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means will allow me to expend in the work is a guinea, or a learners. Besides, Dr. Johnson was but imperfectly acquainted guinea and a half.
with the constituent elements of the English language, and Thomas. Let us set the limit at a guinea and a half
therefore he was not a thoroughly competent etymologist. William. Nay, I am not sure I shall be able to raise that William. To whom, then, are we to look for sound instrucsum, and I am sure it will be a long time first.
tion in etymology ? Thomas. You did not hear me out; I was going to say that Thomas. The science is yet in its infancy; I cannot recomtaking a gainea and a half as the highest price, I would mention mend a wholly satisfactory guide. Even Todd's Johnson's dicseveral dictionaries which range from that down to six or seven tionary comes not up to the mark. Nor could I recommend, as shillings.
a sufficient etymological guide, Dr. Richardson's very valuable William. Thank you, that plan will suit me very well. English dictionary. However, by their price, Johnson's and
Thomas. With a guinea and a half for our highest point, we Richardson's dictionaries are beyond your reach. exclude the dictionary of the celebrated Dr. Samuel Johnson. William. What dictionary then am I to purchase ? I may, however, remark that to that learned man we owe the Thomas. You may possibly find resources to procure a copy commencement of sound lexicography in regard to the English of Webster's, if not the “Grammar School Dictionary," which tongue.
can be had for 3s. 6d., and would answer your purpose in William, Lexicography! what is that?
every way. 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
LESSONS IN ARCHITECTURE.-XIII. of the word ?
William. Graphe means writing.
became sufficiently free from persecution to erect buildings for Thomas. With both; the original Greek is Lexicon, which, their worship, they appear to have beon anxious to avoid, in from lego, I speak (logos, a word), may be rendered word-book.
their structures, any of the forms peculiar to either heathen or William. I wish *word-book” had been in use, I should Jewish temples. They therefore adopted the simple style of then have had no difficulty. I like those Saxon compounds, they the Roman basilicæ, or courts of justice. There was a fitness are so obvious in their import. How much better would word in the general plan of these buildings which rendered its selecbook have been than dictionary or lexicon. But where is the tion natural and appropriate. The basilica were usually endifference between dictionary and lexicon ?
closures surrounded by a colonnade, sometimes roofed, but at Thomas. In general, there is no difference between them, others open to the air, and built designedly so as to be accesthough dictionary is by usage applied to word-books relating to sible to all persons at all times of the day. Occasionally they the English or the Latin, and lexicon is applied to word-books were used as places for the transaction of ordinary business, and relating to the Greek, the Hebrew, and other learned languages. thus in character and purpose they closely resembled some of William. Then, why have we two words?
the buildings known in our own time as "exchanges.” But Thomas. As a matter of fact, we have two words, because their simplicity, the freedom of access which they afforded, and the English has been supplied with its terms from two languages the dignified object for which they were primarily founded-the Greek, whence we get lexicon, and the Latin, whence we namely, the dispensation of justice-no doubt commended their get dictionary. But we have more than two words which, in design as a model to the imitation of the primitive Christians, their general import, correspond to word-book; there is vocabu- and on this model the earliest of their buildings arose. It has lary from the Latin, and glossary from the Greek: the former left its impress on many of the edifices famous in Christian from yox, a voice or articulate sound, signifies a list or collection architecture, and the name of basilica for a church is still of words with or without their several significations, and is current in Italy and in Rome. mostly applied either to all the words of a language considered The usual form of a Roman basilica was a parallelogram, collectively (thus we say, “The English is a rich and varied with a seat for the judges at one of the ends; and in adopting Focabulary"), or to a number of words put together for a certain this form it was natural that the place occupied by this seat purpose, be that number smaller or larger : thus, a Latin voca- should be devoted by the members of the early Church to the bulary would be a selection of such words as a beginner in the purposes of an altar. This, by an easy transition, is believed language ought first of all to learn. Glossary is, so to say, a to have given rise to the formation of the semi-circular recess at learned book, and denotes a list of terms hard to be understood, one end of the building, known as the apse (from the Latin selected and given for explanation.
apsis, a bow or arch), which is characteristic of the ground-plan William. What is the origin of glossary?
of many of the oldest churches. Thomas. It comes from the Greek glossé, or, as the word Occasionally the oblong space enclosed for the basilica was appears in another form, glotté, which means a tongue, the organ divided by rows of columns into three parts, running from end being given for the product of the organ, that is, word. to end, the central being the widest. This form, too, was
William. Then glotté is the term we find in polyglott? adopted for the larger of the buildings devoted to Christian Thomas. Yes, polyglott is from the Greek glotté, tongue, and worship, and was the germ of the idea of the division of its polūs, many, and so signifies a many-tongued book; for instance, more imposing edifices into the nave, or body of the church, and the Sacred Scriptures in Hebrew, Greek, Latin, German, and its side aisles. English.
Being thus Roman in the nature of their ground-plan, the William. You think highly of Dr. Johnson's dictionary ? Roman type of architecture, characterised by the plain round Thomas. Yes.
arch, also impressed itself on the general features of the earlier William. Do you not think I could procure a copy in an old Christian buildings. On the destruction of the Pagan temples book-shop for a small sum ?
by order of the Emperor Constantine in the year 330, the mateThomas. Probably, but though I sometimes go to such places rials of which they were composed were in many cases turned myself in search of book-rarities, I advise you to avoid them. to account for the new edifices for Christian worship; and this Old books are not good for young students ; you will obtain would tend, also, to keep up the Roman character prevalent in more real, because more true, knowledge in one volume of the their design. Thus was formed a style known as the Romanesque, POPULAR EDUCATOR, than by careful searching and sifting, which prevailed throughout the early ages of the Church, and with years of labour, you could obtain from a shop full of old of which the later styles known in our own country as the books. Old books are very much like old clothes--they are worn Saxon and the Norman were only modifications. out. Knowledge is ever in movement, and ever on the advance; As to the external appearance the earliest Christian buildings consequently, the sum of knowledge undergoes incessant change presented, there is little doubt that they were for the most part -what was once thought true, is proved to be false ; what was unpretending in character, and that some time elapsed before once thought exact, is proved to be inexact. Therefore, dic- there arose anything like a definite church architecture, beyond tionaries which contain the sum of knowledge in detailed expla- that comprised in the general features to which we have alluded. natione, come in time to be wrong; consequently, old English But as the Christian Church' grew in security, and more attendictionaries lose, at least, a part of their value as guides to tion became devoted to the subject of its edifices, a departure
from the original ground-plan
the Byzantine style. In this arose, another and more charac
style we still find as a chief teristic design being adopted.
feature the Roman arch applied The form of the basilica fre
in a variety of ways, the dome quently gave place to that
itself being simply this arch, which was the accepted symbol
in a perfect form, used as the of the Christian religion, and
crowning work of the structure. instead of the plain parallelo
Where it was used, the church gram, the figure of the cross
itself generally took the form gradually became used, in one
of the Greek cross, which was or other of its variations. Nor
better calculated to support the did this involve a very great
weight of the cupola. On the alteration of the custom pre
other hand, in the architecture viously in vogue. The basilico
of the West, where the flat frequently had entrances at the
square tower, afterwards deveside, and merely by the throw
loped into the steeple, prevailed ing out of these entrances to
as the finishing-point, the orithe right and to the left, the
ginal form of the Latin cross Christian symbol was at once
was retained, and this is theredeveloped. The plan was avail.
fore the general characteristic able, and probably sometimes
of the ground-plan of the adopted, with regard to buildings
churches of Western Europe. already in existence, as it made
The nations of the West grathem suitably distinctive in
dually departed from the Rocharacter and removed them
manesque style of architeeture, from heathen associations. But
and struck out for themselves a it also commended itself at once
manner and style of their own, for future adoption; and from
which, although it still conthe early times of which we are
tained some of the Romanesque speaking down to the present
features, was nevertheless difday, it has continued to prevail
ferent in character, and graas one great characteristic of
dually became more and more the architecture of the Christian SAXON TOWER AT EARL'S BARTON, NORTHAMPTONSHIRE. 80. In this way the great style Church.
known as the Gothic developed We come, then, here to the second stage in its early history, | itself between the sixth century and the twelfth, when it became when one or other of the forms known as the Latin and the well defined and generally adopted. Whilst it was attaining its Greek cross—whichever might be most convenient in planning full development, there arose those magnificent cathedrals, min. a particular edifice-was usually employed in a building de- sters, and abbeys, of which our own land, as well as France and signed for Christian
Germany, possesses worship. We shall
so many noble exfind these forms
amples. The wealth in the most elabo
lavished on their rate structures
construction, the of which Christian
grandeur of their architecture
design, with the paboast.
tient skill bestowed As time wore on,
on all parts of the the exterior of these
workmanship, cruciform churches
well as its enduring became adornedwith
character, are strika dome, a tower, or
ing proofs of the a steeple, at the
spirit of reverential point where the lines
piety which existed of the cross inter
in what is now consect each other. The
sidered & compadome, however, was
ratively barbarous the characteristic of
age. the architecture of
The term Gothic, Eastern Europe,
as applied to the which acquired the
architecture of the name Byzantine
Middle Ages, was from its having been
first used as one of carried to great per
reproach or fection in Byzan.
tempt, synonymous tium (or Constanti
with barbarous, by nople), the capital
the architects who, of the Eastern Em
in the sixteenth pire. The church of
century, commenced St. Sophia, which
a revival (known as was built in its pre
the Renaissance) of sent form early in
the classical styles, the sixth century,
and their adaptaand converted into
tion to modern uses. a mosque after the
But it has long lost capture of Constan
this signification, tinople by the Turks, was and is the most
ing criticism having perfect example of
NORMAN DOORWAY, HAILES CHURCH, NORFOLK,
a more discriminat
produced a better
appreciation of this grand medieval style, and its peculiar fitness and the pointed styles, and occasionally, in buildings of what is for the religious purposes for which it was chiefly designed. termed the Transition period, both arches were used in the same
We cannot here pause to trace its progress from its earlier edifice. A fine example of this union is found in the rotunda of alements, and in the different countries in which it made its the Temple Church, in London, from which our illustration of war. We must take it up on its introduction into our own the Gothic or pointed arch is taken. The Gothic arch, it will be land, where it followed the rude and primitive Saxon and the seen, occupies the chief position in the structure. The Norman more polished Norman styles. Each of these styles was in its or Romanesque arch, still used, but declining, occupies only a character Romanesque, the arch of Roman shape being the subordinate position in the upper portion of the building. chief feature in both. The Saxon churches were generally very The pointed arch was so picturesque in effect, and gave such humble in character, but scarcely any remains of them are now an entirely new and more suitable character to edifices for in existence. Among the few unquestioned relics of this age religious worship, that, as we have said, but a very little time is the tower at Earl's Barton, Northamptonshire, of which we elapsed before the Norman style was entirely superseded by give a representa
this earlier develoption. Of the Nor.
ment of the Gothic. man stone edifices,
With the round however, very many
arch, the short and beautiful relics are
heavy pillars on preserved, and by
which it had rested these we are made
disappeared, fully acquainted
and were substi. with both the inte
tuted by tall and rior and the exte
slender columns. rior character of
The aisles their buildings.
thrown up to a The Norman style
greater height; may be dated from
loftier and more imthe Conquest in
pressive vistas were 1066, continuing till
thus produced; the towards the close
small and thick-set of the following cen
Norman windows tury, and it is there
gave place to others, fore sometimes
long and narrow, called the twelfth
and pointed like the century style. We
Gothic arch itself; have alluded to its
and the mouldings Romanesque feature
introduced for ornaof the round arch,
ment took & more which in Norman
refined and graceful churches was
form. supported on short
The Early Engand stout pillars,
lish form of Gothic and generally re
architecture peated from end to
succeeded in the end of the building.
thirteenth century A fine exampleexists
by the Decorated in the interior of
style, which prethe abbey at Mal.
vailed throughout vern, and others
the fourteenth cenmay be met in por
tury. In this, as tions of our older
the name implies, cathedrals. The
the ornamentation walls of the churches
was more profuse, were thick and sub
and it was also more stantial, with small
graceful. It is, perwindows, and with
haps, the finest peout much adorn
riod of Gothic archi. ment, except in the
tecture in this coun. doorways, which
try, as the style, were elaborately or
while rich in beauty, namented. An exINTERIOR OF THE TEMPLE CHURCH, LONDON.
had not become too ample, from Hailes
florid, as it did at a Church, Norfolk, is
later date. Hence given in our engraving, and in this the semi-circular arches and the term "pure Gothic” is sometimes applied to the architectheir zigzag mouldings, peculiarly characteristic of the Norman ture of this period. style, are well illustrated. The square flat tower crowning the The Decorated style of the fourteenth century was succeeded edifice was also a not uncommon feature in the Norman period. by the Perpendicular period, which endured through the fif
Towards the close of the twelfth century a wide departure teenth century and a portion of the sixteenth. The tracery of from the Norman style was introduced from the central pro- the doors and windows now consisted chiefly of perpendicular vinces of France, where it is believed to have originated. It lines, the pointed arches of the doorways often being inserted consisted chiefly in the substitution of a pointed arch for the in square compartments. The ornaments introduced in this old rounded form; and this style, now known as the Gothic, period are more varied but less tasteful than in the Decorated came so immediately into acceptance for church architecture, style. But the fine open wooden roofs which are found in some that in a few years after its introduction the Norman style had of the Perpendicular churches, and the still more striking stone fallen almost entirely into disuse. The first period of Gothic roofs of Henry VII.'s Chapel at Westminster and King's College architecture in this country is known as the Early English, and, Chapel at Cambridge—both belonging to this period-must as it lasted from about the year 1185 to 1280, it is generally always challenge admiration. A description of the chief details known as the style of the thirteenth century. At first there characteristic of the different styles, and of the various internal was, as it were, a struggle for predominance between the round features of a church, will form the subject of another paper.
LESSONS IN IN BOOKKEEPING. I X.
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 SUBSIDIARY BOOKS.
Account of Bills Receivable being the Debtor.
3rd. All Acceptances of Bills must be entered in the BILLS PAYABLE BOOK, according
4th. All other transactions (that is, exclusive of Cash and Bills) are to be entered
all the Cash and Bank transactions from January till June, as laid down in the Memoranda
Bank Col.lt Cash Col.
1200 0 0
985 0 31 Balance of Deposits
LESSONS IN ALGEBRA.-V I.
d-a-aa=_40. But this is to be subtracted by
changing the sign. It then becomes + 4a. MULTIPLICATION (continued).
Suppose -a is multiplied by (6-4). As 6–4=2, the EULE FOR SIGNS IN THE PRODUCT.
product is evidently twice the multiplicand, that is, -20. But 81. The rule is that + into + produces t; - into + gives
if we multiply -a înto 6 and 4 separately, Qinto 6 is
- 6a, and -; + into - gives —; and — into - gives +; or, in words,
a into 4 is – 4a [Art. 83]. As in the multiples multiplied by plus gives plus; minus by plus gives minus; plier, 4 is to be subtracted from 6; so, in the product, -4a plus by minus gives minus ; and minus by minus gives plus ; must be subtracted from — 6a. Now, - 4a becomes by sub
- 6a + 4a, which is that is, if the signs of the factors are ALIKE, the sign of the pro- traction + 4a. The whole product then is
equal to - 20. Or thus, multiplying - by 6. duct will be plus, or affirmative; but if the signs of the factors are
4, is the UNLIKE, the sign of the product will be minus, or negative.
same as multiplying ma by 2; and the product of the former, 82. The first case, viz., that of + into t, needs no expla- viz., — 6a + 4a, is equal to the product of the latter, viz., —2a. mation, being the same as that of ordinary numbers.
Hence the general rule may be thus stated :-When quantities 83. The second case is -- into +, that is, the multiplicand is are multiplied by a positive term, their signs are retained in the negative, and the multiplier positive. Thus, -a into +4 is product; but when by a negative one, they are changed.
86. It is often considered a great mystery that the product - 40. For the repetitions in the multiplicand are-a--a -as-4a.
of two negatives should be affirmative. But it amounts to
nothing more than this, that the subtraction of a negative EXAMPLES (1). Multiply 2a--m (2.) h - 3d + 4
quantity is equivalent to the addition of an affirmative one By
[Arts. 58, 59), and therefore that the repeated subtraction of a Product: 6ah -3hm + 2ax --- mc 2hy-6dy + 8y
negative quantity is equivalent to the repeated addition of an
affirmative one. So, taking off from a man's hands a debt of (3.) Multiply -2 70
ten pounds every month, is adding ten pounds a month to the By 36 +h
value of his property. Product: 3ab - 66-216d3b + ah-2h — 7dh ---hor. EXAMPLES.-(1.) Multiply a-4 into 36 —— 6. Answer. 3ab
-- 125 -- 6a + 24. 84. In the two preceding cases, the positive sign prefixed to the multiplier shows that the repetitions of the multiplicand
(2.) Multiply 3ad -- ah-7 into 4 - dy - hr. Answer. 12ad are to be added to the other quantities with which the multi
4ah — 28 — Sady + adhy + 7dy - 3adhr + ahor + 7hr. plier is connected. But in the two remaining cases, the negative
(3.) Multiply 2hy + 3m — 1 into 4d -2x +3. Answer. 8dhy sign prefixed to the multiplier indicates that the sum of the + 12dm --- 4d — 4hay — 6mx + 2x + 6hy + 9m - 3. repetitions of the multiplicand are to be subtracted from the 87. Positive and negative terms may frequently balance each other quantities. This subtraction is performed at the time of other, so as to disappear in the product. [Art. 53.] multiplying, by making the sign of the product opposite to that
(2.) mm -YY Bat this sum is to be subtracted from the other quantities with
mm + yy which the multiplier is connected. It will then become --40
-mmyy [Art. 58]. Thus in the expression b-(4 x a) it is manifest
+ ab — bb
+ mmyy ---YYYY that 4 x a is to be subtracted from b. Now 4 x a is 4a, that is + 4a. But to subtract this from b, the sign + must be
Product: aa -- bb.
-YYYY. changed into -. So that b—(4 x a) is b - 40. And a x-4 (3.) Multiply ad + ab + bb is therefore - 4a.
ab Again, suppose the multiplicand is a, and the multiplier (6-4). As (6 — 4) is equal to 2, the product will be equal to
aaa + aab + abb 24. This is less than the product of 6 into a.
aab To obtain, then,
- abbbbb the product of the compound multiplier (6 — 4) into a, we must
- bbb. subtract the product of the negative part from that of the positive part. Thus, multiplying a by 6 — 4 is the same as
88. For many purposes it is sufficient merely to indicate the multiplying a by 2. And the product of the former, viz., 6a multiplication of compound quantities, without actually multi- 40, is the same as the product of the latter, viz., 2a. But if plying the several terms. Thus [Art. 23], the product of the multiplier be (6 + 4), the two products must be added. a+b-c into h+m+y, is (a + bc) X (h+m+y). Thus, multiplying a by 6 + 4, is the same as multiplying a by 10. And the product of the former, viz., 6a + 40, is the and a +y? Answer. (a + m) (h + x) (d + y).
EXAMPLES.-(1.) What is the product of atm into h to same as the product of the latter, viz., 10a. This shows at once the difference between multiplying by a
By this method of representing multiplication, an important positive factor, and multiplying by a negative one. In the
advantage is often gained, in preserving the factors distinct
from each other. When the several terms are multiplied in 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 form, the expression is said to be expanded. other quantities with which the multiplier is connected.
(2.) What does (a +) 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 Product : ab +62 - ax - bæ.
to nothing, the product will be nothing. Thus a x0=0. And (2.) Multiply 3dy + hx + 2
if o be one of any number of fellow-factors, the product of the
whole will be nothing.
EXAMPLES.--(1.) What is the product of ab X CX 3d X 0? Product : 3dmry + hmre + 2mr -- 3abdy-abhx -- 2ob. Answer. O.
(2.) And (a+b) x (c + d) x (h -- m) x 0? Answer: 0. (3.) Multiply 3h + 3
(3.) Multiply 1 +*+ a2 + 3+ ** + 25 by 1 -*+* Ans. By ad-6
1 + x + + + + x?. Prodact: Badh + 3ad --- 18h - 18.
(4.) Multiply 1 +*+ *? +- 23 + 24 +-75 by 1-+02-23
+- Ans, 1 + 02 + 2*. 26 10. 85. If two negatives be multiplied together, the product will (5.) Multiply a + 2b + c by d-c. Ans, a2 + 2ab --- 2bc-c. be affirmative : — 4 X -a= + 4a. In this case, as in the (6.) Find the continual product of øy-- 1,2-1, and yz -1. preceding, the repetitions of the multiplicand are to be subtracted, Ans. x?y?:? — myz ---- «y2z ----aya? + wy+ ax + yx--1. because the multiplier has the negative sign. These repe (7.) Find the continual product of x2 + y2, y2 + tez, and 2 +äy. titions, if the multiplicand is - Q, and the multiplier - 4, are Ans. 2ay*22 + xy + x3z* + y + xyz + wyz + a*ys.