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HISTORIC SKETCHES.-XXXVIII. Brandenburg. Lord of the territory lying on the westernmost
borders of the empire, and including (since 1525) in his posees. THE RISE OF PRUSSIA, AND THE SEVEN YEARS' WAR.
sions the duchy of Prussia, he was exceedingly powerful, and THE kingdom of Prussia was a creature of very gradual growth. could help or disoblige his neighbours to a very considerable Like all other things that are great and respectworthy, it had extent. The neighbouring princes therefore courted his favour, to be founded by wisdom and industry, and built up by suffering, and, where their interests and not their jealousies were concerned, patience, and perseverance. Not until the Thirty Years' War (see depended upon him to support them against the power of the Historic Sketches, XXVII.) had revealed to them their strength, princes lying to the eastward. They rallied also round him as and also given them the opportunity, did the Margraves of against foreign foes. Notwithstanding all these considerations, Brandenburg think of enlarging their borders till they should the Elector of Brandenburg remained loyal to the imperial be worthy the title of a kingdom. Hitherto the margraves had constitution till he could no longer do so and preserve his selfbeen content to be chief among the feudal dependants on the respect, or even his independence. The Thirty Years' War was, Emperor of Germany, and had found in the government of their as has been shown, a war of religion, a war which went to the own states, and in the assertion of their dignity, employment root of the question whether Protestantism should or should not enough for their energies, and outlet enough for their ambition. exist in Germany in spite of the will of the emperor, who was
From a remote period that portion of Scythia which was wholly opposed to it, and entirely devoted to the Roman Catholic known as Germany had been divided into a number of small faith. In this war, the Elector of Brandenburg, who had emstates, differing as to title and importance according to their braced the doctrines of the Reformation, took part with the size, and according to the influence they were able to bring to Protestant side, and gave in his hearty adhesion to Gustavus bear upon head-quarters. Over all was the imperial ruler, Adolphus and his successors in command. One of the results elected by the chief of the losser potentates, now from one of the war was to show him how strong he was, and also to con house, now from another, not having hereditary dignity—at vince him, after the spirit that had been displayed in conducting least until quite modern times—but chosen because he was con the war, that the old lines of the German constitution were for sidered to be the ablest man, the cunning (i.e., wisest) man, the ever obliterated, that is to say, that between him, those depenkönning, the king, the man best able to serve the common weal. dent on him, and the emperor, the old principle of loyalty could The electors were seven in number—the King of Bohemia, the no longer exist. Duke of Saxony, the Margrave of Brandenburg, the Count Pala In 1701 the Elector Frederick, deeming himself strong enough tine of the Phine, and the Prince-Bishops of Mayence, Treves, to make good his act against all the world, with his own hands and Cologne, and these among themselves decided who should crowned himself king, and announced to the world that his be chief of the feudal union of states which was known as Ger- name henceforth was not Elector of Brandenburg, but King of many. According to the principles of the feudal system, each Prussia. Tho house of Hapsburg sat on the imperial throne, of the seven electors—much more, therefore, those lesser dukes and had procured that the dignity of emperor should be and counts who were not of sufficient importance to have a hereditary in the family. It could ill brook the assumption of voice in the imperial election-was bound to render to the kingly power by the most powerful vassal of the empire in the emperor the allegiance of a vassal to a suzerain, an allegiance west; but exhausted by the sustained efforts of thirty years of which differed from a general and absolute allegiance in this, war, it was not in a position to take exception practically to the that the vassal was in almost every department or relation of move, though it viewed the rise of Prussia with dislike, and life free to act as he pleased within his own territory, but in all waited for an opportunity of knocking it down again. concerns which affected the union as a whole was bound to obey Frederick the First survived for twelve years his assumption the will of the emperor as dictator, to render him military of royal dignity, and during that time did his utmost to weld service, and to contribute towards the common expenses of the into a coherent mass the numerous parts which constituted his empire. Thus, when the Turks by their armaments threatened dominions. Upon his successor, Frederick William, devolved Western Europe, and commenced their attacks on the eastern the task of preparing the new-born kingdom to guard against provinces of Germany, it was incumbent on all the princes of the storm which sooner or later it was seen must burst upon it. the Germanic empire to lend a hand, and to give money towards Not only was there the open hostility of Austria and ber repelling the invaders ; but when it came to be a question of dependent states to be overcome so soon as those states should domestic administration, say in Saxony, the duke of that pro- have sufficiently recovered to allow of their taking the field, but vince was not called upon by his allegiance to consult the there were the jealousies of France and Russia to be met, and by emperor in the matter, bat possessed plenary power himself to some means, probably not without violence, to be allayed. For deal with the matter without right of appeal.
this work of preparation there was no fitter man than the There were very many of these petty states. When the second King of Prussia. A man with few ideas-some great soldier-chiefs who last occupied southern Scythia began to settle ones were among them—he had the courage and the pertinacity down, they took possession of such lands as their own followers to carry his ideas out to the fullest, and his aims were in the happened to occupy, and holding them by the grace of God and main for the advancement and benefit of Prussia as a European the strength of their strong sword-arms, assumed the govern power. He formed and organised the Prussian army on a model ment of the territory, and succeeded in obtaining recognition upon which his successor, Frederick the Great, hardly improved; from the most powerful of their class, who in his turn, and by he laid the foundation of Prussian finance on that basis of thrift virtue of the same title, assumed the title and position of which has been its chief and its most admirable characteristic emperor, the representative of the Western emperor of the ever since. The idea of military organisation throughout the Roman empire, the King of Italy, and the arbiter of European country, so that every man of the population should be liable to affairs.
soldier-service, was this king's; and so was the wisdom which The title of " graf,” or “grave,” was equivalent to count, and placed the domestic laws upon a footing somewhat less unsatiswas the lowest grade of sovereign noble; then came duke (from factory than that on which they had hitherto rested. Yet be the Latin dux, a leader) or herzog, signifying drawn out, elected, was a prince hated quite as much as he was respected, particuraised; and then came king, a title given to the holders of the larly in his own family, where he acted as an insane tyrant, going larger principalities. Markgraf, or margrave, signified a count the length on one occasion, when he had goaded his son, the of the marches or borders, and was equivalent to the word crown prince, by repeated acts of oppression,
into the idea of marquis; a count-palatine signified originally a nobleman deserting
Prussia altogether, of condemning that som to death attached to the imperial household or palace, but was after- as a deserter, and of actually causing his son's friend and comwards made to indicate the sovereign princes of those provinces panion, Lieutenant Katte, to undergo the extreme penalty in the which the emperor had at one time or another conferred upon presence of the prince. Out of the school of this Tyranuns officers of his palace. From these dignitaries, who included came Frederick the Great; from his brain issued, ready-made prince-bishops among their number, were selected the seven and armed at all points, the kingdom of Prussin, as Minerva is electors to the empire, so that the title of elector came to be fabled to have done of old from the head of Jupiter, Into the one of special honour, and was tacked on to the other titles of inheritance left by such a man came Frederick the Great
, in the the possessor of it as distinctive and honourable. It was shared, year 1740, by which time the nations had had leisure to look as already stated, by counts, dukes, kings, and prince-bishops. around, and to take notice of the new peer which had sprung
Certainly not least among the electors was the Margrave of up among them.
France, weakened by the long and exhausting wars of Louis XIV, was quite unable, if she wished it, to crush the new power; but it is probable she did not then see what has since been forced upon her notice, that Prussia might become a first-rate power, capable of disputing the supremacy with her in southern Europe. Austria, however, saw with quick, instinctive eyes, that if she wished to be, as hitherto, first without question in Germany, she must at once, without losing an opportunity, strike a blow which should permanently injure Prussia, and re-assert once and for ever her own superiority. She had recorered pretty well from her sufferings in the Thirty Years' War, and she saw that, in view of the compactness and the organisation which were so visible in the Prussian kingdom, she must even risk something rather than allow Prussia to make such headway. Suddenly she found that through the force of circumstances she was compelled to act on the defensive instead of the aggressive against her rival. The Emperor Charles of Germany died in 1740, and his daughter, Maria. Theresa—for whose right to succeed Charles had been careful to obtain the recognition of the European powers—found herself engaged in a contest with numerous foes who set up claims to the several portions of her empire. The Pragmatic Sanction, by which the assent of Europe had been given to Maria. Theresa's claims, was disregarded by those most interested in doing so, England and some of the lesser German states being alone in their fidelity to their engagements. Frederick, who knew the national feeling of Austria, and the wishes of her statesmen towards him, determined to assume the offensive, and to pick up for Prussia what he could out of the ruins of the empire. While the Elector of Bavaria claimed the Bohemian crown, which belonged essentially to the Austrian Hapsburgs; while the King of Sardinia claimed the duchy of Milan; and the imperial crown itself was claimed by no less than three hostile and powerful rivals, Frederick put in his claim to the province of Silesia, which he asserted to be his by virtue of some right which it is difficult now to follow. His claim being refused, he poured his fine troops into Silesia, and conquered the province, ofering the empress-queen, however, to support her against all claimants to the empire, if she would confirm him in the possession of Silesia. She refused, made an appeal to the nationalities under her for help, and in spite of French, Spanish, Prussian, and Bavarian armies, which swarmed about her territories, presented a bold front, and resolutely set herself to work to overcome her difficulties. By the aid of British money and British troops, Maria. Theresa held her ground, though she was forced, as the price of buying cessation from Prussian attacks, to consent, after a brilliant victory gained by Frederick, to confirm Silesia to him by treaty. The other belligerents were compelled by force of arms to agree to a peace which for a while gave rest to Germany. In 1756 broke out the Seven Years' War. The situation in Europe had changed. Maria. Theresa was dead, and the interests of England required that she should ally herself with the King of Prussia rather than with his foes; while the French, glad of any support against England, with whom she was engaged in a chronic war, joined their forces with those of Austria. Hanover, in the British interest, sided with Prussia; Saxony sided with the empire. The time seemed to have arrived for humbling orussia, and for wresting Silesia again from her grasp. Frederick saw the storm coming, and being always ready, anticipated its arrival by himself invading Bohemia. Now came the tug of war. By fine generalship Frederick made the whole of the Saxon army, encamped at Pirna, lay down its arms, and defeated ..". the imperial forces which were hastening to its relief. This was on October 1, 1756. In the spring of the following year, the Austrians and French were ready. The latter began to march on the southern frontier of Prussia; the former, under Prince Charles of Lothringen, and Field-marshal Broune, moved to attack the Prussians, and came up with them at Prague on the 6th of May. The Austrians lost 24,000 men, the Prussians 18,000, and the Prussians remained victors and masters of the field. Six weeks afterwards the battle of Kollin was lost by Frederick, with a loss of 14,000 men, after a contest of eight hours' duration; and to this succeeded a number of battles, now between Prussians and Austrians, now between Prussians and Austrians allied with Frenchmen, now between Prussians
almost always against the Prussians, who supplied the want
of numbers by the desperation which naturally inspires men
fighting for actual existence, and who on several occasions
achieved wonderful success, considering the proportion of
enemies opposed to them. At Leuthen (5th of December, 1757),
when the Prussians, under Frederick himself, were 32,000
against over 80,000 of Austrians, Bavarians, and Wurtem
bergers, under the best generals of the day, the Prussians
gained a decisive victory. Six thousand of the conquerors fell,
but were revenged by the loss of 27,000 of the enemy, who also
lost 116 guns and 51 flags; and of the strong Austrian army
which had begun the campaign, only 37,000 reached Bohemia.
Breslau, with a garrison of 18,000 men, surrendered, with
all its stores and its military chest, to a force which did
not number more than about 14,000. In other principal
battles the Prussians were now victorious, now ruinously
defeated, and more than once Berlin was occupied by hostile
troops, and the capital of Prussia suffered the penalty of its
king being at war with barbarians like the Russians. At
Kunersdorf, on the 12th of August, 1759, Frederick experienced
the greatest defeat he ever sustained—his army, nearly half
the numbers of the Austrians and Russians, was beaten
with the loss of nearly half its complement, of 170 guns,
and 28 colours. It was a crushing defeat. But the spirit
of Frederick was of the “no surrender” kind; and though,
after this reverse, it seemed impossible for him to hold his
own, and though his kingdom was exposed to all the horrors
of invasion, he remained firm, gathered up his forces for
another effort, and in August, 1760, overthrew the Austrians at
Liegnitz with dreadful slaughter, and with great loss of cannon
and military trophies. From this time to the end of the year 1762 the war went on with varying success, but the Prussians,
aided by British subsidies to the extent during the seven
years of £112,000,000, managed on the whole to win the
mastery. On the 31st of December, 1762, France and Russia having withdrawn from the contest, the representatives of Prussia, Austria, and Saxony met at Hubertsburg, and
arranged the basis of the Treaty of Paris, which restored peace on the basis of mutual restitution of conquests.
Prussia gave up her hold on Saxony, and Austria consented to the integral union of Silesia with the new kingdom of Prussia.
This kingdom entirely changed the whole character of its relations to the other European powers. It came out of the war a recognised entity—a thing capable of being cultivated and of growing ; it had no longer a doubtful or precarious status. Moulded by the second King of Prussia, perfected by the third, it grew in the interval between the Seven Years' War and the wars of Napoleon into avery considerable power, second only in Germany to that still wielded by the house of Austria. The Seven Weeks' War of 1866 has shown what use Prussia, has made of her opportunities since 1815; has proved not only that she is more than a match for her pristine master and later rival, but also a respectable foe for that ambition of France which would include all south of the Rhine within the French dominion, and would desire to claim for itself the right of the strongest among the nations of Europe.
LESSONS IN ENGLISH.—XXXVIII.
IT has been intimated that the French, Italian, and Spanish (and one or two others might be added) are, under the name of the Romance languages, very similar to each other, and similar also to their common mother the Latin. To all these languages the English is indebted. Hence it becomes both interesting and important to see how they are related one to another; and that the rather, because with comparison much may be learnt of the origin and propagation of languages. We therefore place before you a tabular view of
THE LoRD's PRAYER IN
and Frenchmen combined with Russians. The odds were
English. Latin. French. Italian. Spanish. Our noster notre nostro nuestro. Father pater père padre padre. Who qui qui che que.
Art es es sei estas.
In in au in en. Heaven coelo ciel cieli los cielo"
sanctificetur < soit
nos, no. en,
Italian, Spanish. Doge, the chief magistrate in Venice. Sonata, a tune. Hallowed
sanctifié sanctificato sanctificado. Mezzotinto, engraving resembling Piano, soft in music, Be
Forte, strong in music.
Bandit, one outlawed, a robber. Piazza, a talle under a roof sup. Name
ported by pillars.
il tuo el tu. Kingdom regnum règne
ENGLISH WORDS FROM THE SPANISH.
reino. Come veniat
Mulatto, one of mixed breed, Gala, feasting and merriment, Thy tua ta
Armada, a sea-armament,
volonta voluntad Tobacco, a plant used for smoking. Brocade, silk interwoven with gold,etc. Be
Guitar, a stringed instrument of Olio, a medley.
Palisade, an enclosure of palings, On in
Peccadillo, a petty fault.
Barricade, a rough street fortification, As
From very various sources words have come into our English. It sicut comme
Razzia is a very recent term. It came into existence within the In in
last few years, to describe the sweeping destruction with which Heaven colo
the French laid waste whole districts of northern Africa, in order Give da donne dacci da.
to bring the country under their usurpation. According to Us nobis nous oggi
Fuller, the term plunder is of German origin, and was brought This
hither by the soldiers who returned from the campaigns of Day aujourd'hui
Gustavus Adolphus. Our nostrum notre
il nostro nuestro. From the Arabic we have divan, vizier, cipher, zero, arabesque; Daily quotidianum quotidien quotidiano de cada dia, from the Hebrew we have, besides very many proper names, Bread panem
el pan. And
Jehovah, amen, Jeremiad, lazaretto, lazar-house, cherub, serapk, et
y. Forgive remitte pardonne
hallelujah. The birds called canaries take their name from the
remettici perdonn. Us nobis
Canary Isles, and our pheasants from the Asiatic river Phasis,
nos. Our nostra nos i nostri nuestras.
the banks of which are said to have been their original home. Debts debita offenses debiti deudas. Philippic, an invective, comes to us from the title of the orations As ut comme
come como. delivered by Demosthenes against Philip, King of Macedon, We nos
nosotros. of whose designs against the liberty of Greece he was aware. Forgire remittimus pardonnons rimattiamo perdonamos. The word cabal has two origins. In one sense, and generally, Our nostris à ceux qui a nostri a nuestros.
cabala is Hebrew, and denotes the science (falsely so called) of Debtors debitoribus nous ont offensé debitori deudores, And et
the Jewish rabbis. In another, it designates a political intrigue, et
y. Lead inducito indui
and owes its existence to the initials of the names of Clifford, Us nous
Ashley, Buckingham, Arlington, and Lauderdale-C. A. B. A. L., Not neve ne point non
the five celebrated cabinet ministers of Charles II. We have Into in
in English words the names of natural objects, taken from Temptation tentationem tentation tentatione la tentacion. the names of the places where the objects were produced : But sed mais ma
for example, peach, Fr. pêche, that is Persh, or Persian ; BergaDeliver libera delivre liberaci
motte (Bergamum), Indigo, Mocha, Champagne, Burgundy, Us nos nous
Madeira, Port, and other names of wine. We have names of From
de. Evil malo
the products of art taken from the places where they were mal male mal.
fabricated : for example, bayonet, invented at Bayonne, in France; Now, to study this tabular view properly, take each English cachemir (shawls), from Cachemir, in India; cambric, from word in turn, and compare it with the same word, first in Latin, Cambrai, in France ; cordovan, leather prepared at Cordova, in then in French, then in Italian, and then in Spanish. You will Spain; damask, from Damascus, in Syria ; muslin, from Mossul
, gain instruction if you also alter the order, taking the Italian in Asiatic Turkey; nankeen, from Nankin, in China; pistol, from before the French, or the Spanish immediately after the Latin. Pistoia, in Tuscany; marocco (leather),
from Marocco, in Barbary. Now look at these words, father, pater, padre, padre, père. They Having shown the connection of the English with the Romance are, you see, the same term under small modifications. The languages, we subjoin another table, showing its connection with same is the case with several other words. And if you omit the Teutonic languages
. The latter is the more needful, because the English, as belonging to a different family of tongues, and the latter are our cousins-german. compare the rest together, you will find, with a few exceptions, an almost identity. In the comparison you must make some
THE LORD'S PRAYER IN TEUTONIC LANGUAGES. allowance for idiom; for instance, the article appears in French Common English of German of Lower German Gothic where it is not placed in Italian, and so you have la terre, The English. Wiclif (1380). Futher. Saxon (1451). (720 A.D.). Uphilas (300). earth, for terrâ, earth, of the Latin, and terra of the Italian. Our oure
unsar. The Spanish carries the article so far as to place it before Father fadir fater fader fatter atta.
thee possessive pronouns, thus, el tu nombre, the thy name.
de du The
thu. Art art
bist inferiority, too, of the French is seen in that it is unable to
in in. render word for word “forgive our debtors," and is obliged to
Heaven hevene dem himmel den hymelen himele himinam. employ a circumlocution, as "pardon those who have offended Hallowed halowid geheiliget gehylliget us." These remarks are offered merely as suggestions relative Be be
wihi to the manner in which the table may be studied.
dinan thein. A few instances of words in our tongue borrowed from the Name name
name namnn namo. Italian and Spanish are subjoined :
Thy thi dein dyn
Kingdom kyngdom reich ryke rihi thiudinassus. ENGLISH WORDS FROM THE ITALIAN,
Come come to komme to comme chweme quimai.
din theins. Bravo, one who murders for hire. Tenore, middle sound.
wille willo wilja.
wairthai. Canzonet, a little song.
don Capuccio, a capuchin or hood. Violoncello, a bass violin.
in Busto, a statue.
Pantaloon, the buffoon in a panto- Earth erthe erden der erde erdu airthai. Canto, a section of a poem.
mime. Burletta, a musical farce. Harlequin, an outdoor buffoon. It
wie also so swe jah. Broccoli, a kind of cabbage. Gondola, a small boat.
in in. Camisado, an attack in the dark. Gonfalon, a standard.
Henven heavena himm den hymmele himele biminata, Piano-forte, a musical instrument. Gonfalonier, a standard-bearer.
gib gif bip gif.
Common English of German of Loncer German Gothic of that is, bodies which have organic analogies, but which are made English, Wiclif(1380). Luther. Saxon (1451). (720 A.D.). Ulphilas (360). by synthesis. For instance, oralic acid, which is purely a vegeUs to us uns uns uns uns. table product, being the acid which imparts the sour taste te This this heute hyte hintu himma. sorrel, lichens, and other plants, can be produced by heating Day day daga. mercuric cyanide, and allowing the cyanogen to pass into water. Q: oure tion Hon. ois unsarana. Here it is dissolved, and the two compounds react on each : breed :. .. ike jo hlaif. :::::::::::opod One of the products is ammonium : +/ ‘’s “2-3* to. :* *::: oblaz †. - Upon the addition of a mineral acid, oxalic acid is t’s to us uns Tuns uns turns. liberated. - - Our oure unser unse unseero thatei. Or perhaps a more remarkable example is the manner in which Debts dettig schuld schulde sculdi skulanosijaimo. Berthelot built up alcohol from its elements. He caused a As as wie alse so swaswejah. current of galvanic electricity to pass between charcoal points in we we . wir wy wir wels. an atmosphere of hydrogen. By this means the carbon of the * to." vergeben o * to. points was made to combine with the hydrogen, forming * dor. ... semideneratulanemoum." acetylene (C.H.). By submitting this acetylene to the action of Lead lede führe enleyde firletti briggais. nascent hydrogen when it was in combination with copper, two Us us uns uns unsih uns. atoms more of hydrogen were introduced into the compound, Not not micht nicht ni ni. and ethylene (C.H.) was produced. With sulphuric acid C.H.SO, Into into in in in in. is formed; and when this is diluted and distilled, alcohol is Temptation temptacioun versuchungbekoringe khorunkafraistubnjai. liberated. But but sondern sonder uzz .. ak. . Every year adds to the list of organic bodies which can be * * :* . † lausei. built up by inorganic processes; yet the distinction between From from . o }. * the two divisions of Chemistry is not thereby impaired. Eril yvel dem ûbel obele ubile ubilin. 2. Organic Chemistry is the Chemistry of the carbon compounds.
This table is full of instruction. Go through it carefully word for word, making due allowance for diversity of spelling. For instance, our word come re-appears in come to, comme, to comme, chtreme, and quimai. In the “bist” of the Lower Saxon, we recognise an old mood common in the south of England in our boyish days, where and when the present tense of the verb to be was thus conjugated, I be, thou bist, he bees, we *, on be, they be. The Gothic of Ulphilas offers the most striking points of comparison. We will go through it, and point out the words which still form a part of the English tongue:– Unsar, our; thu, who ; in, in; himinam, heaven; weihnai, ored; thein, thy; namo, name; quimai, come; wilga, will; ana, on; airthai, earth; gif, give; uns, our; daga, day; unstana, our; hlaif, loaf; briggais, bring; lausei, loose; af, of; abilin, evil. It is thus seen that our mother tongue had a substantive existence as early as the year of our Lord 360. And it is curious to observe that in this, the oldest form of the Teutonic languages, we find in several instances the nearest approach to or modern words and forms. For example, himinam, heaven; thein, thy, thine; airthai, earth; gif, give; uns, us; daga, day; Haif loaf, the ancient word for bread; briggais, bring; lausei,
LESSONS IN CHEMISTRY.-XXVIII.
"He characteristics of Organic Chemistry will be best shown by
Of the vast number of bodies which are considered under this subject, so widely different in their properties, one and all contain carbon. In most of them hydrogen and oxygen are combined with the carbon. Some also contain nitrogen, and a few contain other elements. No subject can better reveal the wisdom of the Mind which made all these things. It is wonderful indeed that, by ringing the changes on some four simple bodies, three gases and a solid, such an endless variety of different substances, all exhibiting different properties, can be produced. Since all organic bodies contain carbon, they are all combustible—all are destroyed by high temperatures. This fact is used as the basis of organic analysis. 3. Organic Chemistry is the “Chemistry of compound radicals.” This is Liebig's definition. In Inorganic Chemistry the compounds are generally made up by the union of elements, and the various changes which they undergo are produced by replacing one element by another, according to their atomicities. If in these changes elements only were concerned, then there would be a clear line between the two branches of the subject, but this is not always the case. Thus— AgNO, 4: NaCl = AgCl4 NaNO,. Here the NO, acts as an element, being a molecule, or, in the language of Organic Chemistry, a radical. The changes which take place in organic bodies are carried on by an interchange of radicals, which play precisely the same part as the elements in Inorganic Chemistry, having their peculiar atomicities, and the replacement taking place accordingly. For example, ethyle (C.H.) is monatomic. If the hydrogen of the water type,
# O, be replaced by this radical, we have § ) O, which is
those bodies which can be built up from their elements;
vary from each other by a fixed increment; so that formulae