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aujourd'hui ou demain ? 14. On nous dit qu'il doit avoir lieu are brought to me (R. 2] every day, but I have no time to read cette après-midi. 15. Il aura lieu à cinq heures et demie. 16. them. 7. What should one do (doit on faire) when one is sicki Avez-vous envie de venir au lieu de votre frère ? 17. Mon frère 8. One should send for a physician. 9. Do you send for my doit venir au lieu de notre cousin. 18. Avez-vous l'intention brother? 10. I am to send for him this morning. 11. Do you de lui dire ce qu'il doit faire ? 19. Il sait ce qu'il doit faire. | hear from your son every day? 12. I hear from him every time 20. Savez-vous ce qu'on dit de nouveau ? 21. On ne dit rien de that your brother comes. 13. Does the sale take place to-day ?

22. Trouve-t-on beaucoup d'or en Californie ? 23. 14. It takes place this afternoon. 15. At what time does it On y en trouve beaucoup. 24. Y trouve-t-on aussi des diamants ? take place ? 16. It takes place at half after three. 17. I have 25. On n'y en trouve point, on n'y trouve que de l'or.

& wish to go there, but my brother is sick. 18. What am I to

do ? 19. You are to write to your brother, who, it is said (dit EXERCISE 64.

on), is very sick. 20. Is he to leave for Africa ? 21. He is to 1. What do people say of me? 2. People say that you are leave for Algiers. 22. Do you come instead of your father ? not very attentive to your lessons. 3. Is it said that much gold 23. I am to write instead of him. 24. Does the concert take is found in Africa ? 4. It is said that much gold is found in place this morning ? 25. It is to take place this afternoon. 26. California. 5. Do they bring you books every day? 6. Books Do you know at what hour? 27. At a quarter before five.

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LESSONS IN PENMANSHIP.-XX. made in the form of a loop, the pressure of the pen being

relaxed, and the down-stroke narrowed gradually until it is The simplest method of writing the letter f, and that which is turned at the bottom in a hair-stroke, which is carried upwards most generally used in writing large-hand copies, is shown in and across the down-stroke about the line c c, or centre of Copy-slip No. 73. In this form, which is repeated in Copy-slip the letter, in a small loop. Sometimes the loop at the upper No. 74, where f is given in conjunction with other letters, it is part of the letter is omitted, the down-stroke being commenced commenced with a fine hair-stroke a little above the line cc, at the line ee (see Copy-slip No. 10, p. 60, for the height of which is carried upwards until it reaches the line kk, where it this line above a a), and thickened very gradually until it reaches us turned towards the left and brought downwards across the its thickest part about the line bb, when the pressure on the fine up-stroke, the pressure on the pen being gradually increased pen is immediately lessened to narrow the stroke into the fine until a thick down-stroke is formed, which terminates at the line that forms the loop below the line bb. Examples of the line gg. The letter is finished with a hair-stroke carried out methods of making the letter f that have just been described from the back of the letter, about the line cc, to the left, and will be found in future copy-slips. In Copy-slip No. 75 then brought to the right in a curve across the down.stroke. the learner will find the elementary strokes that form the la small-hand writing, the lower part of the letter f is generally i letter k.

49

LESSONS IN ARITHMETIC.—XIX. figures, we get the rest by dividing as in ordinary division by

the last divisor, 2828423. SQUARE AND CUBE ROOT (continued).

11. We might extract the square root of a perfect square by 9. THE square root of a fraction is obtained by taking the splitting it into its prime factors, but unless the number is not square root of the numerator for a numerator, and the square large this would be a tedious method. root of the denominator for a denominator. This follows at once EXAMPLE.—Find the square root of 441. from the consideration that the multiplication of fractions is Following the method given in Lesson VIII., Art. 5 effected by multiplying the numerators for a numerator, and the

3) 441 denominators for a denominator. When either the numerator or the denominator is not a complete square, in which case the

3) 147 fraction itself evidently has no exact square root, instead of finding an approximate root of both numerator and denominator in decimals, and then dividing one by the other, it will be better Therefore 441 = 3? x 72; of which the square root is 3 X 7, first to reduce the fraction to a decimal, and then to take the or 21. square root.

Obs.-Unless a number is made up of prime factors, each of EXAMPLE.—To find the square root of z.

which is repeated an even number of times, it is not a perfect

square. Reducing a to a decimal, we find it to be •285714 (see Lesson

EXERCISE 39.
XVI., Art. 21).
Hence we should find by the previous method the square root

1. Find the square root of the following numbers :-
1. 529.

11. •81796 to 4 places. of .28571428571428 ... to as many decimal places as we please,

2. 5329.

12. 1169'64. by continually taking in more and more figures of the recurring 3. 784.

13. 3.172181 to 4 places. periods.

4. 4761.

14. 10342656. Similarly, in finding the square root of ], we should proceed

5. 7056.

15. 23. 123, 18, s. 6. 9801.

16. to 4 places. thus :-) = ·4, and then find the square root of .400000, etc., to

7. 27889.

17. 174 to 4 places. as many places as we please.

8. 961.

18. 9645192360241. Obs.-It does not follow that because the numerator and 9. 97 to 4 places of decimals. 19. 00000625. denominator of a fraction are not complete squares, that the 10. 190 to 5 places. fraction has no square root; for the division of numerator and

2. Find the square root of the following numbers by the denominator by some common measure may reduce them to abbreviated method :perfect squares. Thus, 23, when nimerator and denominator are

1, 365 to 11 figures in the root. I 3. 3 to 17 figures. divided by 7, gives , the square root of which is . A fraction

2. 2 to 12 figures. must be reduced to its lowest terms iɔ determine whether it be

3. Extract the square root of 2116, 21316, and 7056, by a complete square or not. 10. Abbreviated Process of Extraction oj* Square Root.

splitting them into their prime factors. When the square root of a number is required to a consider. 12. Extraction of the Cube Root. able number of decimal places, we may shorten the process by

To extract the cube root of a given number is the same thing the following

as resolving it into three equal factors. Rule for the Contraction of the Square Root Process.

As in the case of the square root, we must content ourselves Find by the ordinary method one more than half the number with giving, without explanation of the reason of its truth, the of figures required, and then, using the last obtained divisor as Rule for the Extraction of the Cube Root of a given number. & divisor, continue the operation as in ordinary long division.

Mark off the given number into periods of three figures each, EXAMPLE.-Find the square root of 2 to 12 figures.

by placing a point over the figure in the unit's place, and then 2.0000, etc. (1•414213 | 56237

over every third figure to the left (and to the right also, if there be any decimals). Put down for the first figure of the root the

figure whose cube is the greatest cube in the first period, and 24) 100

subtract its cube from the first period, bringing down the next 96

period to the right of the remainder, and thus forming a number

which we shall call a dividend. Multiply the square of the part 281 )

of the root already obtained by 3 to form a divisor, and then,

having determined how many times this divisor is contained in 2824 ) 11900

the dividend without its two right-hand figures, annex this 11296

quotient to the part of the root already obtained.* Then deter

mine three lines of figures by the following processes :28282 ) 60400

1. Cube the last figure in the root. 56564

2. Multiply all the figures of the root except the last by 3, and the

result by the square of the hist. 282841 ) 383600

3. Multiply the divisor by the last figure in the root. 282841

Set down these lines in order, under each other, advancing 2828423) 10075900

each successively one place to the left. Add them up, and 8485269

subtract their sum from the dividend. Bring down the next

period to the right of the remainder, to form a new dividend, 15906310

and then proceed to form a divisor, and to find another figure of 14142115

the root by exactly the same process, continuing the operation

until all the periods are exhausted. 17641950

13. In decimals, the number of decimal places in the cube 16970538

root will be the same as the number of points placed over the 6714120

decimal part, i.e., as the number of periods in the decimal part. 5656846

Obs.If, finally, there be a remainder, then the given number

has no exact cube root, but, as in the case of the square root, an 10572740

approximation can be carried to any degree of nearness by 8485269

adding ciphers, and finding any number of decimal places.

The rule will be best understood by following the steps of an 20874710

example. 19798961

. It will be found necessary sometimes, as will be seen by the 1075749

example given in Art. 15, to set down as the next figure in the root, Here, having obtained by the ordinary process the first seven one less than this quotient.

1

400
281

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238136

10. 6.

Placing the points as indicated in the rule, wo observe what the cube of 4 is the greatest cube in the first period 78. Sub. And so on to as many more decimal places as we may desire. tracting 43, or 64, from 78, we get a remainder 14, to the right

Obs.—Exactly as in the case of the square root, when one of which we bring down the next period 314, to form a dividend.

more than half the number of figures required of the root have Multiplying the square of 4 by 3, we get for a divisor 48, which been found by the rule, the rest may be found by simply dividwill go 2 times in 143 (the dividend without its two right-hand ing, as in ordinary division, by the last divisor. figures). We set down 2, therefore, to the right of 4 as the

16. Obs.It will be observed that although 27, the first next figure in the root, and then proceed to form the three lines divisor, is really contained 6 times in 176, we only put down 5 according to the rule.

in the root. The reason is that, on examination, we find that 6

would be too large, for it would make the sum of the three 1. 8 is the cube of 2.

lines which we add up greater than the dividend 17600. This 2. 48 is 3 * 4 * 2.

explains the note at page 318. We must, therefore, always be 3. 96 is the product of 2, the last obtained figure in the root; and careful to observe whether the figure put down in that root will 48, the divisor.

or will not make the sum of the three lines too large. The Placing these three lines under each other, but advancing each dividing the dividend without its two last figures by the divisor successively one place towards the left, and adding, wo get is not, thereforo, an infallible guide to the next figure of the 10088, which we subtract from the dividend 14314, leaving a

root. remainder 4226. To the right of this we bring down the next

EXERCISE 40. period 601, thus forming another dividend.

Find the cube root of the following numbers :The next divisor 5292 is 3 X 422, and is contained 7 times in

1. 2197.

6. 11543.176.

11. 376. 42266. Putting down, then, 7 as the next figure in the root, we

2. 91125.

7. 20:570824.

12. 575. form three lines as before :

3. 571787.

8. .241804367. 13. 114. 4, 2515456.

9. 37.

14. 492. 1. 343 is the cube of 7, the last figure in the root.

5. 10218313.

15. 399501.352125. 2. 6174 is 3 x 42 x 7o. 3. 37044 is 7 x 5292.

Where the given number is not a complete cube, the root

may be found to seven decimal figures in each case, attention Adding these up when properly placed, we get 3766483, being paid to Obs. of Art. 16. which we subtract from the previous dividend 4226601, leaving a remainder 460118. There are now no more periods left. Hence 427 is the num.

LESSONS IN ARCHITECTURE-I. ber whose cube is the nearest cube number to the given number, and less than it. If there were no remainder, the root obtained ARCHITECTURE is the art of planning, constructing, and adornwould be the exact cube root of the given number.

ing public or private buildings according to their intended use. 14. In such an example as that worked out above, we could The word architecture is derived from the Greek apxw (ar'-ko), I place a decimal point and as many periods of ciphers as we may command, and TEKTW (teck-tone), a workman. This etymology wish after the original number, and thus, by continuing the indicates the operatives eng-ged in the building on the one process according to the rule, get as many decimal places as hand, and the leader or chief, the man of science and practical may be required as an approximation to the cube root.

skill, putting in action all his resources in order to execute In finding the cube root of a decimal, the periods must be his plan on the other. Such a division as this was, no completed by adding ciphers, if necessary.

doubt, established from the beginning of the art. According, 15. When the cube root of a fraction is required, the cube therefore, to the literal meaning of the etymology, mankind root of the numerator and the cube root of the denominator will must have, at the origin of architecture, possessed a degree of be the numerator and denominator respectively of the fraction civilisation sufficient for the organisation of different kinds of which is the cube root of the original fraction. If the nume- industrial operations, and acquired a degree of skill in the art, şrator and the denominator are not both perfect cubes when the which enabled some men by their experience to be the leaders fraction is reduced to its lowest terms (vide 9, Obs.), the best or directors of others. In this way, we may suppose that the plan generally will be to reduce the fraction to a decimal, and art itself, or rather the symmetry, the harmony of proportions, then to find the cube root of that decimal. In the case of and good taste in structures, at first began to be developed. mixed numbers, they must be reduced to improper fractions, in Before arriving at this point, mankind must have overleapt order to see whether the resulting improper fraction has its ages. One of the first wants of society was a covering or shelter namerator and denominator both perfect cubes. Thus, 533 from the inclemency of the weather, whether of heat or of cold. reduced to an improper fraction gives 3, of which the cube Simple was the art employed in constructions of this kind. iroot is , or 14. But if, when so reduced, the numerator and Grottoes or caves hollowed square to make them more habitable, denominator are not perfect cubes, then it will be better to and cottages constructed of branches of trees and blocks of reduce the fractional part of the mixed number to a decimal, stone—such were the primitive constructions in wood and stone and placing the integral part before it, find the cube root by which formed the rudiments of architecture. From the simplithe above rule.

city of early structures men passed to the study of proportions ; they then dared to attempt the grand; and, at last, reached the study of these will be duly appreciated by the historian, the sublime.

philosopher, the archæologist, and the artist, who, each with his The origin of architecture cannot be assigned to any particular own particular view, knows how to find a great lesson in these country. Every nation produced its own art, or style, by silent witnesses of past civilisation, as well as in those existing employing the various materials within its reach, and by giving in full vigour around us. to them such forms as their wants required. Proceeding at first Architecture is founded upon three great principles, which from the high table-lands of Asia, in order to people the earth, ought to be immutable : 1, the useful, without which states and the early fathers of our race could have but little idea of archi- private individuals would be led into superfluous and ruinous ture, or of a well-established system of construction. As wan- expenses ; 2, the true, because it ought to express in all its dering and pastoral tribes, like the Hottentots of the present varied forms the great principles of construction upon which it day, they lived in tents or wretched huts, which had no preten- rests ; 3, the beautiful, which is the end of all the arts depend. sions to architecture. It was not until they became more ing upon design, and no less of architecture the most useful. settled that they sought the means of rendering their buildings on these principles, every style of architecture has the same more durable, by employing in their construction wood or value ; and an artist should not curb his genius by confining stone, and bricks baked in the sun.

himself to the study of one particular style. It is only the From the differences in the materials, and from the variety of man of talent, to whom the construction of an edifice is entrusted, tastes and feelings, arise the varied appearances which the who can combine the different arrangements and forms, har. monuments of different nations present, and which constitute ! monise the various parts, and particularly express by plans, their peculiar style of

skilfully worked out, architecture. Thus

the disposition of the the Egyptian, born

whole or of every part in the hot climate of

of the building. Upon Africa, in a country

these arrangements destitute of wood fit

and plans rests the for building, and near

reputation of an arthe mountains of the

chitect, and science valley of the Nile, con

demands of him a taining large blocks of

well-grounded assur. freestone and granite,

ance of the good concreated for himself

struction and dura a vigorous style of

bility of his work. buildings, which com

Architecture is not pletely sheltered him

an imitative art, like from the burning rays

her sister arts, sculpof the sun. These

ture and painting. buildings were formed

We see nothing in of colossal masses,

nature like our buildwhich were easily

ings as a whole; or transported along the

rather nothing which waters of that famous

could serve to guide river. The Greek, in

us in its applications, habiting a milder cli.

or in the harmony of mate, surrounded by

its lines. In this art, forests and quarries,

man has done everygave a lighter form

thing himself. He to his edifices, and em.

has employed matter; ployed wood in their

he has invented forms construction, which

and proportions to harmonised well with

produce in the minds the marble-a mate

of his fellow-creatures rial of which the fine- THE BUT OF THE HOTTENTOT : AN EXAMPLE OF THE PRIMITIVE ATTEMPTS ideas correlative of ness admitted of a OF MAN TO CONSTRUCT A DWELLING.

order, harmony, gran. greater delicacy of

deur, richness, and structure and arrangement. The Chinese, surrounded by rivers | durability. He has been enabled, by the force of art, to give, bordered with bamboo, had only a meagre and tortuous species as it were, thought to matter, without being indebted for his of architecture, as ephemeral in its duration as it was fragile in ideas to any of the external forms of nature. Like the poet its origin and construction. The very different character exhi. and the musician, the architect can transport the spectator bited in local architecture enable us to judge of a country by into an ideal world, by creating forms and effects formerly its monuments, inasmuch as the buildings themselves are the unknown ; but, very different from them in results, he renders expression of the various wants of the people who constructed his creations palpable, and gives them durability. Moreover, them. It is easy to understand how their different arrange the useful, the true, and the beautiful, must be ever present ments and structures are but the reflection of the religion or the to his view; and, however fruitful his imagination may be, manners of the people. The general style of the monuments of he cannot emancipate it from science, the eternal basis of " a country is a durable image of the different phases of its the productions of his art. civilisation. In these, we see it in its primitive, refined, or de- The architect should therefore spend his youth in the study graded state, as civilisation arose, approached to perfection, or of his art, and of the splendid examples left on the face of decayed.

the old world by ancient civilisation. In conjunction with Nations naturally established great divisions in their architec- these studies he should make himself master of the exact tare. They first built their private dwellings, then their public sciences, in order that he may execute his plans with precision, buildings, and these, in their numerous subdivisions, constituted and study the nature of their construction. He should also civil architecture. Religion caused them to build temples and become familiar with the physical sciences, in order that he other edifices, attaching to them ideas of duty and moral obliga- may understand the nature of the materials which he must tion: thus arose sacred architecture. The fortification of their some day employ, and be able to calculate their effects. In frontiers, their towns, and their conquered countries, gave birth short, he should devote himself to practical experience, and to military architecture. In this hasty sketch, we see how to the working part of architecture, in order to render himself extensive is the series of buildings which cover the face of the capable of executing public or private buildings, and to globe, soine of which belong to the first ages of its history, and make himself responsible for the stability of edifices entrusted others of which are being re-discovered in our own day. The I to him.

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ANIMAL PHYSIOLOGY.-X.

and which is of a more animal character, is enjoyed in a greater

dogree in the brute than in man; while the true gustatory senise, THE ORGAN OF TASTE (concluded).

being more connected with the exercise of the mental powers In treating of the objects which excite the sense of taste, we of comparing and distinguishing, is certainly weaker in the most draw attention to the distinction between tasto proper, lower animals. and the alimentary sensation of relish. That these sensations Brutes may be roughly divided into two great divisions, the are different, will appear from the consideration that many camivora, or flesh-eaters, and the herbivora, or vegetablo-eaters. things which are very appetising, and in the eating of which the type of the first class is the tiger, or, to give a more famithere is great pleasure, have bat little distinctive taste. Butter liar example, the cat; while the other is represented by the and animal flesh are good instances of this. The tip of the ox. In each of these, the whole body seems to have been contongue applied to these would give but little indication of the structed in relation to the food. The tiger has jagged back presence of sapid bodies; but the suoceeding parts of the organ teeth, and pointed side fangs which lock deeply into one an. and the mouth declare them very good. On the other hand, other, but have no grinding surface. The jaws that wield sweet and bitter principles are detected at once by the tip of these are short, strong, and can play only to and from one the tongue, though they be entirely indifferent to the sense another. It can therefore grip and hold, but cannot chew. of relish. Alam is thus sweet to the sense of taste, but dis. The stomach is small and intestines short, becaase flesh is very gusting to the sense which we have called alimentary. The nutritious, and needs but little digestion. The fore limbs can sense of taste proper, or the appreciation of what is sweet, move freely in all directions, and are furnished with claws to bitter, sour, etc., is more connected with the intelloct than the strike and seize. The ox has long jaws, rough but fat hind sense of whatis

teeth, and a savoury; and

close - fitting hence it is less

row of front dependent on

ones in the the state of the

front of the body, and it

lower jaw, leaves behind

playing on a it a multitude

pad in the of distinct

II

upper, and the ideas which

lower jaw can can be held in

swing sido the memory

ways and 80 Thus & person

grind the food. when suffering

III He can therefrom sea-sick

fore clip and ness can well

chow, but candiscriminate

IV

not grip. between sugar

This compeand quinine ;

rison might be but he would

carried into be a very in

almost every different judge I

detail of strucof the flavour

ture. We oanof a beef-steak

not, then, in at such a time.

speaking of The multitude

the sense

of of flavours

taste in aniwhich can be

mals, speak of distinguished

the class as a is truly re

whole, because markable ; for

the objects of not only does

the sense are apricot,

80 different in plum, cherry, I. TONGUE OF A CAT,

the two divi. II. FILIFORM PAPILLE OF A LEOPARD. III. TONGUE OF A FIELDSARE, and apple each IV. TONGUE OF AN OSTRICH. V. TONGUE OF A CHAMELEON.

sions of the have a charac

class. It must teristic taste,

not be supthough they all belong to the same order of plants, but a posed that this division of brutes is sharply drawn; for hundred varieties of apples all challenge recognition from between the two types of tiger and ox, animals of every this sense.

The grape produces a thousand wines, each with grade of intermediate structure are found. Moreover, the a bouquet of its own, even though alcohol and water are the division is not a good one for the purposes of zoological main constituents of them all, and that which causes the classification; for though both the tiger and the Tasmanian difference is so small in quantity, that the chemist oannot devil eat flesh, and the kangaroo eats grass like the ox, pot separate it. Some sensations described as tastes, are but little even the tiger is more like the ox, and the Tasmanian devil removed from those of touch ; thus, the taste of nutgalls, called more like the kangaroo, than are those animals when crossan astringent taste, and the fiery taste of alcohol, are probably coupled, as in the first sentence. Further, some brutes made caused by mechanical action on the outer skin. In the first on the flesh-eating type, eat all kinds of vegetables, as the case, the forcible contraction of the parts occasions a roughness; bear does; and others built on the plan of herb-eaters, will and spirit will produce a burning sensation on any delioate part eat flesh, as the pig will. In fact, the division is a falso one of the body.

when we are treating of the classification and structure of We have now to apply our experimental knowledge of the animals, but is nevertheless a useful one when we are writing sensation derived through the tongue and month to the inquiry, of their powers and functions. In other words, it is a good How far do brutes participate in these sensations? In order to physiologioal bat a bad anatomical division. Wo have onanswer this question we must observe the gestures and exhibi. tered so far into the question, not only because it bears on our tions of animation of animals while foeding on those substances special subject, but also because it explains the term “physiowhose tastes we are ourselves acquainted with. Observation logy," with which these lessons are headed. seems to lead to the conclusion which we should naturally have Of carnivorous animals, it may be stated that the alimentary arrived at from reasoning on the question. The conclusion is this, sense, which is associated not only with the tongue, but with that the sensation which we have called the alimentary feeling, the throat and palate, is keen and pleasurable in the extreme,

21 VOL. L

the

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