liquid, is, say, positive, may have its polarity reversed by changing the liquid. Thus, as in the battery now under consideration, lead is positive and copper negative when the liquid employed is nitric acid, but in pentasulphide of sodium the copper plate becomes positive and the lead negative. Consequently, in each element the current through the wire will be in the direction of the upper arrow, and through the liquid in the direction represented by the lower arrows.

In speaking of constant batteries it should be understood that the term is used relatively, no battery being absolutely constant.

POLITICAL GEOGRAPHY.

VII. HOLLAND.

HOLLAND, OF THE NETHERLANDS, is a kingdom of Western Europe, lying along the shores of the German Ocean between lat. 50° 44′ and 53° 34' N., and long. 3° 30′ and 7° 10′ E., and bounded on the north and west by the German Ocean, south by Belgium, and east by Germany. It has an area of 12,586 square miles, and a population (in 1880) of 4,012,693, of whom 2,469,814 were Protestants, 1,439,137 Roman Catholics, and 81,693 Jews. The principal towns, with their populations, are Amsterdam, 326,196; Rotterdam, 152,517; The Hague, 117,856. Holland forms the western extremity of the great plain of Europe, and its surface is low and flat, with the exception of some inconsiderable hills that traverse the provinces of Gelderland, Overyssel, and Utrecht. The land has for the most part been formed of the deposits of the three principal rivers which flow through it the Rhine, Meuse, and Scheldt. These have as far as possible been confined by embankments within narrow channels, and numerous canals have been formed to carry off the superfluous water, and to serve as means of internal communication. The land thus acquired is nowhere much above the level of the sea, and in many parts is considerably below it. Hence a great part of the coast has to be protected by enormous dykes, partly formed of huge blocks of granite brought from Norway, partly of mud and clay, with wickerwork. The rivers here divide near their mouths into various branches, forming numerous islands, the principal of which are Walcheren, North Beveland, South Beveland, Schouwen, Tholen, Over-Flakee, Voorne, and Beyerland. The great shallow gulf called the Zuyder Zee was formed in the thirteenth century by the bursting in of the sea on an inland lake. The former line of coast is marked by a chain of islands, the chief of which are Texel, Vlieland, Terschelling, Ameland, and Schiermonnikoog. The Haarlem lake, which had a circumference of thirty-three miles, has recently been drained, and its site is now occupied by cultivated fields. The climate generally is variable and very

451

moist. In winter the rivers and canals are frequently frozen over for two or three months. The greater part of the land is in pasture, and the rearing of cattle and the making of butter and cheese are more attended to than agriculture. The principal crops are rye, barley, oats, wheat, buckwheat, potatoes, peas, beans, flax, hemp, tobacco, and madder. Apple, pear, cherry, and other fruit trees are common. The soil being almost entirely alluvial, Holland has no mineral resources. The principal manufactures are linen, cotton, woollen and silk fabrics, bricks, gin, tobacco, sugar, beer, paper, and leather. Diamond-cutting employs about 1000 hands in Amsterdam. Ship-building and the herring and other fisheries are actively carried on. At one time the foreign trade of the Netherlands exceeded that of any other European country, and it is still very large. In 1879 the total value of the imports for home consumption was £70,554,000; the exports of home produce and manufacture, £48,471,000. The imports were chiefly from Great Britain, Belgium, and Germany; the exports chiefly to Germany, Great Britain, and Belgium. More than onefourth of the trade was with Great Britain. There entered the various ports 7820 vessels of 9,134,888 tons, and left 7620 vessels of 9,007,770 tons. The chief exports are cheese, butter, cattle, sheep, sugar, flax, gin, and madder; the imports, colonial and manufactured goods, corn, wine, cotton, wool, and coal. Besides its navigable rivers and canals, Holland possesses excellent roads and 1180 miles of railway.

The government is a constitutional representative monarchy. The executive power is vested in the king; the legislative in the king and the States-General, which is composed of two chambers, the first of 39 members elected by the provincial councils; the second of 86 members chosen by the people of the several electoral districts. By the budget of 1881 the expenditure is estimated at £10,372,244, and the revenue at £8,759,217, the national debt being £78,522,604. The permanent army on the peace footing consists of 2,334 officers and 62,779 men, besides a militia, and a colonial force of 15,788 Europeans and 18,211 natives. The navy consists of 163 steamers and 17 sailing vessels, having in all 542 guns, and manned by 5,914 men. Education is well attended to, and there are three universities-Leyden, Utrecht, and Groningen. The kingdom is divided into eleven provinces. The colonial possessions of Holland have an area of 666,000 square miles, and a population of 25,000,000, including the islands of Java, Celebes, and the Moluccas, with portions of Borneo, Sumatra, and Papua or New Guinea, in the East Indies; Surinam, or Dutch Guiana, in South America; and Curaçao, etc., in the West Indies. The king of Holland is also grand duke of the neutral territory of Luxemburg, lying between Belgium, Germany, and France, and having an area of about 1000 square miles and a population of 209,570.

BELGIUM.

BELGIUM, as an independent state, dates only from 1830, previous to which time it formed

part of the kingdom of the Netherlands. It is bounded on the north by Holland, north-west by the North Sea, south-west and south by France, and east by the Grand Duchy of Luxemburg, Rhenish Prussia, and Dutch Limburg. It is somewhat triangular in form, its greatest length from north-west to south-east being 174, and its greatest breadth from north to south 105 miles. Its area is 11,373 square miles or about one-eighth that of Great Britain, and its population (1880) 5,536,654, about one-fifth that of Great Britain. It is thus much more densely populated than Britain, and is in fact the most densely populated country of Europe, having on an average about 487 inhabitants to the square mile. It is divided into nine provinces-Antwerp, Brabant, East and West Flanders, Hainault, Liége, Limburg, Luxemburg, and Namur. The principal towns, with their populations, are Brussels, 170,345; Antwerp, 163,011; Ghent, 132,839; Liége, 121,787.

The surface is generally flat, having few elevations, and these rarely exceeding 2000 feet. They occur principally in the east and south-east, while in the north and north-west the country resembles Holland, and like it has parts of the coast protected by dykes. The principal rivers are the Scheldt and Meuse, with their tributaries, having in all a navigable length of 630 miles, in addition to which there are 376 miles of canal navigation. Length of railways 2559 miles. The climate is more temperate and salubrious than that of Holland, resembling more closely that of England, but it is somewhat colder in winter and hotter in summer. In the south-east the atmosphere is more pure and bracing than in the north-west, where it is frequently damp and hazy. About nine-tenths of the land is under cultivation, and about one-fourth of the population are employed in agriculture. The soil is fertile, and is cultivated with great care, but the holdings generally are small, more than one-half of them not exceeding two and a half acres. The principal crops are rye, wheat, oats, barley, potatoes, peas, beans, flax, hemp, beet, tobacco, chicory, hops, and madder. The rearing of cattle also receives a considerable degree of attention. Belgium is rich in various kinds of minerals, as coal, iron, lead, and zinc. As a coal-producing country it is next to England, yielding annually upwards of 15,000,000 tons. Iron is also abundant. There are likewise quarries of marble, freestone, granite, limestone, and slate. The chief manufactures are hemp, flax, linen and cotton yarn, linen, cotton and woollen stuffs, carpets, wrought iron, hardware, machinery, firearms, sugar, paper, glass, and lace. The chief imports are colonial produce, and the raw materials for cotton and woollen manufacture; the exports, coal, flax, wrought iron, machinery, woollen stuffs, yarn, sugar, hides, grain, etc. The trade is principally with France, Germany, England, Holland, the United States, and Russia. In 1879 the total imports amounted to £61,020,000; the exports to £47,616,000. The government is a constitutional hereditary monarchy. The legislative power is vested in the king, the Chamber of

Representatives composed of 132 members elected for four years, and the Senate of members elected for eight years. The members of both houses are elected directly by the people paying a certain amount of direct taxES Almost all the people are Roman Catholis except about 15,000 Protestants and 300 Jews, but full liberty is accorded to all. Educatio is very generally diffused; and there are fr universities. About 57 per cent, of the perte are Flemings, a branch of the Teutonic fami. speaking the Flemish, a branch of the L German; and about 42 per cent. Walloons, French extraction, and speaking Walloon, a dialect of the French. The army on the pea footing numbers 46,272, and is capable being raised in war to 103,683 men. revenue and expenditure for 1881 are estimate at £11,454,745 respectively, and the pu debt at £70,393,458.

DENMARK.

T

THE kingdom of Denmark comprises the por ern portion of the peninsula of Jutland. 2: the neighbouring islands of Fünen. Zea 221. Laaland, etc. It lies between lat. 54° 34 57° 44' N. and long 8° 5' and 12' 40′ E., and e bounded, north by the Skager Rack, west !T the North Sea, south by Prussia and the Fa and east by the Baltic, the Sound, and the Ca”gat. Area 14,784 square miles, and populat (1880) 1,969.039. By the Dano-German W. Denmark lost the duchies of Schleswig, ⠀ stein, and Lauenburg, having an area of square miles, and a population (188))) 1,124,862. Denmark also possesses the Fr Islands, Iceland, Danish Greenland, and West India Islands of Santa Cruz, St. Tt a and St. John, having together a populati 130,350.

The country forms part of the great pla Europe, and is low and flat, none of its e tions much exceeding 500 feet above the 3 Jutland forms about two-thirds of the e area. A considerable part of the surface in t west and centre is occupied by bare sa heaths, while in the east are fertile cort-a interspersed with woods. The largest of islands is Zealand, which has an area of 2*» ¦ square miles, and is separated from Swe by the Sound, and from Fünen by the G. Belt, while the Little Belt separates F from Jutland. Zealand is well cultivated fertile, and has on its east coast the capel Copenhagen. Fünen, the next in size, has area of 1270 square miles, and Lasland 4' At some distance from the others is the is of Bornholm, in the Baltic, which has an area ! 220 square miles. There are no considera. rivers, but numerous small streams, and a gras many lakes. The climate resembles that Scotland, but is more humid, and the extr of heat and cold are usually greater. Am ture is extensively carried on, and affords en ployment to the greater part of the pop The principal crops are oats, barley, rye, wa peas, beans, potatoes, rape-seed, hemp da hops, and tobacco. The rearing of hre cattle, and sheep also receives grest aftentr particularly in Jutland. The fishers

The

actively carried on along the coasts. mineral resources are inconsiderable, except in the island of Bornholm, where an inferior kind of coal is found, and porcelain and other clays. Peat is everywhere abundant. The manufactures are unimportant, consisting chiefly of linen and woollen articles for domestic use, earthenware, beer, brandy, glass, leather, paper, sugar, and tobacco. The chief articles of export are grain, cattle, butter, cheese, horses, brandy, beer, hides, and fish; of import sugar, coffee, tea, wine, salt, cotton, wool, coals, timber, and iron. In 1879 the total imports amounted to £10,782,000, and the exports to 8,562,000, about one-fourth of the former and three-fifths of the latter being with England. There are 988 miles of railway in operation.

The government was formerly an absolute monarchy, but the people are now represented in a Diet or Rigsdag, composed of two chambers-a Landsthing or upper house, and a Folksthing or house of commons.

The

ARITHMETIC.

XLI.

EQUATION OF PAYMENTS.

453

WHEN several sums of money are due each at different times, and it is desired to pay them all off at one time, so that neither debtor nor creditor may suffer any loss of interest, the time for paying them off must evidently be so chosen that the interest for that time on. the sum of the debts shall be equal to the sum of the interests on the several debts for their respective times. For example, if, instead of paying a debt of £100 3 months hence, and another debt of £100 9 months hence, I wish to pay the £200 at one time, I

former consists of 66 members, 12 of whom are nominated for life by the king, the others elected for eight years by the various districts; the latter of one representative for every 16,000 inhabitants-102 in all-chosen directly by the people for three years.

In 1880 the revenue amounted to £2,574,094, the expenditure to £2,392,575, and the public debt to £9,629,000. The inhabitants belong to the Scandinavian branch of the Teutonic race, and speak the Danish language, a form of the old Norse. They are almost all Lutherans, with the exception of about 3000 Roman Catholics and 4000 Jews. Education is national and compulsory, and there is a university at Copenhagen. Personal military service is obligatory on all males, commencing at twentytwo years of age, and lasting for sixteen years. The army and reserve comprise 1470 officers and 49,780 men. The navy consists of 33 steam vessels of 30,527 horse power, with 245 guns and 1122 men. The chief town, Copenhagen, has 234,850 inhabitants.

For by so

ought to do so 6 months hence. doing I gain the interest on the first £100 for 3 months, but I lose an equal amount of interest on the second £100, and thus the interest on the united debts (namely, £200) for

months is the same as the sum of the interest on £100 for 3 months, and £100 for 9 months.

The time at which the united debts can be paid off together is called the equated time.

We shall best see our way to a rule by taking an example:-Find the equated time at which I can pay together two debts, one of £200, due 3 months hence, and the other of £800, due 10 months hence.

The united debts amount to £1000, and the question is in what time will the interest on £1000 amount to the same as the interest on £200 for 3 months, together with the interest on £800 for 10 months? Now, Int. on £200 for 3 mths. £800,, 10,,

.. the sum of the int.

int. on £600 for 1 mth.;

£8000,, 1 £8600,, 1

The above process is equivalent to the following rule. To find the equated time:-Multiply each debt by the time it has to run, add the products, and divide the sum so found by the sum of the debts. The quotient is the equated time.

In finding the equated time we have hitherto considered only mercantile discount. A slight change in the rule will be necessary if we reckon true discount. The rule in this case will be:-Multiply the present worth of each debt by the corresponding time, and divide the sum of the products so found by the sum of the present worths.

Example.-Find equated time of £312, due 8 months hence, and £212, due a year hence, at 6 per cent. per annum. The true present

worth of

The English and most other modern governments have, for the purpose of meeting extraordinary demands on the national purse, borrowed at various times large sums of money from all who were willing to lend it. When we say that they borrowed the money, this is not always strictly accurate, because they do not generally undertake to repay it. They only undertake to pay interest at a given rate on the money thus raised, so long as it remains unrepaid; but they reserve to themselves the right to repay the original sums if they see fit to do so. Of course the original lenders may sell or give to any one they please, and for any price they can get, their right to the annual interest, and the buyer stands in the place of the original lender. The money lent to the government on these conditions is called Stock. The money annually raised by taxes to make a fund for paying the annual interest on the stock is properly called the Funds, but now the stock itself is often called the funds. Thus suppose A had originally lent £1000 to the government on the above conditions, he would be said to be the owner of £1000 of stock, or to have £1000 in the funds; and he would get the fixed interest originally agreed on-say 3

per cent., or £30 for his £1000. Now, sup pose he wanted his money he could not get ** from the government, but a stockbroker would probably be able to find him some one L. wished to buy his claim against the gove ment, and would give him a fair price for 2. The buyer would then have his name put dow as the owner of £1000 of stock, and the goverment would regularly pay him £30 a yar "The price of stock at any time is the pre for which £100 of stock can at that time i got in the market.

Thus, when it is said that the price of 3 pr cent. stock is 91, or that the 3 per cent, fi: 2 are at 91, the meaning is that £100 of ston can be bought in the market for £91. In eta words, that for £91 I can buy the right ↑ receive from the government £3 per auLE for ever.

Since the interest on £100 of stock rera de always the same, while the interest which a be got by other investments is constantly var ing, it is clear that the price of stock wiror fall according as the interest which can' got by other means falls or rises. Thu. after I have bought £100 of stock at the pr of £91, I find that the rate of interest is guar up in the market, I think I can get more th £3 for my £91, and so I wish to sell my sto But the same motive which induces me to *. keeps others from buying, and so I probably cannot get as much as £91 for my stock. am glad perhaps to sell it for £89 or less. If = the contrary, the rate of interest in the mark had fallen considerably, I should be very 251 to get £3 for my £91, and others would very glad to buy my stock, and so if I war to sell at all I should demand more than £1.

When the price of £100 of stock is £1 the stock is then said to be "at par"; wher below £100 it is said to be "at a discount and when above £100, "at a premium."

Different kinds of stock go by different ! names: e.g., Consols, an abbreviation of ac- { solidated annuities, are so called becaze several different stocks were consolidated in one, at the rate of 3 per cent. Reduri annuities," and "new 3 per cent. annuities are the most important of the other 3 pr cent. stock, and get their names from tb circumstances of their creation. The wa amount of stock on which our gover at present pay interest is over 700 mila e the result chiefly of borrowings to defray th expenses of former wars.

Government stock is bought or sold thr a broker, who charges a commission of re cent. (i.e. 2s. 6d. per £100) on what is t or sold. Thus the buyer of stock at £9! bato pay £91 2s. 6d., and the seller of the sam receives only £90 178, 6d.

We have hitherto spoken only of government stocks. But there are some public compa. m. such as the Bank of England, the East 1922 Company, railway companies, etc.. capital is also called stock, and is st similar conditions.

Shares in companies are also similar, bet they are generally subject to more compliant conditions, and their value is liable to ma

greater variations, the interest on ordinary shares not being a fixed amount, but depending on the profits of the concern.

Examples. Questions in stocks, shares, etc., are all done by the rules of proportion. We shall show how to deal with them by a few examples.

1. When 3 per cent. consols are at 901, find (a) what income will be derived from £7500 consols, and (b) what is the selling price of that amount of stock.

(a) Every £100 of stock gives an income of £3.. £100 £7500 :: £3: required income. (b) The selling price of £100 of stock is 901. .. 100 7500 :: 904 selling price.

2. What sum must I invest in the 3 per cent, stocks at 931, so as to produce an income of £1000 yearly?

I must invest £931 to get an income of £31. 3:1000: 931: required sum.

To find the sum required for the investment and to defray broker's charge, we have the following statement :

31: 1000: 934 : required sum.

3. If I invest £1000 in the consols when they are at 90, and sell out at 92, what do I gain by the transaction after paying broker's charges?

I pay £901 and receive £914,.. I gain £14 on every £901.

.. 90 1000: 14: nett gain.

4. What rate per cent. do I obtain for money invested in consols when they are at 93 ? Here £934 produces £3 per annum.

.. 93: 100 :: 3 rate per cent.

5. How much 34 per cent. stock at 95 must be sold to realize £1000?

Here £100 of stock must be sold to realize £95. .. 95 100 1000: stock to be sold.

6. Which is the better stock to invest inthe 34 per cent. at 90 or the 3 per cent. at 88? In the first stock, I get £34 for every £90; 31 .. for £1 I get £ or £1$s •

90

In the second, I get £3 for every 88; .. for £1 I get £.

If we compare these fractions we find that the former is the larger ( 7 x 88 is greater than 3 x 180); .. the former stock yields the larger income.

Exercises in Stocks.

1. A person buys £1000 worth of stock at 984, and sells it again at such a price that he gains £42 108. by the transaction. At what rate did he sell?

2. When the 3 per cents. are at 75, how much of them can be bought for £285?

3. How much money will be required to buy £800 of 4 per cent. stock at 89?

4. I buy £5050 of stock when it is 85: what sum do I invest ?

5. What is the money value of £1500 of stock the selling price of which is 924?

6. What is the income arising from £1000 invested in the 3 per cents. at 884?

7. What sum must be invested in the 34 per cents. at 90 to produce an income of £35 yearly?

455

8. A person invests £94 in the 31 per cents. when they are at 94; how much does he receive annually from this investment ?

9. What is the income arising from £1000, g of which is invested in 34 per cents. at par, and the remainder in 3 per cents. at 98.

10. £5000 of 4 per cent. stock is transferred at 90 into 3 per cents. at 72. What is the difference between the new income and the old?

Answers.

1. 103; 2. £380; 3. £712; 4. £4311 8s. 9d.; 5. £1387 10s.; 6. £33 17s. 118§d.; 7. £900; 8. £3 148. 54d.; 9. £33 4s. 104zd.; 10. £12 10s.

CHEMISTRY.

XXXIX.

BREWING AND DISTILLING.

Manufacture of

malt.

THE first step in the manufacture of beer consists in the conversion of a portion of the starch of some grain-generally barley-into sugar by the action of diastase. The barley is first moistened and allowed to undergo germination up to a certain point; when this is reached, that is to say when the grain has just begun to sprout, further growth is checked by drying it in an oven or kiln at a temperature of about 150°. The barley has now been converted into malt, as it is termed, the degree of drying or roasting to which it is subjected varying for different kinds of beer. The amount of sugar present in malt will be found to be greatly in excess of that which originally existed

Different kinds

ef malt.

in the barley; a portion of the Changes effected starch has also been converted by malting. into gum or dextrine.

Action of

diastase.

Conversion of starch into sugar

by diastase

We have already drawn attention to the fact that the action of that singular natural compound termed diastase is similar to that of sulphuric acid in the conversion of starch into sugar. The mere presence of either body is sufficient, while neither appears to suffer any decomposition. Such action is termed catalytic, and is very rapid, as may be exemplified in the following manner: If to a thick viscid solution of starch we add about a tablespoonful of strong infusion of malt, keeping the temperature up to 160° Farenheit, a change soon becomes apparent. The whole mass assumes a liquid condition, owing to the formation of dextrine. At first there is no sweetness; this, Dextrine formed however, soon follows, and in the course of a few hours abundance of sugar will have been formed. When in this experiment we begin with Weight of sugar a determinate weight of starch that of starch. we shall find that of the sugar produced somewhat in excess of it.

in malt.

before

sugar.

in excess of

This may