gas. 2. 10s. 9d. to the decimal of £1.
Saline springs, such as those at Epsom, abound in magnesium 3. 17s. 70. to the decimal of £1. 4. 6]d. to the decimal of a shilling.
sulphate. The Cheltenham springs also contain saline matter5. 2 furlongs 2 rods to the decimal of a mile.
sodium sulphate, Na, S0,--and common salt. 6. 3 hours 3 minutes to the decimal of a day.
The presence of these salts may be readily detected by the 7. 5 lbs. 4 oz. to the decimal of a cwt.
tests given under the various substances. 8. 15 minutes 30 seconds to the decimal of an hour.
Most of these waters are medicinal, but none of their contents 9. 7 ounces 8 drachms to the decimal of a pound.
are pernicious. This is, however, not the case with organic 10. 1 guidea to the decimal of a moidore, and 25. 6. to that of matter, which some “surface” waters contain. We shall take
i guinea. Deduce from your results what decimal 25, 6d. is London as an instance. The city is built on gravel, below of a modore.
which is a bed of clay, known as the “ London clay.” The rain 11. 2 roods 10 perches to the decimal of an acre. 12. 188. 101a tn the decimal of a guinea,
percolates through this gravel, and is arrested by the clay; a 13. What decimal is a day of a year, and 3s. 7.d. of 18s. 27d. ?
well which is sunk down to the clay is soon filled with this water. 14. What decimal is a pound of a cwt., and 2s. 9;d. of 13s. 10 d. ? The liquid is bright, sparkling, very refreshing, and in about 15. Express of 3 lbs. 8 oz. as a decimal of 2 qrs. 15 lbs. 7 oz. the same proportion as its apparent good qualities recommend 16. Reduce 43 of £2 17s.6d, to the decimal of £5 15s.
it, so are its contents deleterious. Animal and vegetable matters Find the value of
as they decompose give rise to the formation of nitrates, which
ase readily soluble, and the water becomes impregnated with 17. 2725 in shillings, etc.
these salts, and it also holds some of the animal matter in solu18. £.1325 in shillings, etc.
tion. These impurities are classed under the name of "organic 19. •825s, in pence, etc. 20. .435 lbs. in ounces and drachms.
matter.” To the use of such water the origin of the malignant 21. .275 miles in rods, yards, etc.
epidemics which sometimes scourge our towns is frequently 22. '4258 days in hours, etc.
traced. Water containing organic matter, when evaporated to 23. *845 hours in minutes, etc.
dryness, leaves a brown residuum, which chars when sufficiently 24. Reduce 4s. 7d. to the decimal of .01 of £1.
heated. It may, also, be tested for by permanganate of potash. 25. Find •3 of a pound in shillings, pence, etc.
If a dilute solution of this salt be added to distilled water which 26. Reduce of £1 to the decimal of a guinea.
has been acidulated with a few drops of sulphuric acid, and 1 + +
then raised to 60° Cent. for half an hour, it will be found to reFind the value of
tain its pink colour ; but if water containing organic matter be 27. •890825 of £1 in shillings, pence, etc.
used, the solution is rendered colourless in a few minutes. The 28. •27 .i of 29. 9 d., and reduce the result to the decimal of a chalk which lies beneath the clay.
water with which the companies supply London is got from the pound to 4 places. 29. •23 of £2 + 345 of 8s. 6d. - 1.35 of 5s.
The reader must have frequently noticed that it is a disagree. 3 + 125
able and indeed difficult matter to wash in some waters. These 30.
of a cubic yard. 235 - 03
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 KEY TO EXERCISE 48, LESSON XXIX. (Vel. II., page 198).
soap act upon each other, or, in chemical language, undergo N.B. The fractional parts of a farthing are neglected in these results. a double decomposition, the result of which is the formation d. S. d.
of insoluble compounds of the fatty acids of the soap (oleic 1. 1 01 5375 0 0 17. 865
and stearic) and the bases of the salts. These oleates and 2. 1625
10. 12951 18 9 18. 1358 0 63 stearates of lime and magnesia, being insoluble, are, of course, 3 212
precipitated, but they are of a stringy nature, and adhere to 4. 411 13 10} 12. 691 0 10 20.
7 32 5. 2290 13, 962 18 2
any kind of textile fabric, rendering it difficult to wash clothes 21. 1895
0 111 6. 135 12
in such waters. 8 14. 214 5 53 22. 163 7. 78742 15. 388 1 23. 2226 8 51
Various ways have been proposed to “soften” water, the 8. 3456 16 16. 569 6 31
object of which will be at once comprehended when we state that these salts are not by nature soluble in water, but are ren
dered so by the presence of carbonic acid gas. If, for instance, LESSONS IN CHEMISTRY.-VIII.
some powdered chalk be shaken up in a bottle of water, the
liquid will become milky, but if the experiment be repeated with WATER (continued).-PEROXIDE OF HYDROGEN.
a bottle of “soda-water” freshly opened, the chalk will dissolve, The purest water in nature is rain-water. The sun evaporates and the water retain its transparency. If by any means the moisture, which is condensed in the upper regions of the atmo- carbonic acid gas can be driven out of the hard water, its salts sphere, and descends again as rain—thus undergoing the process will be precipitated, and it will become soft. This may partially of distillation. The only impurities rain-water can contain be effected by boiling; hence the explanation of the calcareous are small quantities of the gases which compose the atmo- deposit found at the bottom of boilers. This fact may be readily sphere-oxygen and nitrogen ; and in passing through the air exhibited by boiling a flask of hard water ; after some mi
will become milky, owing to the precipitation of the salts. A the atmosphere we breathe, the fish would have to pass through similar effect may be produced by adding a little lime-water; the their gills double the quantity of water—thus entailing much lime appropriates the carbonic acid, and consoquently the salts greater wear and tear of life. The fact that fish require air may originally in the water and the newly-made carbonate of limo be shown by boiling water, which expels the air from it, allowing are precipitated together.
it to cool, and then putting some "gold and silver” fish into it. The formation of stalagmites and stalactites in caverns, and The animals will come to the surface to breathe, and endeavour likewise the petrifaction of bodies placed in the water of many to "aërate” the water by agitating it with their tails. wells-for example, the “ Dropping Well," at Knaresborough, in The last form we shall notice in which water is given to the Yorkshire—is due to this suspension of calcium carbonate by earth, is dere. carbonic acid gas. When the water is distributed over the sur- During the day, as we have seen, the sun evaporates mois. face of the body undergoing petrifaction, or as it drips from the ture, filling the air with water-vapour—steam. When the sun roof of the cavern, the carbonic acid gas escapes, and the calcium sets all bodies begin to radiate off their heat into tke sky. The carbonate, being no longer capable of existing in solution, is leaves of the vegetation are good radiators of heat, and there deposited.
fore the grasses, etc., soon lose their heat and become cold. But When water is required for delicate experiments, for pho- not only are they good radiators, but they are also bad contographic purposes, or for making solutions for laboratory use, ductors, and therefore they receive no further addition of heat distilled water must be used.
from the earth out of which they grow; upon their cold surfaces To distil water, the glass tube in Liebig's condenser should be the moisture in the air is condensed, forming dew. replaced by a metal one lined with block tin; and to be quite No dew is found on the bare earth, because it is never cold, sure that the water in the retort is not acid, it is safer to add heat being radiated from it all night; neither do we find dew a little carbonate of soda. Acidulated water, after the process under the overspreading branches of trees, nor on a cloudy of distillation has been continued for some time, begins to be- night; for the branches and the clouds throw back the heat come acid.
radiated from the earth, and thus the grasses beneath them are Water should never be kept in a lead cistern ; for if it con- never cold. On a windy night the vegetation is warmed by tain any carbonic acid gas, a lead carbonate would be formed, “ convection "—that is, the disturbance of the atmosphere which renders the water poisonous.
brings in contact with the blades of grass, etc., warm particles Water is a perfectly neutral body, being capable of combining of air, and by this means their temperature is kept up. with acids and likewise with alkalies. When it enters into Thus, the conditions for a copious fall of dew are a hot day, a chemical combination with a substance it forms a hydrate, while clear, still night. If the temperature be below freezing point a body which contains no water is said to be anhydrous. during the deposition of the dew, the particles of water freeze, Crystals also contain water, which is necessary to their exist- and hoar-frost is formed. ence; it is called the “ water of crystallisation," and when driven off by heat the crystal falls to powder. It is thus ex.
THE PEROXIDE OF HYDROGEN (H,0.). pressed in symbols
It will be remembered that in procuring oxygen from the air, Na,0,00, + 10 HO, = soda crystals ;
one method was to pass a current of air over barytes, Bao, this that is, sodium carbonate and ten atoms of water of crystallisa- Bao, Upon raising the temperature, this peroxide of bariam
oxide, combined with another atom of oxygen, thus forming tion.
Water is a great solvent; being capable of holding in solution, parted with the second atom of oxygen, assuming its original more or less, almost all bodies As a general rule, more of the condition, Bao. But if we take this Bao,, and dissolve it in boly is dissolved by hol than by cold water. When a quantity dilute hydrochloric acid, the following equation will indicate the of water will not take up any more of a substance, the solution
Bao, + 2HCl = BaCl, + 1,0,; is said to be a saturated." if it be warm water, theu, on cooling, that is, barium chloride and peroxide of hydrogen are formed the dissolved substance will be deposited in crystals; if cold, the 'The barium chloride, BaCl,, is withdrawn from the solution, by crystals will appear on evaporating. This may be interestingly submitting it to the low temperature of a freezing mixture, at shown by adding alum or salt to boiling water until the water which the BaCl, cannot remain in solution, and therefore it will dissolve no more; then suspend a bunch of thread, etc., in "crystallises out," and is thus removed. More peroxide of the vessel, and set it to cool in a dark, quiet place. The greater barium and hydrochloric acid are added to the solution, and the the quantity of the solution the larger will be the crystals on the thread.
process repeated until we get an appreciable quantity of the perThe ocean is the great reservoir of water. But sea-water chloride in the solution ; by adding silver sulphate, a double
oxide of hydrogen; besides this, there will be a little barium holds in solution a great number of salts. The effect of this is to increase its density; hence ships can bear much greater cargoes
decomposition takes place, thusin salt than in fresh water. As we shall find that some elements
BaCl, + Ag.10, = 2AgCl + BaSO.; are always got from sea-water, we give an analysis of that in and seeing that both the products, silver chloride and barium the British Channel :
sulphate, are insoluble, they are precipitated. To separate the Water
water from the peroxide of hydrogen, the mixture is placed Sodium Chloride
under the receiver of an air-pump-the same arrangement as in Potassium Chloride
the freezing of water by its own evaporation, given in the last Magnesium Chloride
chapter. The sulphuric acid absorbs the vapour formed by the Magnesium Bromide
0-02929 Magnesium Sulphate .
rapid evaporation, and the H,O, is left in the vessel. It is a
2.29578 Calcium Sulphate
transparent syrupy liquid, possessing a peculiar odour, and Calcium Carbonate
decomposes at even the low temperature of 20° Cent; at high Iodine
temperatures it decomposes with explosion. By its means fibrin Ammonia
may be distinguished from albumen—the two great components Oxide of Iron in some seas.
of flesh; the former decomposes it, the latter does not. It is Silver
remarkable that finely-divided gold, platinum, or silver are 1000-00000
capable of decomposing this body into oxygen and water, with.
out undergoing any change themselves. Some protoxides, such Ships are now fitted with appziatus for distilling sca-water; as that of lead, have the same effect, but in the process they but the fresh water thus procured is insipid ; if, however, it become higher oxides, whilst the oxides of the noble metals be filtered through charcoal it is “aërated,” and assumes the not only are capable of causing the decomposition, but at the same refreshing taste of spring water.
time lose their own oxygen, and are reduced to the metallic state. All water contains air; but the air in water has double the This substance has a powerful bleaching action, and should a proportion of oxygen in it than in atmospheric air. This is one process for producing it at a cheap rate be discovered, it would of the chies of aquatic
plants--they give off oxygen to the prove a great boon, for it does not destroy the fabric it bleaches ; ich require oxygen for their existence, pass the and the result after the bleaching is accomplished being only
gills, which apparatus retains the gas. If water, the necessity of great cleansing of the bleached material ame proportion in the air in the water as in | is precluded.