Thomas. Let us set the limit at a guinea and a halfWilliam. Nay, I am not sure I shall be able to raise that sum, and I am sure it will be a long time first.

Thomas. You did not hear me out; I was going to say that taking a guinea and a half as the highest price, I would mention several dictionaries which range from that down to six or seven shillings.

William. Thank you, that plan will suit me very well. Thomas. With a guinea and a half for our highest point, we exclude the dictionary of the celebrated Dr. Samuel Johnson. I may, however, remark that to that learned man we owe the commencement of sound lexicography in regard to the English tongue.

William. Lexicography! what is that?

Thomas. Dr. Johnson himself shall inform you; in his celebrated dictionary he defines lexicography as "the art or practice of writing dictionaries." Now, can you tell me the derivation of the word?

William. Graphé means writing.

Thomas. Yes; what does the former part of the word mean? William. Is it connected with lego or logos? Thomas. With both; the original Greek is Lexicon, which, from lego, I speak (logos, a word), may be rendered word-book. William. I wish "word-book" had been in use, I should then have had no difficulty. I like those Saxon compounds, they are so obvious in their import. How much better would word book have been than dictionary or lexicon. But where is the difference between dictionary and lexicon?

Thomas. In general, there is no difference between them, though dictionary is by usage applied to word-books relating to the English or the Latin, and lexicon is applied to word-books relating to the Greek, the Hebrew, and other learned languages. William. Then, why have we two words?

Thomas. As a matter of fact, we have two words, because the English has been supplied with its terms from two languages -the Greek, whence we get lexicon, and the Latin, whence we get dictionary. But we have more than two words which, in their general import, correspond to word-book; there is vocabulary from the Latin, and glossary from the Greek: the former from vox, a voice or articulate sound, signifies a list or collection of words with or without their several significations, and is mostly applied either to all the words of a language considered collectively (thus we say, "The English is a rich and varied vocabulary"), or to a number of words put together for a certain purpose, be that number smaller or larger: thus, a Latin vocabulary would be a selection of such words as a beginner in the language ought first of all to learn. Glossary is, so to say, a learned book, and denotes a list of terms hard to be understood, selected and given for explanation.

William. What is the origin of glossary?

Thomas. It comes from the Greek glossé, or, as the word appears in another form, glotté, which means a tongue, the organ being given for the product of the organ, that is, word.

William. Then glotté is the term we find in polyglott? Thomas. Yes, polyglott is from the Greek glotté, tongue, and polus, many, and so signifies a many-tongued book; for instance, the Sacred Scriptures in Hebrew, Greek, Latin, German, and English.

William. You think highly of Dr. Johnson's dictionary?
Thomas. Yes.

William. Do you not think I could procure a ccpy in an old book-shop for a small sum?

Thomas. Probably, but though I sometimes go to such places myself in search of book-rarities, I advise you to avoid them. Old books are not good for young students; you will obtain more real, because more true, knowledge in one volume of the POPULAR EDUCATOR, than by careful searching and sifting, with years of labour, you could obtain from a shop full of old books. Old books are very much like old clothes-they are worn out. Knowledge is ever in movement, and ever on the advance; consequently, the sum of knowledge undergoes incessant change -what was once thought true, is proved to be false; what was once thought exact, is proved to be inexact. Therefore, dictionaries which contain the sum of knowledge in detailed explanations, come in time to be wrong; consequently, old English dictionaries lose, at least, a part of their value as guides to

Thomas. The science is yet in its infancy; I cannot recommend a wholly satisfactory guide. Even Todd's Johnson's dictionary comes not up to the mark. Nor could I recommend, as a sufficient etymological guide, Dr. Richardson's very valuable English dictionary. However, by their price, Johnson's and Richardson's dictionaries are beyond your reach.

William. What dictionary then am I to purchase?

Thomas. You may possibly find resources to procure a copy of Webster's, if not the "Grammar School Dictionary," which can be had for 3s. 6d., and would answer your purpose in every way.

LESSONS IN ARCHITECTURE.-XIII.

CHURCH ARCHITECTURE.-I.

IN the early ages of the Christian Church, when its members became sufficiently free from persecution to erect buildings for their worship, they appear to have been anxious to avoid, in their structures, any of the forms peculiar to either heathen or Jewish temples. They therefore adopted the simple style of the Roman basilice, or courts of justice. There was a fitness in the general plan of these buildings which rendered its selection natural and appropriate. The basilice were usually enclosures surrounded by a colonnade, sometimes roofed, but at others open to the air, and built designedly so as to be acces sible to all persons at all times of the day. Occasionally they were used as places for the transaction of ordinary business, and thus in character and purpose they closely resembled some of the buildings known in our own time as "exchanges." But their simplicity, the freedom of access which they afforded, and the dignified object for which they were primarily foundednamely, the dispensation of justice-no doubt commended their design as a model to the imitation of the primitive Christians, and on this model the earliest of their buildings arose. It has left its impress on many of the edifices famous in Christian architecture, and the name of basilica for a church is still current in Italy and in Rome.

The usual form of a Roman basilica was a parallelogram, with a seat for the judges at one of the ends; and in adopting this form it was natural that the place occupied by this seat should be devoted by the members of the early Church to the purposes of an altar. This, by an easy transition, is believed to have given rise to the formation of the semi-circular recess at one end of the building, known as the apse (from the Latin apsis, a bow or arch), which is characteristic of the ground-plan of many of the oldest churches.

Occasionally the oblong space enclosed for the basilica was divided by rows of columns into three parts, running from end to end, the central being the widest. This form, too, was adopted for the larger of the buildings devoted to Christian worship, and was the germ of the idea of the division of its more imposing edifices into the nave, or body of the church, and its side aisles.

Being thus Roman in the nature of their ground-plan, the Roman type of architecture, characterised by the plain round arch, also impressed itself on the general features of the earlier Christian buildings. On the destruction of the Pagan temples by order of the Emperor Constantine in the year 330, the materials of which they were composed were in many cases turned to account for the new edifices for Christian worship; and this would tend, also, to keep up the Roman character prevalent in their design. Thus was formed a style known as the Romanesque, which prevailed throughout the early ages of the Church, and of which the later styles known in our own country as the Saxon and the Norman were only modifications.

As to the external appearance the earliest Christian buildings presented, there is little doubt that they were for the most part unpretending in character, and that some time elapsed before there arose anything like a definite church architecture, beyond that comprised in the general features to which we have alluded. But as the Christian Church grew in security, and more attention became devoted to the subject of its edifices, a departure

But

it also commended itself at once for future adoption; and from the early times of which we are speaking down to the present day, it has continued to prevail as one great characteristic of the architecture of the Christian Church.

the Byzantine style. In this style we still find as a chief feature the Roman arch applied in a variety of ways, the dome itself being simply this arch, in a perfect form, used as the crowning work of the structure. Where it was used, the church itself generally took the form of the Greek cross, which was better calculated to support the weight of the cupola. On the other hand, in the architecture of the West, where the flat square tower, afterwards developed into the steeple, prevailed as the finishing-point, the original form of the Latin cross was retained, and this is therefore the general characteristic of the ground-plan of the churches of Western Europe.

The nations of the West gradually departed from the Romanesque style of architecture, and struck out for themselves a manner and style of their own, which, although it still contained some of the Romanesque features, was nevertheless different in character, and gradually became more and more In this way the great style known as the Gothic developed itself between the sixth century and the twelfth, when it became well defined and generally adopted. Whilst it was attaining its full development, there arose those magnificent cathedrals, minsters, and abbeys, of which our own land, as well as France and

As time wore on, the exterior of these cruciform churches became adorned with a dome, a tower, or a steeple, at the point where the lines of the cross intersect each other. The dome, however, was the characteristic of the architecture of Eastern Europe, which acquired the name Byzantine from its having been carried to great perfection in Byzantium (or Constantinople), the capital of the Eastern Empire. The church of St. Sophia, which was built in its present form early in the sixth century, and converted into a mosque after the capture of Constantinople by the Turks, was and is the most perfect example of

So.

Germany, possesses

the

as

so many noble examples. The wealth lavished on their construction, grandeur of their design, with the patient skill bestowed on all parts of the workmanship, well as its enduring character, are striking proofs of the spirit of reverential piety which existed in what is now considered & comparatively barbarous age.

The term Gothic, as applied to the architecture of the Middle Ages, was first used as one of reproach or CORtempt, synonymous with barbarous, by the architects who, in the sixteenth century, commenced a revival (known as the Renaissance) of the classical styles, and their adaptation to modern uses. But it has long lost this signification, a more discriminating criticism having produced a better

appreciation of this grand medieval style, and its peculiar fitness for the religious purposes for which it was chiefly designed.

We cannot here pause to trace its progress from its earlier olcments, and in the different countries in which it made its way. We must take it up on its introduction into our own land, where it followed the rude and primitive Saxon and the more polished Norman styles. Each of these styles was in its character Romanesque, the arch of Roman shape being the chief feature in both. The Saxon churches were generally very humble in character, but scarcely any remains of them are now in existence. Among the few unquestioned relics of this age is the tower at Earl's Barton, Northamptonshire, of which we give a representa

given in our engraving, and in this the semi-circular arches and their zigzag mouldings, peculiarly characteristic of the Norman style, are well illustrated. The square flat tower crowning the edifice was also a not uncommon feature in the Norman period. Towards the close of the twelfth century a wide departure from the Norman style was introduced from the central provinces of France, where it is believed to have originated. It consisted chiefly in the substitution of a pointed arch for the old rounded form; and this style, now known as the Gothic, came so immediately into acceptance for church architecture, that in a few years after its introduction the Norman style had fallen almost entirely into disuse. The first period of Gothic architecture in this country is known as the Early English, and, as it lasted from about the year 1185 to 1280, it is generally known as the style of the thirteenth century. At first there was, as it were, a struggle for predominance between the round

this earlier develop

ment of the Gothic. With the round arch, the short and heavy pillars on which it had rested now disappeared, and were substituted by tall and slender columns. The aisles were thrown up to a greater height; loftier and more impressive vistas were thus produced; the small and thick-set Norman windows gave place to others, long and narrow, and pointed like the Gothic arch itself; and the mouldings introduced for ornament took a more refined and graceful form.

The Early English form of Gothic architecture was succeeded in the thirteenth century by the Decorated style, which prevailed throughout the fourteenth century. In this, as the name implies, the ornamentation was more profuse, and it was also more graceful. It is, perhaps, the finest period of Gothic architecture in this country, as the style, while rich in beauty, had not become too florid, as it did at a later date. Hence

the term "pure Gothic" is sometimes applied to the architecture of this period.

The Decorated style of the fourteenth century was succeeded by the Perpendicular period, which endured through the fif teenth century and a portion of the sixteenth. The tracery of the doors and windows now consisted chiefly of perpendicular lines, the pointed arches of the doorways often being inserted in square compartments. The ornaments introduced in this period are more varied but less tasteful than in the Decorated style. But the fine open wooden roofs which are found in some of the Perpendicular churches, and the still more striking stone roofs of Henry VII.'s Chapel at Westminster and King's College Chapel at Cambridge-both belonging to this period-must always challenge admiration. A description of the chief details characteristic of the different styles, and of the various internal features of a church, will form the subject of another paper.

IN our two preceding Lessons we have laid down a set of Transactions for the student to
enter in the subsidiary Books, according to the rules given in our former lessons. We
now proceed to show the manner of making these entries, according to the date of each
transaction, viz. :-

1st. All Receipts and Payments of Cash are to be entered in the CASH-BOOK, in the
proper Cash columns, Cash Account being made Dr. to every personal or fictitious account,
from whom, or on account of which, money has been received; and Cr. by every such
account, to whom, or on account of which, money has been paid away. Moreover, all
moneys drawn from or lodged with the Bank must be also entered in the CASH-BOOK, in
the proper Bank columns, Cash Account being made Dr. for every sum withdrawn from
the Bank; and Cr. for every sum deposited in the Bank.

2nd. All Drafts or Remittances in Bills must be entered in the BILLS RECEIVABLE

Book, according to the directions placed at the top of each column, the persons from whom
they are received being the Creditors in each transaction of this description, and the
Account of Bills Receivable being the Debtor.

3rd. All Acceptances of Bills must be entered in the BILLS PAYABLE BOOK, according
to the directions placed at the top of each column, the persons by whom they are drawn
being the Debtors in each transaction of this kind, and the Account of Bills Payable being
the Creditor.

4th. All other transactions (that is, exclusive of Cash and Bills) are to be entered
in the DAY-BOOK, or in such other Book as may be peculiarly appropriated for the entries
of particular classes of transactions, such as the Purchases and Sales of Cotton, etc. In
cases where such peculiar transactions are not passed through the Day-Book, the books
containing the records of these transactions must be considered as so many Day-Books or
Subsidiary Books in the general system.
The following is the form of the CASH BOOK which we recommend, with the entries of
all the Cash and Bank transactions from January till June, as laid down in the Memoranda
of Transactions, given in the two preceding lessons.
BOOK.

LESSONS IN ALGEBRA.-V I.

MULTIPLICATION (continued).

RULE FOR SIGNS IN THE PRODUCT.

81. THE rule is that + into + produces +; into + gives -;into- gives —; and into gives +; or, in words, plus multiplied by plus gives plus; minus by plus gives minus; plus by minus gives minus; and minus by minus gives plus; that is, if the signs of the factors are ALIKE, the sign of the product will be plus, or affirmative; but if the signs of the factors are UNLIKE, the sign of the product will be minus, or negative. 82. The first case, viz., that of + into +, needs no explanation, being the same as that of ordinary numbers. 83. The second case is into +, that is, the multiplicand is negative, and the multiplier positive. Thus, a into +4 is -4a. For the repetitions in the multiplicand area—a— a -4a.

EXAMPLES (1). Multiply 2a- m

By 3h+x

Product: 6ah

(3.) Multiply By

(2.) h—3d+4 2y

Product: 3ab-6b21bd3bx+ah - 2h — 7 dh — hx. 84. In the two preceding cases, the positive sign prefixed to the multiplier shows that the repetitions of the multiplicand are to be added to the other quantities with which the multiplier is connected. But in the two remaining cases, the negative sign prefixed to the multiplier indicates that the sum of the repetitions of the multiplicand are to be subtracted from the other quantities. This subtraction is performed at the time of multiplying, by making the sign of the product opposite to that of the multiplicand. Thus + a into - 4 is -4a. For the repetitions of the multiplicand are, + a + a + a + a = But this sum is to be subtracted from the other quantities with which the multiplier is connected. It will then become -4α (Art. 58]. Thus in the expression b— (4 × a) it is manifest that 4 X a is to be subtracted from b. Now 4 x a is 4a, that +4a. But to subtract this from b, the sign + must be changed into. So that b-(4 × a) is b-4a. And a X-4 is therefore 4a.

Suppose -a is multiplied by (6-4). As 6-4=2, the product is evidently twice the multiplicand, that is, 26. But -a into 6 and 4 separately, if we multiply a into 6 is 6a, and -a into 4 is -4a [Art. 83]. As in the multi-4a plier, 4 is to be subtracted from 6; so, in the product, traction + 4a. The whole product then is 6a. Now, 4a becomes by sub-6a4a, which is equal to 2a. Or thus, multiplying -a by 6. 4, is the same as multiplying -a by 2; and the product of the former, Hence the general rule may be thus stated:-When quantities viz., 6a4a, is equal to the product of the latter, viz., -2a. are multiplied by a positive term, their signs are retained in the product; but when by a negative one, they are changed.

86. It is often considered a great mystery that the product of two negatives should be affirmative. But it amounts to nothing more than this, that the subtraction of a negative quantity is equivalent to the addition of an affirmative one [Arts. 58, 59], and therefore that the repeated subtraction of a negative quantity is equivalent to the repeated addition of an affirmative one. So, taking off from a man's hands a debt of ten pounds every month, is adding ten pounds a month to the value of his property.

Again, suppose the multiplicand is a, and the multiplier (6-4). As (6-4) is equal to 2, the product will be equal to 24. This is less than the product of 6 into a. To obtain, then, the product of the compound multiplier (6-4) into a, we must subtract the product of the negative part from that of the positive part. Thus, multiplying a by 6 4 is the same as multiplying a by 2. And the product of the former, viz., 6a -40, is the same as the product of the latter, viz., 2a. But if the multiplier be (6+4), the two products must be added. Thus, multiplying a by 6+4, is the same as multiplying a by 10. And the product of the former, viz., 6a+ 4a, is the same as the product of the latter, viz., 10a.

This shows at once the difference between multiplying by a positive factor, and multiplying by a negative one. In the former case, the sum of the repetitions of the multiplicand is to be added to, in the latter it is to be subtracted from, the other quantities with which the multiplier is connected. EXAMPLES.-(1.) Multiply a + b

a -b a+b

(2.)

mm- -yy

mm + yy

* -bb. aa + ab + bb a—b

mmmmmmyy

+mmyyyyyy

mmmm

-yyyy.

88. For many purposes it is sufficient merely to indicate the multiplication of compound quantities, without actually multiplying the several terms. Thus [Art. 23], the product of a+b-c into h+m+y, is (a + b · c) × (h + m + y). and d+y? Answer. (a + m) (h + x) (d + y). EXAMPLES. (1.) What is the product of a +m into h + x

By this method of representing multiplication, an important advantage is often gained, in preserving the factors distinct from each other. When the several terms are multiplied in form, the expression is said to be expanded.

(2.) What does (a + b) x (c + d) become when expanded? Answer. ac ad + bc + bd,

89. With a given multiplicand, the less the multiplier, the less will be the product. If, then, the multiplier be reduced to nothing, the product will be nothing. Thus a X 0=0. And if 0 be one of any number of fellow-factors, the product of the whole will be nothing.

EXAMPLES. (1.) What is the product of ab cx 3d × 0? Answer. 0.

(2.) And (a + b) × (c + d) × (h—-m) × 0 ? Answer, 0. (3.) Multiply 1 + x + x2 + x3 + x2 + æ3 by 1 −x + œ2.

Ans.

(4.) Multiply 1+x+x2 + x2 + x + 203 by 1-æœ3 —x3 Ans. 1+x2 + x1 - 26 ——— x8 — x10.

(5.) Multiply a + 2b + c by a-c. Ans. a2+2ab 2bc-c2. (6.) Find the continual product of xy-1, az- -1, and yz -1. Ans. x222 — x2yz — xy2z — xyz2 + xy + xz + yz−1. (7.) Find the continual product of x2+yz, y2+xz, and x2+xy. Ans. 2x2y-z2 + x3y3 + x3z3 + y3z3 + xyz1 + xyz♦ + x^yz.