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cular would be as much entitled to the name altitude or height determine the number of square inches which are contained in of the triangle to the base A B, as the perpendicular Au is to

Fig. 7.

a rectangle of any size, as A B CD (fig. 7), the name altitude or height of the triangle to the base Bc. The

measure the number of inches in its same may be said of a perpendicular drawn from the ver.

length, and the number of inches in its tex B.

breadth or altitude; then mul:iply these DEFINITION 2.-The altitude of a parallelogram is the per

two numbers together; and the product pendicular which measures the distance

Fig. 3.

will be the number of square inches it

contains. Thus, if the length AD measures 10 inches, and the of its two parallel sides. Thus, in the A

B parallelogram AB D C (fig. 3), if a per.

breadth or altitude A B 4 inches, then, multiplying 10 by 4, you

have 40 for the number of square inches in the rectangle ABCD. pendicular be drawn from the point B, or from any other point in the side A B,

The reason of this process is also very obvious. For if the

inches be carefully marked along the sides A D, A B, and straight to the opposite side cd, it will measure the distance of the parallel sides a B,

lines parallel to these sides be drawn through each inch-mark с

as before, it is plain that, like the case of the square, there CD, and will be the altitude of the parallelogram A B D C, to the base cd. If a perpendicular were drawn will be 10 rows of 4 square inches, and these altogether will from the point c, or from any other point in the side ac, to the contain 40 square inches; for 4x10=40. Also, as in the case opposite side BD, it would measure the distance & the parallel of the square, the area of the rectangle will be in square inches, sides a C, BD, and would be the altitude of the parallelogram square feet, square yards, or square miles, according as the

measurements of the dimensions (that is, of the length A B C D, to the base B D.

DEFINITION 3.-The altitude of a trapezoid is the perpendicu- and breadth) are taken in inches, feet, yards, or miles of
lar which measures the distance of its two parallel sides. Thus, length.
Fig. 4. in the trapezoid ABCD (fig. 4), if a per.

PROBLEM 3.-7' find the area of a given parallelogram. In pendicular be drawn from the point D, or order to determine the area of a parallelogram, draw a perpenfrom any other point in the side A D to the dicular from any point in the base to the opposite side, or to opposite side B c, it will measure the that side produced ; measure the length of the base, and th: distance of the parallel sides A D, B C, and length of the perpendicular or altitude, multiply these two will be the altitude of the trapezoid to lengths together, and their product will be the area of the pathe base B C.

rallelogram. This rule is founded on the 35th proposition of DEFINITION 4.—The altitude of any rectilineal figure, or Book I., Euclid's Elements, in which it is demonstrated that polygon, is the greatest of all the perpendiculars which can parallelograms upon the same base and between the same parallels be drawn to any side, or to any side pro- Fig. 5.

are equal. Hence, if a rectangle and a parallelogram stand on duced, assumed as the base, from the ver

the same base and between the same parallels, they are also tices of its different angles. Thus, in the

equal. Now the breadth of the rectangle is the same as the polygon A BCD B (fig. 5), the perpendicular

breadth of the parallelogram ; whence the area of the parallelodrawn from the vertex c to the base A E,

gram is obtained, by finding the area of the rectangle that being greater than the perpendiculars drawn

stands on the same base, and has the same breadth or altitude, from the vertices B and D, to the same

namely, the distance between the parallels. It is plain that the base, is the perpendicular of the polygon

length of the oblique side of the parallelogram, that is, oblique ABG D E to the base A E.

to the assumed base, is not to be taken into consideration, in DEFINITION 5.—The extent of surface contained within the calculating its area ; for, if it extended to an indefinite num. boundary of any plane figure, is called its area. Thus in the ber of miles between the parallels, still its area would be the triangle a BC (ågs. 1 and 2), the extent of surface contained within the three sides A B, BC, ca, is called the area of the

PROBLEM 4.- To find the area of a given triangle. For this triangle A BC. Again, in the parallelogram A CD B, the extent purpose draw a perpendicular from the vertex of any angle, to of surface contained within the four sides AB, B D, DC, CA, is the opposite side considered as the base, or to the base procalled the area of the parallelogram ACDB.

duced, if necessary; measure the length of the base, and the Definition 6.—Surfaces of ordinary extent are measured by length of the perpendicular or altitude, multiply these two the

number of square inches, square feet, or square yards, which lengths together, and half their product will be the area of the they contain, according as inches, feet, or yards, in length,

have triangle. This rule is founded on the 41st proposition of Book been used in taking their dimensions, namely, their length, and I., Euclid's Elements, in which it is demonstrated that if a their breadth. A square inch is a square whose side is one inch parallelogram and a triangle be on the same base and between the long. A square foot is a square whose side is one foot long. A same parallels, the parallelogram is double of the triangle. Now, square yard, is a square whose side is one yard long.

since the rectangle formed by the base and the perpendicular PROBLEM 1.-To find the area of a given square.--In order to base and of the same breadth or altitude, it follows that the

breadth or altitude, is equal to the parallelogram on the same determine the number of square inches, which are contained area of this rectangle is double the area of the triangle. Hence, in a square of any size, as A B C D (Eg. 6), measure the number the truth of the rule is evident. of inches long in its side, and multiply this number by itself; the product will be the area or number of square inches which

PROBLEM 5.—To find the area of a given trapezoid. For this it contains. Thus, if a B the side of the square be measured, purpose, draw a perpendicular from any point in the base to and found to be 6 inches long; then multiplying 6 by 6, you the opposite side, or to that side produced; measure the hare 36 for the number of square inches in the square A B CD. length of the base, the length of the opposite side, and the The reason of this process is very obvious.

length of the perpendicular or altitude; then add the lengths For, if the inches be carefully marked along

Fig. 6. of the two parallel sides, and multiply their sum by the length the sides A B, BC, and straight lines parallel

of the perpendicular, and half this product will be the area of to these sides be drawn through each inch

the trapezoid. This rule is plainly founded on the principle mark, it is plain that there will be 6 rows

that if a diagonal be drawn joining two opposite extremities of six square inches; and these will all to

of the parallel sides, it will divide the trapezoid into two gether contain 36 square inches; for 6X 6

triangles, whose areas might be found separately, by Prob. 4, 336. If the side of a square were mea

or conjointly by this rule. sured and found to be 6 feet long; then, on

PROBLEM 6.—To find the area of a given rectilineal figure, the same principles, its area would be 36 square feet. Or, if the Divide the given rectilineal figure into triangles by drawing side of a square were measured and found to be 6 yards long; straight lines from one angular point to another, as shown in its area would be 36 square yards. In like manner, if the side fig. 8. Then find the area of each triangle in this figure by of a square were measured and found to be 6 miles long, Prob. 4. Add all these areas together, and their sum will be then, its area would be 36 square miles; and so on, for any the area of the figure. It will shorten the process a little, and other measurement, in inches, feet, yards, or miles.

save fractions in the operation, first, to multiply the lengths PROBLEM 2.-To find the area of a given rectangle. In order to of the bases and perpendiculars of the triangles together; then,

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to add all these products together, and

Were there no such laws the science of grammar oould not exist

Fig. 8, take half their sum, for the area of the

The sciences are in each case a systematic statement of generalised Agure.

facts, in other words of definite laws; and grammar rests un In fig. 8, the contour or boundary of the

phenomena clearly ascertained, invariable in themselves, capable rectilineal figure is denoted by the full

of being distinctly stated, and equally capable of being wrought lines ; and the straight lines drawn within

into a system of general truths. In many instances, indeed, the it, to form the triangles necessary for de

facts with which grammarians have to deal present themselves in. termining its_area, are denoted by the

the actual state of language, in a fragmentary and almost evanescens dotted lines. The perpendiculars requisite

condition. The quick and piercing eye, however, of modern to be drawn and measured for the com

philology has succeeded in detecting no few of these, and the putation of the triangles, are not shown ;

highly-cultivated powers which have been applied to the subject, but from the explanations already given,

have been able of themselves to supply deficiencies, and to construct they can very easily be conceived,

edifices out of ruins. Still many things remain involved in dark. A more convenient mode of finding the area of a rectilineal ness; in relation to others sagacious conjecture has authorised only figure, and one more frequently used in practice, is to divide it bare probability. These, however, are not embraced within the Fig. 9.

into trapezoids and triangles, as science of grammar. When doubt begins science ends. What is
shown in fig. 9. Then and the still unascertained or subject to difficulties remains to be explored,
area of each trapezoid by Prob. and can take its place as part of scientific grammar only when it
6, and of each triangle by Prob. 4; has ceased to be a subject of doubt and debate.
add all these areas together, and If the conditions under which thought became speech had been
their sum will be the area of the in all cases the same, there would only have been one language on
figure. In planning this division of the face of the earth. Descending as mankind did from a common
the figure it is best to draw as near progenitor the various tribes would have spoken a common tongue.
as possible a straight line across the But diversities soon arose. The organs of speech, while in all cases
middle of it, and then from the they remain substantially the same, vary in minor particulars with
angular points or vertices of the each individual. Outward influences are most diversified. Men's
angles on each side of this straight pursuits were different almost from the first. Climate and soil
line to draw perpendiculars to it. change with every change of locality. And both original endow-

In fig. 9 these perpendiculars are ments and the degree of culture superinduced by external influshown by the dotted lines. The contour or boundary, and the ences (or what may be termed indirect education) would be as central line, are deno by the full lines. It will be seen diverse as the tribes, not to say the individuals which the species from the consideration of this figure, that the areas of most of consisted. All these diversified influences would speedily beget the triangles will in this case require to be subtracted from varieties in speech which time would increase and harden into those of the trapezoids of which they form a part, because they different languages. are on the outside of the figure. "Cases, however, can easily From this diversity, there arise two kinds of grammar, the ani. be supposed in which they will have to be added, - viz., when versal, the particular. Universal grammar is formed by studying they are within the figure. In all such cases the computer of language in general, by passing in review the several languages areas must use his judgment, or he may produce a serious error which exist (or most of them), and selecting

and classifying those in the resulta

facts' which are common to all. Particular grammar is the result The problems and rules we have just given, are sufficient to of the study of any one given language. By a careful consideraenable the intelligent and careful student to measure the area tion of the usages of the best English writers we discover what conof any rectilineal figure, polygon, or surface, that may be pre stitutes English grammar. If, after we have ascertained the laws sented to him. The fact is that they are the foundation of all of a number of separate languages, we then compare our discoverien the common processes of menguration and land-surveying. one with another, and mark and systematise what we find common With a foot rule, or a yard measure, the student may, if he to them all, we compose a treatise on general grammar. Particular understands these problems, proceed to measure surfaces of all grammar resembles the anatomy of the human frame, and limits kinds bounded by straight lines, in engineering, carpentry, its teachings to one set of objects. Universal grammar is like plastering, roofing, building, painting, &c. With a measuring comparative anatomy which treats of the general laws of animal chain and measuring rods, he may also proceed to measure life, as deduced from a minute study of the animal kingdom in fields, commons, estates, and even townships, that are tolera

general. bly level and accessible to the taking of measurements. When

It is with particular grammar that I am here concerned ;-of greater accuracy is required, he will learn from future lessons the grammar of our nation, namely, the English, I have to treat, what is necessary to be done, to accomplish this end,

Grammar and logic, or the laws of expression and the laws of thought are, we have seen, closely connected together in the

nature of things. Not easily, then, can they be sundered in LESSONS IN ENGLISH. No. II.

manuals of instruction. If separate they are related sciences; as By John R. BEARD, D.D.

being related to each other, they may afford mutual light and aid,

Requiring separate treatment, they each give and receive illustra. INTRODUCTORY,

tion. Grammar assists the logician to put his thoughts into a LANGUAGE is the expression of thought by means of articulate lucid form; and logic assists the grammarian to make his utter. sounds, as painting is the expression of thought by means of form ances correspond to the exact analogy of his thoughts. No one and colour. The relations which subsist between our thoughts, can be a good grammarian who is without skill in logic; and no when carefully analysed and set forth sytematically, give rise to logician who neglects grammar can successfully convey his ideas logic. The laws and conditions under which the expression of our to others, thoughts takes place form the basis of grammar. The logician has But in a manual which proposes to handle the subject of gram. to do with states of the intellect, the grammarian is concerned with mar, and of English grammar, reference to logic must be tacit and verbal utterances.

latent; it may be felt, it must not be displayed. Yet, in at least That there are laws of speech a cursory attention to the subject one or two terms will our obligations to logic be more positive and will suffice to prove. There is, indeed, no province of the universe outward, for I shall borrow from that science, the words subject, of things but is subject to law. Each object has its own mode of attribute, predicate, &c.; and this I shall do, because these terms, existence, which, in conjunction with the sphere of circumstances when once their import is understood, afford facilities for explanı. in the midst of which it is, gives rise to the laws and conditions tion far greater than the ordinary terms employed in English gramby which it is controlled. Accordingly language takes its laws mars. In these cases, however, and in other things in which I from the organs by which sound is made articulate, from the cul- shall depart from what is usual, I shall also supply the customary ture of the intelligent beings by whom these organs are employed, views and the ordinary terma, from the purposes for which speech is designed, and from even the As the English language, like other languages, was spoken medium and other outward influences in anion with which these before its laws were formed into a systematic treatise called purposes are pursued.

grammar, so the real facts of the language in their primary and

their model form, exist and are to be looked for in the every day and the errors to be noted; the lst supposition to be multiplied by the speech of well-educated mothers and fathers. But for the constant second error, and the 2nd supposition by the first error; and then the change, to which language is subject, I should not have needed to difference of the products divided by the difference of the errors, when add the qualifying epithet "well-educated." But as language the errors are both in excess or both in defect; but the sum of the pro. changes, so grammar changes; and thus what was good grammar ducts divided by the sum of the errors, if one be in excess and the other

in defect. under the Tudors is not good grammar in the age of Queen Victoria.

In this question suppose the less cup to weigh 7 ounces, then adding Consequently it is not all usage that is of authority, but only the to this 5 ounces (the cover), the weight is 12 ounces ; this is double the usage of the educated. Yet what is now educated usage will by weight of the greater cup, which accordingly weighs 6 ounces. Now, and by become bad grammar and be accounted vulgar. So has it adding 5 ounces to this, the weight of the greater cup and cover is 11 been in the past. Many of the present inaccuracies of the un. ounces ; but by the question, this weight is three times 7 ounces, or 21 educated once possessed the authority which belongs to cultured ounces, this gives an error of 10 ounces in excess. speech, Provincialisms in word, in idiom, and in pronunciation Again, suppose the less cup to weigh 9 ounces; then, adding to this, may be traced back to lips which of old gave laws to other sounces (the cover), the weight is 14 ounces; this is double the weight fashions besides the fashion of utterance. It may seem strange, of the greater cup, which accordingly weighs 7 ounces. Now, adding 6 but strange as it seems it is true, that among our forefathers legis- but by the question, this weight is three times 9 ounces, or 27 ounces ;

ounces to this, the weight of the greater cup and cover is 12 ounces ; lators talked and harangued in terms and in tones the faithful repre- this gives an error of 15 ounces in excess. sentatives of which may now be heard at the ploughtạil and in the

Now, the product of the first supposition 7, by the second error 15, is smithy. Yet was that language the correct language of the day: 105; and the product of the 2nd supposition 9, by the first error 10, is And it was the correct language of the day because it was the 90; whence, the difference of these errors is 15; but the difference of language of the educated. Hence the speech of educated persons the errors is 5; whence, 15 divided by 5, gives 3 ounces for the weight is of authority in grammar no less than the language of the best of the less cup. authors. Nay, we seem likely to find a language in its greater Now, to find the weight of the greater cup, add the weight of the purity when we take it from the lips of educated persons generally cover, 5 ounces to 3 ounces the weight of the less cup, and the whole is than when we derive it from the somewhat artificial shapes which it 8 ounces; by the question, this is double the weight of the greater cup, assumes in the learned or the popular volume. If sp • household which is accordingly 4 ounces. Thus, the answer is 3 ounces the less words” are good for grammar as well as for practical wisdom. cup and 4 ounces the greater cup. And so it is in the nursery we may look for the English tongue in ounces, the weight of the greater cup, and you have 9 ounces ; by the

The proof is as follows:-Add 5 ounces, the weight of the cover, to 4 a form the most simple and yet the most idiomatic. Of all teachers question, this is three times the weight of the less cup, which accordingly of English grammar the best is a well-educated English mother. is 3 ounces, as it ought to be. Speaking from her own Saxon soul, and speaking to her own Saxon offspring, she pours forth from that " well of English undefiled," the Saxon element of our language, a stream

LITERARY NOTICES, of words and sentences which are sterling coin of the royal mint, current in all parts of the kingdom, the very substra- LIVES AND WORKS OF THE PAINTERS OF ALL NATIONS.-On tum of English thought, whether found in books, in living July the 1st, JOHN CASSELL will publish the first part of a magnificent speech, or in time-honoured institutions. Hence it is evi- work, in imperial quarto, under the ubove title, containing a portrait of dent that a nursery in a cultivated English home, is the best Murillo, and seven specimens of his choicest works including the “Conschool of English grammar. As a matter of fact, it is in such ception of the Virgin,” lately in the collection of Marshal Soult, and schools that, among the upper classes of this country, the young recently purchased by the French Government for the Gallery of the learn to speak correct English from their earliest days. Were all be intrusted to Mr. M. DIGBY 'Wyatt, architect.

The general editorship will

Each Monthly English children trained in such schools, the language would be Part will consist of sixteen pages of letter press, with numerous illustraeverywhere well, and grammatically spoken. Consequently, could tions inserted in the type, together with several separate plate engrav. we place our students in cultivated nurseries, they would soon ings, and will appear on the first of every month, at 28. each, and will speak and write their mother tongue with correctness and pro- be supplied through every bookseller in town or country. priety. We are unable to accomplish this. In nurseries of a dif. CASSELL'S SHILLING EDITION OF EUCLID.-In consequence of the inferent kind have they been brought up. They have been in schools, terest excited among all classes of the readers of the POPULAR that is, their own houses, where they have learnt inaccuracies, EDUCATOR, since the publication of our Lessons in Geometry in that where they have formed practices wrong in word, wrong in pro-work, John Cassell has determined to issue a Popular Edition of TAB nunciation, wrong in form. They have, therefore, not only to learn ELEMENTS OF GEOMETRY, to contain the First Six, and the

Eleventh

and Twelfth Books of Euclid, from the text of Robert Simson, M.D., the right, but they have also to unlearn the wrong. A twofold

Emeritus Professor of Mathematics in the University of Glasgow; with difficulty attaches to their task. This twofold difficulty I shall corrections, Annotations, and Exercises, by Robert Wallace, A.M., of constantly bear in mind, while I endeavour to introduce into these the same university, and Collegiate Tutor of the University of London, pages the language and the training of a cultivated English home, This work will be ready the first week in July, price 18. in stiff covers, in such a way as to exhibit the fundamental usages and essential or 18. 6d. neat cloth. laws of the English language, as spoken by educated persons, and SCRIPTURE LIBRARY FOR TIIE YOUNG, in Shilling Volumes. --The written by first-class authors. I cannot place the young of the Srst two volumes of this instructive series of works,“ The Life of working classes in cultivated nurseries, but I'may attempt to do the JOSEPH," illustrated with sixteen choice engravings and maps, and

“ The TABERNACLE, its PRIESTS, and SERVICES," with twelve engrav. next best thing; and that is, to bring forth and set before them in a living and organic form, the spoken language of such nurseries. ings, are now ready. The “ LIFE OF Moses" is in the press. And this sball i undertake, the rather because, as the mother is the First Volume of this splendidly embellished work, handsomely bound,

THE ILLUSTRATED EXHIBITOR AND MAGAZINE OF ART. - The child's

natural educator, or, to speak more correctly, as the mother price 68. 6d., or extra cloth gilt edges, 78. 6d., will be ready July 1, is an educator of God's own appointment, so every system of educa- and will contain upwards of Two Hundred Principal Engravings, tion will be good and effectual in proportion, as it is in form, sub- and an equal number of Minor Engravings, Diagrams, &o. stance, and spirit, motherly.

COMPLETION OF JOAN CASSELL'S LIBRARY. - This invaluable Work is now complete, in 26 Volumes, 7d. each in paper covers ; double Volumes, cloth, 1s. 6d., or when 8 Vols. in 1, 28. 8d.

may be had, bound in cloth, 198. 6d., or arranged in a Library Box CORRESPONDENCE.

The EMIGRANT'S HANDBOOK, a Guide to the Various Fields o DOUBLE POSITION.

Emigration in all Parts of the Globe, is now ready, price 6d.

THE PATHWAY, a Monthly Religious Magazine, is published on the A correspondent requests an intelligible solution to the following ques

18t of every month, price twopence-32 pages enclosed in a neat tion, No. 773, in “ Walkingunie's Arithmetic" (1826), under the rule of

wrapper. Vols. I. and II., neatly bound in cloth and lettered, price Double Position :

28. 3d. each, are now ready. * A man had ? silver cups cf unequal weight, having one cover to PORTFOLIOS for enclosing 26 numbers of THE POPULAR EDUCAboth of 5 oz.; now if the cover be put on the less cup, it will be double Tor, price 18. 6d., may be procured at our office. These Portfolios are the weight of the greater ; and if set on the greater cup, it will be thrice so constructed as to form, upon the completion of each volume, a neat as heavy as the less; what is the weight of each your

Case for binding the same, which will be done at a trifling expense by The rule of double position requires two euppositions to be made, any bookbinder.

The entire Series

258.

GESS (Manchester): We have not forgotten penmanship.-W.S. WALTON ANSWERS TO CORRESPONDENTS.

(Fife) has sent us good solutions of several problems. WILLIAM SMITII.-We thought we had explained all the more LATIN.-W. S.: Verbs of motion take after them the accusative with difficult terms in our Lessons on Physiology, and that what we have left ad. The dative case is immediately dependent on a verb or an adjecundefined could be found in any common English dictionary. But as tive. Your words are not Latin.-A. Y. (Manchester) is informed that it is our duty to teach, if he will favour us with a list of the terms, we ornament is from orno, from which is also formed adorn with the aid of promise to furnish him with the meaning and pronunciation of each of the preposition ad. Delight, delectable, &c., are from the Latin deliciae, them. Let him persevere.

delecto. The querist will in time learn that in etymology one vowel J. A. STANLEY (Macclesfield).- Allor must be a misprint; aller passes into another, under certain conditions.—J. C.'s exercise will do ; means to yo ; bon is pronounced bong, exactly like our English word long. let him look to his English spelling.–T. G. should pronounce the words -C.K.K. - The first c in succès is pronounced like k.-L.W. has not

as if written, thus, judex, judisis, judisi, judisem, judex, judise. A list quoted the passage correctly. We do not see his difficulty.-J.G. (Kelso) of books will be given; at present keep exclusively to the lessons of the is right on the subject of the nines and the misprint in the Latin.

P. E.-SELF-TAugut's progress will depend on the intensity of his G.A. (Stafford): The disk of the moon is covered with a great variety application. Two hours a day for twelve months ought to enable any of spots, which are quite permanent, but differ very much in brightness young man to read Latin with ease.- Parvus is informed that amo The inequalities of illumination are visible to the naked eye. Since

denotes the love of a parent, and diligo the love of a friend. -CAESAR'S the invention of the telescope, they have engaged the attention of cxercise is carelessly done, and therefore full of errors, such as plantas astronomers, and their relative positions ascertained and laid down in (for plantae) florent; if he does not know that the suliject of n preposilunar maps, and globes. of the latter, Miss Readehouse, and of the tion must be in the nominative case, he should begin his grammatical

studies afresh.-INVESTIGATOR : Neuter nouns of the third declension former, Mr. Nasmyth, had fine examples in the Great Exhibition. The bright spots are considered to be the tops of lunar mountains en.

have in the accusative the same ending as in the nominative; dele lightened by the sun, the dark spots or places are thought to be carities (rose) the words or N. p. 91, 2nd. col. line 17, from the bottom.-J. D.

ORR: “Inversion" is a Latin word which strictly means changing. In similar to our valleys, or even deep and wide caverns which have no parallel on the earth's surface. At first, they were supposed to be seas,

the grammatical use of the word, it significs a change in the position but this opinion is exploded.

of words, and such a change as puts the words into an order different

from that which they commonly Lold in English. Inversion in the T. D. R. should apply to the editor of the Working Man's Friend, as

case of the words “the knight was bold" would place them thus, " Bold his queries are out of our province.-J. D—Y, Joiner, is right; the solu.

was the knight." The effect thus produced is an effect of emphasis; the tion bears upon the question, but it borrows principles from the 6th

word bold is made prominent and noticeable. The Latin inversion is book of Euclid.-On: we forgot to acknowledge bis solution of query similar in character and produces a similar effect. 7, No. 2.-A Friend to Greek is right; we must attend to his suggestion whenever it is possible.-C. LEWIS (Ilaversordwest); yes.-EXCEL- our earliest possible attention.-G. A. (Reading): Mental arithmetio

H. W. T. (Colchester): His suggestions are good, and will meet with s10R deserves praise for his good intentions, we hope he will persevere ; will And a place.-W. M. STEPHENSON, jun. (Bramley): We shall be his questions have been answered among our notices to correspondents. Thanks to Mr. R. J. Raleil for his kind suggestions - E. 1. (Brad glad to insert one of his questions a little more ingenious than what we

have received.-S. G. (Belfast): We request him to read our remarks ford): his letter to us does his head and heart great credit; we say to

at p. 22, col. 2, near the top.-D. KEAY (Dundee) has sent us a clever him persevere in the acquisition of knowledge under all difficulties; his

solution of Prob. 1, p. 111, which requires the 21st of the 1st Book of poetry is very fair, but we do not approve of the subject. An Emi. grant has no right either in the sight of God or of man, to leave his Euclid.-L. A. Y. D. (Dewsbury): See note at bottom of p. 72, col. 2. wife and child ; and if the poem were written with an angel's pen and where in Somerset, wishes us to give lessons in writing, with a drawing

PHILOMATHES (Temple): Yes, to all his inquiries.-A Draper somepower we would not, we could not approve.--"Somebody we don't of the hand as it should be when holding a pen; also remarks on the dif know” at Trowbridge, has sent us some remarks on phrenology, offerent styles of caligraphy. This is a very capital suggestion, and ene which we entirely approve. As to the Latin, perseverantia vincit om that would be of great advantage to himself; as we find it almost im. nia. We are of the same opinion as to phrenography, that he is as to possible to make out the name of the place in Somerset, or the name of phrenology.-BENJAMINUS (Cottingham): We expect they will be suf

the writer of the letter; although we can make out all the rest pretty ficient for any one. Let him study the books he mentions also, they are

well. He says that he holds a situation where there are sixteen young very excellent. As to our journal being cent to America, why should it be an exception to the general rule ?–11. W.: The verb taceo is neuter, R. M°C. (Smethwick): The rule for pronouncing Latin is very plain :

men, not one of whom holds his pen in an easy, gentlemanly manner.that is, neither active nor passive ; and so is its meaning in English. Pronounce it like English. In vincis, the pronunciation vinkis is contrary --AMOR (Carlisle): His solutions are correct.-X. Y. Z. (New Baxford): Caligraphy means beautiful writing, whether of the charac

to the general rule in English, that c sounds soft like s before e, i, and

y; and hard like k before a, o, and u. This rule is not without excepters or of the style. As to the characters, we shall give instructions under the head of penmanship; and as to the style, let him study Then as to curro, were it an English word, the u would be pronounced

tions in English, but there is no need for any exceptions in Latin. Dr. Beard's Lessons in English.—DAVID CADWALLADER (Tipton): short like u in current, because of the double r in the middle; but if it His answer to query 2, No. 7, is correct. - WALTER GALT (Glasgow): Thanks for his corrections, he is quite right; they are shame, thank him for the suggestion regarding a plan for tracing problems ;

were curo, the u would be pronounced long like u in curious. We fulmisprints. The letter & is not sounded at the end of a word but we do not see how the figures so drawn can be sent to us by post.unless acutely accented ; but the letter i is sounded. - TROIS SERVANT : His ruie wants explanation beyond 19 times 19.-L. ECOLIERS ATTENTIFS (Liverpool). Très is used with an adjective or an adverb, to mark excellence or excess ; it is rarely used with a participle CYMRW (Peckham): Ditto.-P. M. C. (Aberdeen): Correct solutions of

(Dublin): His solution of Prob. 1, p. 111, is very neat and correct.or a reflective verb; it should only be employed in affirmative phrases ; of Prob. 1 and 3. p. 111.-L. E.: 1. Christianity was established in negative phrases, bien and fort are used instead.

from the beginning of the world. 2. Its founder called himsell the DARBY (Rathfriland): We shall be glad to indulge her in her favourite Messiah first.

3. Neither Saturday nor Sunday ; but the Lord's study, when possible. The Celts, according to Herodotus, the oldest histo-day-R S. N. F.: Jolin Cassell's Edition.-G. F. A. SPILLER: The rian extant, were a people who in his time inhabited the remotest part word obtuse, line 26 from the bottom, is a misprint; it should be of Europe westward, at the source of the Inter or Lower Danube. The oblique, as may be seen in the 8th line above it. Salient means coming Seven Wonders of the world were, the Colossus of Rhoder, the Mauso-forward, literally leaping forward; re-entrant, means going back. O temleum of Artemisia, the Labyrinth of Crete, the Hanging Walls of 'por:1! O mores! an exclamation indicating the degenerate state of Babylon, the Pyramids of Egypt, the Statue of Jupiter Olympus, and public morals and practices; it literally means, Oh what times! Oh the Temple of Diapa at Ephesus. As to heraldry, we must refer her to schat manners ! the word what being implied though not expressed. the Royal Herald office.- Dinoma 9: We thank him for his useful sug- John Wutaker (Colne): Being well supported, we shall give in time gestions. LAND O' Cakes (Alloa). The sounds and many words of the the higher part of the sciences. We request him to look at our supeGerman, are more like those of the Lowland Scotch than those or rior edition.–J. B. S. (Haworth): His suggestion is good; it will be the modern English. WILLIAM GRIFFITH (Sheffield) is informed that considered.- A. B (Colne): By all means learn English first.-DAVID portfolios may be had at this office, price 18. 64. each ; and when the CRAWFORD (Largo): His solution of Prob 7, p. 32, is very clever.volume is complete, it may be bound in one of them.--U. I. (the initials G. W.'s solution of Prob. 8, p. 32, is correct --JOHN (Berwick-onof an inquirer at Hull) is advised to write direct to the “ Governesses” | Tweed): His solutions do not come up to the mark.-J. H. GATES (CanBenevolent Institution," Kentish Town, for the information she wants. terbury): Must be in a mistake about the equaring of his circle. -D. A. DRIFFIELD: Two studies, at least, may be carried on together

W. L., of Douglas Forge, will find from the first paragraph of Lesson with advantage; especially the two he likes best. “Common placing” | v. on Physiology, that the word chyme in the connexion which he is useful for reference. He has very nearly hit our idea on the mathe-indicates in Lesson IV. is an error of the press for “LYMPH.” We are matics.-J. M. (Haggerston): Right; but there is a more elegant way. happy to think that we have so attentive and devoted a student. -J. 8. (Ayrshire): His answers are right.-H. B. (Holmfirth): His so. lutions are very correct; let him go on and prosper.-E. C. HUGHES Printed and Published by John Cassell, 335, Strand, and Ludgate-hill, (Luard street): His solutions and observations are correct.-Joux BUR

London.- June 12, 1852,

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Xanton, Ypern, Zürich.

Grau, theurer Freund, ist alle

Grau, theurer Freund, Theorie,

ist alle Theorie, Doch grün tes Lebens goldner Baum.

goldner Baum. SECTION IV.

language, are regarded as being of the opposite gender in In German the definite Article has, in the Nominative singu- another : thus, in French, apple (la pomme) is feminine, while lar, a distinct form for each gender. Ex.:

grape (le raisin) is masculine. In German the word head (der Der Mann, the man ; der Brider, the brother ;

Kopf; is masculine ; in French (la tête) it is feminine; and in Die Frau, the woman; die Schwester, the sister;

Latin (caput) it is neuter. The word hand (bie Hand, la main, Das Haus, the house; das Glas, the glass.

manus) is feminine in the three languages. I. Some nouns, denoting inanimate objects, are in German, CONJUGATION OF THE PRESENT TENSE SINGULAR

or y aben. as in most languages, called masculine or feminine ; and some, Assertively.

Interrogatively. denoting animate objects, are called neuter. Ex.:

Ich habe, I have

habe ich ? have I? MASCULINE: Der Apfel, the apple; der Baum, the tree;

Sie haben, you have.

Huben Sie? have you? FEMININE: Die Traube, the grape ; bie Nadel, the needle ;

he has.

has he? NEUTER : Das Kind, the child; das Pferd, the horse.

Observation.--The pupil should invariably make himself so Many words that are trented as masculine or feminine in one familiar with the meaning of the words given in the several Exer. VOL. I.

12

Gr yat,

bat er?

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