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Believing the pupil now to be master of the method of draw. tone to be given to these portions of the shadow, the pupil mast ing a single line under any one of the conditions above named, be guided by his own judgment, which the more it is exercised whether straight or curved, we will proceed to apply them, or the keener will be his perception of the tone of a shadow or rather to combine them so as to form tints required in shading. reflection by comparing it with other shadows and reflections, Of course we can do little for the pupil towards helping him in for by comparison only we can undertake to say how dark er his judgment regarding the tones of shadows; his own observa- how light a tint must be. tion must be his guide in deciding how dark or how light a Fig. 87 is drawn from a cast of a geranium leaf, where a shadow is. Shadows and tones must be compared with one mixture of lines is employed, some more curvilineal than others, another, because the circumstances surrounding them will so far according to the rotundity of the surface to be copied; for it influence their intensity that it would be impossible to give rules must be observed that in proportion as a rounded surface ap for shadows under all conditions. They are so varied and so proaches the flat, so will it require straighter lines to reprechangeable that we can do no more than give him a few general sent it. principles to guide his practice.
In a former lesson we mentioned the stump, an instruWe have said before that cast shadows are, for certain reasons ment used for laying on a tint by rubbing; this may be used already given, generally darker than broad shadows; we will for the first instalment of a shadow, that is, for rubbing in add now that the highest light and darkest shadow are together; a flat tint over the broader and more decided parts of the and as the strength of the light upon an object or collection of shadow, the whole being afterwards passed over by the line objects gradually diminishes, so the depth or intensity of the method. In using the stump, the tint must not be made as dark shadows diminishes also. Take an example :-Place a chair as the shadow ought to be when finished, nor must it be carried near to a window, and another chair in the part of the room into the half tones uniting the shade with the high light. An farthest from the window; the light which falls upon the chair effect can be much more readily produced wi the stump, bat near to the window will be much stronger than that which falls the danger is lest the shadows should be made dirty or cloudy. upon the farther chair. Observe the broad shadows and the cast After a little experience this method will be found to be quicker shadows from the legs upon the ground, the latter especially, of the than doing it altogether by lines, inasmuch as it saves a little first chair. Compare them with the corresponding shadows of the labour; but the shadows must be passed over with lines after second chair, or that farthest from the window. We venture to the stump has laid the foundation, otherwise all the crispness, say, without more comment, that the pupil will have seen enough clearness of tone, and definite precision of character will be from this experiment to satisfy him upon this point. This prin- sacrificed. We strongly advise the pupil to provide himself ciple of the darkest shadow being near to the highest light is with a few plaster casts of leaves, fruit, and ornament. The found to be the same respecting the shadow on a ball (Fig. 85), advantages of casts are many. They can be placed in any light
, or on the side of a column (Fig. 86), and in thousands of cases and they present so many different views that they may be said besides, so numerous that we need not look far for examples. to be inexhaustible copies. The great difficulty in shading is the management of the half tints. Any one can make an extreme shade of black; and if the right LESSONS IN ENGLISH.-XII. feeling for half tints and semi-tones is not a natural one-something analogous to that of a good ear for music-it can be
DERIVATIONS: PREFIXES (continued). to a great extent acquired, though in some cases it will demand PAUSING for a moment in the details of our subject, I would a much greater amount of practical experience and observation ask you whether you know what words are. Take the word than in others before they begin to perceive the many va- father. What is it? Father, as it stands here on the page, is rieties of tone which are spread upon the surface of an object, a combination of straight and curved lines. What does the especially if it be an irregular one. But when we have to add combination of lines represent? A combination of sounds. colour in connection with light and shade, we go farther into a What does the combination of sounds represent?. A state of field of change and variety that is unbounded. And here is the mind; a mental conception. What does the mental conception test of the painter. It is the management of the minor tones represent ? An external object; an external object that has the which makes all the difference between a first-rate artist and a quality of being a father, or that bears the relation which wə common country sign-painter. The latter may paint a red cow designate by the term father. So then the whole connection sufficiently well to answer the purpose of giving a title to the between an external object and the written or printed name of village alehouse. We will grant that he has the ability to make this book may be set forth thus :-Lines make letters ; letters a tolerable representation of the animal in outline, but when he make syllables; syllables make words ; words represent sounds ; attempts to paint it he will do nothing more than fill up the sounds represent ideas; ideas represent outward objects—that outline with red, and darken the parts in shade with black, is, persons or things. Consequently, objects are the basis of because he can see nothing further; but the eye of the true language ; ideas are its essence ; sounds are its medium, ani artist would seize upon the innumerable tints spread all over the lines are its forms. These outward objects, and internal realities, surface—the various degrees of colour influenced by the position are set forth by signs, --signs made by the mouth-signs made and strength of the light, some parts more brilliant, some more by the hand. The lips, then, and the fingers are the intersubdued, intermingled with greys of various hues in every preters of the person. What progress in civilisation is implied portion--added to which are the reflections of colour and of in this connection of the pen with the mind and with the universe; light amongst the shadows, some warm, some cold : in short, to the pen describing, and the press diffusing, so as to be univer name all the changes and tones that would require his especial sally understood, the most subtle of all essences ; states of attention can only be done by him who is able to paint them. thought and feeling ; and the widest, as well as the wisest of Here, then, is the secret why one painter is greater than all generalisations which we term the laws of God, or God's another; and their comparative excellence is determined by their own operations in the government of the universe! The study of ability to perceive and represent few or many of the infinite language, thus viewed, is the study of the mind of man, as well varieties of tones scattered over every object in Nature.
as the study of the works and the will of God. Deep and mys. It will be readily seen, on referring to Figs. 85, 86, and 87,where terious study, worthy of our best powers, and sure to be curved lines in working the shadows are used in preference to attended by an ample reward! And if the study of language is straight ones, and, on the contrary, where straight are preferred the study of the human mind, and the Divine mind in their to curved ; curved lines must be used to represent curved sur. activity and their utterances, then no one who has not made faces, either convex or concave. The ball (Fig. 85), is altogether some proficiency in the study is, or can be, competent to inte shaded by curved lines, which render such important service in pret or expound man's will or God's will, profane or sacred giving effect to rounded forms. Straight lines are the principal literature. To resume our subject : composing lines of the shadow on the cylinder (Fig. 86). On Olig, of Greek origin (oxiyos, pronounced ol'-i-gos, a few), is the account of its uniformity of surface and because it is perpen- first part of oligarchy (Greek, apxn, pronounced ar'-ke, government)
, dicular, perpendicular lines are employed; whilst the apparent government by a few; oligarch, one of a small number of rulers. rotundity of the cylinder is made to depend upon the tone of the Omni, of Latin origin (omnis, all), is seen in omniscient (Latin, shadow rather than upon the lines which compose it; the shadow scio, I know), all-knowing ; omnipotent (Latin, potens, powerful), having its reflection, its deep shade, and its half tint, the last all-powerful; omnipresent, existing everywhere; omnivorous, al. blending into the highest light. As to the proper strength of devouring.
Ortho, of Greek origin (Greek, opdos, pronounced or'-thos, Paradise is a' Persian word, denoting a park, and has no constraight, right), as in orthodoxy, right opinion; orthogonal, right- nection with the Greek para ; in Hebrew, pardes, a garden. angled; orthopædic, right-footed, etc.
Par, of Latin origin (pars, partis, a part), appears in partici" Athanasius is commonly accounted the very rule of orthodoxality pate (Latin, capio, I take) -—that is, to partake. This word par. in this point."-Cudworth, “ Intellectual System."
take is a hybrid, being formed of an English and a Latin word; This prefix forms part also of orthography (Greek, ypapn, pro
it is therefore a cross in the breed between Latin and English. nounced graf'-fe, writing), right writing, that is, in the spelling
Pent, or penta, of Greek origin (TEYT€, pronounced pen'-te, five), of words; as orthoepy (Greek, enos, pronounced ep'-os, a word) is the name given to what are called “the five books of Moses
as in pentagon, a figure having five sides; Pentateuch (fivefold), right pronunciation. Over
, of Saxon origin, as in overarch, overbalance, overbear, namely, Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. overcharge, overboard, over-boil, over-bounteous, frequently de- It is found in perambulate (Latin, ambulo, I walk), to walk
Per, of Latin origin, through, by; as, peradventure, by chance. noting too much, as over-careful, that is, careful to excess. Overcome has two significations, to conquer, and to come over
through, over. or upon.
“ The ancients used to crown virgins with the flowers of this plant "He found the means to subdue both the one and the other, com- thereto." -Miller, "Gardener's Dictionary.”
(milkwort) when they perambulated the fields, to implore fertility pelling as well the overcomers as the overcome to be his tributaries." — Brende, “ Quintus Curtius."
The per passes into pol in pollute (Latin, polluo, per, and lutum, Can such things be
mud). Pol is found also in pollicitation, a promising, from the And overcome us like a summer's cloud,
Latin polliceor, I promise.
Peri, of Greek origin (Tepi, pronounced per'-re), meaning around; Over when employed for above, as “ over two hundred,” is to be as, periphery (Greek, pepw, fer'-ro, I bear), a circumference ; avoided as an Americanism. To overtake is to come up with in also in periphrasis (Greek, ppaois, fra'-sis, a phrase, a speech), walking or running.
a circumlocution, or roundabout mode of utterance; as, the " And had he not in his extremest need
loss of life, for death. Been helped through the swiftness of his steed,
Phil and philo, of Greek origin (piros, fill-los, a lover), as in He had him overtaken in his flight."-Spenser.
philologer, a lover of science (particularly the science of lanIn the passive the verb overtake seems to denote the being sud- wisdom; philomel (Greek, melos, mel-los, a song), applied to
guage); philosopher (Greek, copia, sof'-i-a, wisdom), a lover of denly surprised into an action ; surprise is from the French sur- the nightingale; philanthropy (Greek, av@pwtos, an-thro'-pos, a prendre consisting of sur, above or over, and prendre, to take), man), the love of mankind. whence surprise is the same as overtake in both derivation and
Phys, of Greek origin (Greek, puous, fu'-sis, nature), physic, meaning.
and physician, originally meant natural philosophy and a natural "Brethren, it a man be overtaken in a fault."-Gal. vi. 1.
philosopher; but derivatively, the words came to refer to a It is not difficult to see how to overtake may mean to get over, knowledge of such natural objects as were held to conduce to overcome, surprise, but how it means to come up with is less the art of healing. Physics, plural, still means Natural Philoeasy to conceive. The notion of over, or of superiority may, sophy; and the French word physicien means a Natural Philohowever, lie in the act by which you succeed in coming up to sopher, or one acquainted with the laws of nature. the person you wish to overtake; thus, by walking more quickly
Physiognomy consists of the Greek words quois, fu'-sis, nature, than he, you overtake your friend, you take a step over his, and and yyywow, gi-no-sko, I know; and so properly denotes a get beyond him.
knowledge of nature by outward appearances; but, as employed, Out, of Saxon origin, beyond a certain limit, is a very common the word signifies a knowledge of a man's character, as gained prefix, as in outbid, outdo, outface, outlaw, outlive, outstrip, etc. from his countenance. Physiology is the science of nature, but Outrage has nothing to do with out. Outrage comes from the in a particular way; a science, that is, of the structure and laws mediæval Latin word ultragium, through the French oultraige, of the human frame in particular, and of animal organisation in outrage. Ultragium, from ultra, beyond, denoted & surplusage
general. paid to the lord by his subject on failure of paying his dues in “ I find that the most eminent and original physiologist of the present proper time, whence outrage came to signify something in excess age (M. Cuvier) has been led, by his enlightened researches concerning and to have an offensive meaning.
the laws of the animal economy, into a train of thinking strikingly Pan, of Greek origin (tas, pas, m.; hara, pa'-sa f.; tav, pan, n., similar."— Dugald Stewart, “ Philosophy of the Mind." all), is found in panacea (Greek, akeojai, pronounced a-ke'-o-mi, Pleni, of Latin origin (plenus, full; hence plenty), is found in I heal), all-heal, a universal remedy; in pancreas (Greek, kpeas, plenipotentiary (Latin, potens, powerful), one who has been pronounced kre'-as, flesh), all flesh-that is, the sweetbread ; entrusted with full power or authority. and in pandects (Greek, dexouar, pronounced dek'-o-mi, I receive), a common title of the Greek miscellanies. The term is known matic sophisters of France in what manner right is to be corrected by
“Let tho plenipotentiary sophisters of England settle with the diploin history in its application to a digest of the civil law published an infusion of wrong, and how truth may be rendered more true by a by the Emperor Justinian. Again, pan occurs in pantheism due intermixture of falsehood." —Burke. (Greek, deos, pronounced the'-os, God), all-goodness—that is, the system which regards God and the universe as the same. Pan
The Greek word meos (ple'-os) is the same as the Latin plenas, forms the tirst part of pantomime (Greek Millos, pronounced found in our “plenty.” This word supplies the first syllable in mi'-mos, a mimic; and the word mimic is from mimos), all. pleonasm, a fulness of expression so as to become excessive. mimiory, because the performance consisted solely of imitation. “It is a pleonasm, a figure used in Scripture, by a multiplicity of
“ The pantomimes who maintained their reputation from the age of expressions, to signify some one notable thing."-South. Augustus to the sixth century, expressed, without the use of words, Poly, of Greek origin (Tolus, pol'-use, many, much), appears the various fables of the gods and heroes of antiquity; and the per in polyanthus (Greek, avôos, an'-thos, a flower), so called from section of their art, which sometimes disarmed the gravity of the phi- its many flowers; and in polygamy (Greek, yauos (gam'-os], losopher, always excited the applause and wonder of the people."Gibbon, “ Roman Empire."
marriage), having many wives. Para, of Greek origin (tapa, pronounced par-ra, by the side of,
" Polygamy was not commonly tolerated in Greece, for marriage as in parallels, i.e., parallel lines), has in English various accepta
was thought to be a conjunction of one man with one woman."-Potter,
“ Antiquities of Greece." tions. In parable (Greek, Bartw, pronounced bal-lo, I throw), something put by the side of another thing, a comparison, a Poly is also the first syllable of polyglot (Greek, gwtta, gloat'-ta, similitude. In Scripture, the parables of the Old Testament are a tongue), one who knows many languages; also a book written short, pithy, and weighty sayings; the parables of the New in many languages, as the “ Polyglot Bible.” Testament are short tales, setting forth religious truth under Post, of Latin origin, after, afterwards, appears in postdate, similitudes; the former are apothegms; the latter allegorios. to date after the time of writing, at some later time; in postpone Para appears in paraclete (Greek, kaleiv, pronounced kaline, to (Latin, pono, I place), to put off ; and in postscript (Latin, call), the Advocate or Comforter (John xiv. 16).
scriptum, a writing), something added to a letter.
Postumous, erroneously spelt posthumous, from the Latin postu- explorer was not successful in penetrating as far into the mus, the same as postremus (from post, after), signifies late, very interior as he intended, and another journey will be necessary late, the latest, the last. This word is applied to a child born to ascertain from what sources sustenance is derived by the after the father's death, or a book published after the author's herds of deer that come from the interior of the country to the death.
coasts at certain periods, and after a short stay return onoe Sometimes the word is spelt posthume, for postume. We more to their yet undiscovered haunts. In Alaska Mr. Frederick have here an instance of the effect on spelling of a supposed Whymper, an artist attached to the late Russo-American Tele. etymology. Postume was thought to be composed of post, after, graph Expedition, has been more successful, having advanced and humus, the ground, and hence the word was written post more than 1,200 miles into the heart of the country along the hume. It is, however, the superlative of the Latin posterus, course of the Kwichpac or Youcon River, a magnificent stream and is used in the Latin language with the same applications as that discharges its waters into the ocean nearly opposite the in English. Richardson is wrong in the etymology which he Isle of St. Lawrence, that lies like a breakwater across the gives of this word.
entrance to Behring Strait, between the opposing coasts of Asia Pre, of Latin origin, before, as in precaution (from Latin, and America. cavere, to beware), forethought.
Mr. Frederick Whymper's journey into the interior of Alaska “Precaution trudgeth all about
was made in 1866-7. He travelled by sledge from Norton To see the candles fairly out."
Sound, a deep inlet to the south-east of Behring Strait, to the Churchill, “ The Ghost.”
banks of the Youkon River, spending the winter months at Pre is found in precede (Latin, cedo, I go), in precipitous (Latin, Nulato, the last of the trading ports that the Russians have caput, the head), headlong; in precocious (Latin, coquere, to established along the course of the river and the interior of the cook), cooked before, forward, too soon ready.
country. In the spring he re-commenced his journey, and made “I had heard of divers forward and precose youths, and some I his way up the stream in a boat, consisting of a framework have known, but I never did either heare or read of anything like to covered with skins, to a point about 600 miles distant from this sweete child.”-Evelyn, "Memoirs."
Nulato, where the Porcupine River enters the Youkon. He then turned, and descended the course of the river to the sea.
The Youkon is navigable for 1,800 miles from its embouchure LESSONS IN GEOGRAPHY.-XI.
during the summer months, but for at least eight months of the
year it is frozen over. The natives on the coast are Esquimaux, In our last lesson it was stated that it is generally believed while in the interior, and on the banks of the river, parties of by geographers in the present day that the southern pole of Indians are occasionally met with. Public attention has recently the axis on which the earth revolves once in the course of been directed to Alaska, formerly Russian America, on account every twenty-four hours, is situated in the midst of a vast of its sale by the Russian government to the United States in continent to which access is forbidden by the masses of ice 1867, for the sum of 7,000,000 dollars, or about £1,400,000. that fringe its coasts, and the steep rampart of volcanic Some hundreds of miles lower down the west continent of mountains that rises abruptly from the very edge of its shore. North America, a little to the north of the boundary line The northern pole of the earth's axis, on the contrary, is between the British dominions and the United States, lies a supposed to be in the midst of an open ocean, navigable by broad belt of forest land and fertile pasture ground, watered vessels, if a ready and practicable means of entrance to its by the head-streams of the Saskatchewan and the Red River, waters could be found through the iee-fields that encircle it. which stretches from the western confines of the new dominion Possibly we are on the eve of solving the problem, and dis- of Canada to the Rocky Mountains. This region was visited by covering with certainty what may be the condition of the Viscount Milton and Dr. Cheadle in 1861-63; the expedition regions that lie around the North Pole, for an expedition being “undertaken with the design of discovering the most thither is preparing under the anspices of the French Govern direct route through British territory to the gold regions of ment, which will in all probability set out for its destination Cariboo (in British Columbia), and exploring the unknown in 1869, under the command of its originator, M. Gustave country on the western flank of the Rocky Mountains, in the Lambert. It is M. Lambert's intention to avoid the routes neighbourhood of the sources of the north branch of the Thomptaken by former explorers, and to push his way to the north son River." This expedition has furnished us with much through Behring Strait.
valuable information about a country that has hitherto been To tell the story of Arctic explorations since Sir John entirely abandoned to Indians and trappers, but which contains Franklin left England on his third expedition of discovery to upwards of 65,000 square miles of land, of unsurpassed fertility, the north in 1844, to die three years after on the dreary wastes abounding in mineral wealth, and which is destined to become, of King William Land, hard by Point Victory-an apt name at no very distant period perhaps, one of the principal centres for the last resting place of a man to whom belongs the merit and of British colonisation, affording the true north-west passage honour of having discovered the “north-west passage from by land from Europe, through our colonies of Canada and British England to the shores of Asia by sea——“barren honour as it is Columbia, to the splendid harbours of Esquimault and the great and must be to all save himself and his companions, as its dis- coal-fields of Vancouver Island, which offer every advantage for covery can never be attended with results useful to commerce the protection and supply of a merchant fleet trading thence to would occupy too much space. It will, therefore, suffice to say India, China, and Japan. Our illustration* will give the reader that of late years the most active and successful explorers of some idea of the beauty and grandeur of the scenery on ihe eastern the regions that lie north of the line of waters that stretch from slope of the Rocky Mountains. It is a view of the valley Dear Baffin Bay on the east to Banks Strait on the west, are Dr. Jasper House, or Fort Assiniboine, a little trading station on the Elisha Kent Kane and Dr. Isaac J. Hayes. Both of these bank of the Athabasca or Elk River, which emerges from the travellers are Americans, and both have received a gold medal heart of the Rocky Mountains through a narrow gorge near this from the Royal Geographical Society as an acknowledgment of point, and expands into a lake about three or four miles long, the eminent services rendered to geography by their discoveries the shores of which are beautifully wooded with clumps and -the former having received the Founder's Gold Medal in clusters of dark-green pines, and covered with luxuriant verdure, 1856, for his services in connection with the American expedi- In the background, on the right of the picture, is an ice-capped tions sent out in search of Franklin in 1850 and 1853, and conical mountain called the Priest's Rock, which forms a prothe latter the Patron's Gold Medal in 1867, for his memorable minent feature in the landscape, while on the left is seen the expedition in 1860-61, towards the supposed open polar sea, in flattened top and profile of a steep ascent rising almost perpen. which he attained lat. 81° 35' in Smith Sound, a more northern dicularly from the plains below, called the Roche à Myette. point of land than has been reached by any previous navigator. Passing still southwards through the United States--the
Coming southward from Smith Sound, up which Dr. Hayes western parts of which are now being opened up by strong and penetrated to within 9° 25', or somewhat less than 600 miles of resolute backwoodsmen from the outlying districts of the Central the North Pole, we have Greenland or Danish America on our right, which was visited by Mr. Edward Whymper, a well- * This illustration is taken from the "North-West Passage by known Alpine explorer, in 1867. Owing to an epidemic, which Land," by Visconnt Milton, M.P., and Dr. Cheadle. had carried off about ten per cent. of the population, this Cassell Petter & Galpin.
States, the pioneers of advancing civilisation and through Mexico | the Tapajos River, another vast tributary of that river, which -the most ill-conditioned country under the sun, as far as its drains the central and northern part of the province of Matto people are concerned, yet in itself fair, rich, and fruitful, and Grosso. worthy of being the home of an energetic and industrious race, Of the semi-organised republics of South America, which have instead of a paradise of thieves and cut-throats—we come to scarcely recovered the effects of the revolution which separated Central America, which deserves a passing mention here for the them from Spain in the first quarter of the present century, and explorations of Captain, now Admiral, Bedford Pim and others, which (especially La Plata, or the States of the Argentine Conwho are seeking to turn the stream of emigration setting steadily federation) have much to do in eradicating the sources of intesout from the southern parts of the United States into British tine discord before they can attain the condition of prosperous, Honduras, a country especially adapted for the prodaction of peace-loving countries, there is little or nothing new to say ; and cotton, sugar, and indigo; and the attempts that have been turning eastward across the Atlantic we reach the last of the six made to bring about the cutting of a ship canal across the great divisions of the world, the continent of Africa, in which narrow slip of land that separates Lake Nicaragua from the it is necessary to trace the history of geographical discovery waters of the Pacific, to form with the lake itself and the river since 1820. St. Juan & water-way through the isthmus for ships trading After the travels of Sportman, Shaw, Norden, Bruce, Lo from Europe and the eastern coasts of America to India, China, Vaillant, Mungo Park, and Horneman, which threw a flood of Japan, and the shores and thousand islands of the vast Pacific. light upon the geography of Africa in the last century, we
Southward yet a little further, and we come to South America, owe much to Adams, Tuckey, Bowditch, Mollien, Major Laing,
a continent of whose central regions little more is known with , and Messrs. Ritchie and Lyon in the present century. The any degree of certainty than has been yet learnt of the unex. labours of Messrs. Denham and Clapperton, and Dr. Oudney, plored heart of Africa. But even here travellers have been busy in exploring the interior of this continent in 1822, added conin collecting facts to add to our limited knowledge of these parts siderably to our knowledge of North-Central Africa. When we of the world's surface, for Mr. Henry W. Bates, the present look upon a modern map of Africa, all the geographical posiassistant secretary of the Royal Geographical Society, explored tions which are laid down in Bornon, roand Lake Tchad, the the countries on either bank of the mighty river Amazons between lake itself, the direction of the course of rivers in this region, the years 1848 and 1859, giving us a series of vivid and animated the rectification of the course of the Niger, and other topodescriptions of the habits of animals, sketches of Brazilian and graphical details, such as the position of mountains, etc., are Indian life, and aspects of nature under the equator, during due to the last-mentioned travellers. Clapperton closed his eleven years of travel, in his work entitled "The Naturalist on successful career by reaching Sockatoo from the Gulf of Benin, the River Amazons." Mr. Bates's researches have been ably and died in 1826, leaving his labours unfinished, after having supplemented by Mr. W. Chandless, who received the Patron's accomplished the remarkable journey from Tripoli to Benin, and Gold Medal in 1866 for his exploration of the river Purus, one enriched geography with a vast collection of new and accurate of the southern afluents of the Amazons, which he ascended discoveries. Timbuctoo, that singular object of African travel. for a distance of 1,800 miles, making, by observations as he lers, was reached by Major Laing in the same year, but at a proceeded, an accurate map of the windings of the river. Pre- later period, when he also paid the debt of nature. In 1830, rious to this journey of discovery Mr. Chandless had travelled Richard and John Lander undertook to resolve the problem of through South America from the head-streams of the Paraguay, the direction of the Niger from the point to which it had been a river which rises in the Brazilian province of Matto Grosso, traced by Park and Clapperton. They proposed to descend thọ and joins the Parana near the town of Corrientes, in the Argen- river along its course from Boussa, where it had so far been tine State of that name—to the mouth of the Amazons, down traced, and to follow its course to the Atlantic Ocean, in order to ascertain its embouchure. After encountering many and great able variation for an immense number of centuries. Now, it is dangers, they reached the sea by the central or principal branch found that this time is 365.24224 (i.e., about 365.25, or 3654) of the Niger, which is the river called Nun, and which disem. mean solar days, a solar day being the interval which elapses bogues itself into the Atlantic Ocean, between the Bight of between noon and noon—that is, between the times when the Benin and the Bight of Biafra. The source of this river, as sun is successively highest in the heavens.* determined by Laing, is at the foot of Mount Loma, in the The year is made to consist of 365 days-i.e., about of a day Kong Mountains. From this point to Timbuctoo its course was less than the time of the revolution of the earth in its orbit. known; but the brothers Lander made it known from Boussa To every fourth year (Bissextile or leay year, as it is called) one to the ocean, and so solved a part of the geographical problem day is added, and thus at the end of every four years the earth which had so long existed without a satisfactory solution. is again very nearly in the same part of its orbit as it was at the
beginning of them. We say very nearly, because the carth
actually revolves round the sun in 365.24224 days, which is less LESSONS IN ARITHMETIC.-XXI. than 365 days by .00776 of a day. This error in excess amounts
to a day in about 128 years—i.e., to very nearly 3 days in 4 CONCRETE OR COMMERCIAL ARITHMETIC. centuries. Hence, to make our reckoning still more accurate, 1. We have hitherto been concerned with what are called we omit 3 days in 4 centuries ; and this is done by making the abstract numbers—that is to say, numbers abstracted from their year which completes every century not a leap year, except such connection with any special thing, object, or magnitude ; and centuries as are divisible by 4. Thus A.D. 1700, 1800, and 1900 we have established all the principles connected with them are not leap years, but A.D. 2000—i.e., the year completing the which are necessary to be known by the student of elementary
twentieth century-is a leap year. arithmetic. We now proceed to apply these principles to con
The establishment of the leap year is due to Julius Cæsar ; crete numbers—that is to say, to numbers which indicate some
that of the omission of the leap year three times in 400 years to actual magnitude, object, or thing—as, for instance, time, money, amounted to ten days, caused the ten days which followed
Pope Gregory XIII., who, in the year A.D. 1582, when the error length, etc.
Theoretically, we are already in possession of principles which October 4th to be omitted in the reckoning. October 5th conenable us to perform any calculation with reference to any con
sequently was called October 15th. crete number. Take length, for instance. Suppose that we fix
This latter system, the New Style, as it is called, was not upon a certain length, and call it a mile. By means of this mile adopted in England until A.D. 1752, when the difference between we could measure any other length whatever. For by fractions this and the old mode of reckoning amounted to about eleven or decimals we could express any part or parts of a mile whatso- days. The difference between the old and New Style amounts ever; we could add, subtract, multiply, or divide any number of Christmas Day and Lady Day, for instance-010 Style, would
at present to about twelve days. Thus any fixed day – miles or parts of a mile, etc. etc. But it is manifest that, although this could be done, great inconvenience would arise
occur twelve days later than our present Christmas and Lady from the cumbrous nature of the operations. In treating, for Day, Russia is now the only country in Europe which retains instance, of fractional parts of a mile, it would be often very
the Old Style. difficult to realise the length indicated. What idea would most
Having, then, thus established a fixed invariable standard people have of ass of a mile? But if they were told that this whereby to measure time, we are enabled to make any further length is very nearly indeed equal to a foot, they would form a
subdivisions for convenience. very clear conception of the length. Hence, in measuring all
DIVISIONS OF TIME. magnitudes, the method of subdivision has been employed. 60 seconds
= 1 minute, written thus, 1 m., or 1'. Certain magnitudes have been fixed upon and named, and then 60 minutes
= 1 hour these again divided and subdivided, and names given to the 24 hours
= 1 day divisions, as convenience best suggested.
7 days Quantities expressed in this way by means of different sub- 4 weeks
= 1 common month divisions are called compound quantities. Thus, a sum of money,
12 calendar months, or
} expressed in pounds, shillings, and pence, is a compound quan
365 days tity. The names of the various subdivisions are generally called Any number of seconds are written either thus-35", 23", or denominations.
35 sec., 23 sec. 2. Accurate Standard or Unit.
It is better, however, in indicating time, to use the abbrevia. On proceeding to measure any magnitude or quantity, it is tions sec. and min. for seconds and minutes, inasmuch as the evident that it is of the utmost importance to come to an exact same names and the marks' and" are used for certain divisions definition of some one fixed magnitude of the same kind, with of the circle (Art. 18). which we may compare all such magnitudes. Such a fixed The Calendar months into which the year is divided do magnitude is called a standard. When this has been done, not each contain the same number of days. The number in then the standard can be subdivided, or multiples of it can be each month, however, may be remembered by the following taken, as we please, and names given to the subdivisions or lines :multiples. The subdivisions which are employed in England in the
Thirty days has September, coinage and weights and measures are, as might be expected,
April, June, and November; not founded upon one carefully prepared and philosophical
February twenty-eight alone
AU the rest have thirty-one ; system, but havo gradually grown up during long centuries,
But leap year comes one year in four, having often been suggested by special convenience or local
And February then has one day more. usage. The subject has of late received much attention, and the possibility and advantage of establishing a uniform decimal system of coinage, weights, and measures, have been discussed 4. Having determined, as above explained, an exact measure with considerable warmth.
of time, we are enabled, curious as it may appear, to deduce On July 29th, 1864, an Act of Parliament was passed to from it a fixed and invariable measure of length. We might, of render permissive the use of a decimal system of weights and course, take any object-a piece of metal, say—and, giving to measures called the “Metric System.” Contracts and transac. its length a particular name, thus obtain a means of measuring tions, therefore, based on this system are now legal. We shall, all other magnitudes. But this object, whatever it might be however, return to this subject hereafter.
and however carefully preserved, would be liable to be lost, to We proceed now to treat of the subdivisions of various con- alteration from decay, variation of temperature, etc. It is crete quantities which are now generally in use.
therefore very desirable to have some invariable and independent
= 1 week
= 1 year
MEASURES OF LENGTH.
MEASURES OF TIME.
3. The time of the revolution of the earth in its orbit can be times in the year rather longer, and
at others rather shorter, than its
* A solar day is not actually of unvarying duration, but is at some shown by the calculations of astronomical science to be an
average length. It is this average length of the solar day which is unvarying quantity, or, at any rate, to be subject to no appreci- called the mean solar day, and is divided into 24 hours.