« ΠροηγούμενηΣυνέχεια »
England more than three years; and he arrived at Portsmouth islands of Watehoo and Otakootai, in the same seas. Sailing to on the 13th of July, 1775. In the interval, some other voyages the north of Tahiti, he arrived at the Sandwich Islands, where were made in the South Seas; and the islands of Marion and he was taken for a superior being, and as such received by the Crozet, as well as that called Kerguelen Land, were discovered natives. On the 1st of January, 1778, he made the discovery
by the navigators whose name they bear. Again the inde- of this important group. Captain Cook then prepared for the fatigable Cook resumed his voyages of discovery. This time he accomplishment of the principal object of the expedition. He intended to search for the north-west passage to India, by pass- sailed along the north-western coast of the New World, until he ing through Behring Strait. He left England on the 12th of reached a point of land which he called Icy Cape, in latitude
Huly, 1776, with the ships Resolution and Discovery under his 700 27'. Here a solid mass of ice, ten feet thick, extending to command. He first visited the islands above mentioned, and the opposite coast of Asia, presented to him an insuperable then touched at Van Diemen's Land and New Zealand. Soon barrier. He returned to the Sandwich Islands, where, alas ! after he discovered the central Polynesian group Toubouai, the his fate awaited him. On the island in this archipelago called archipelago of Hervey Islands or Monaian group, and the Owhyhee, he fell by the hands of a savage; and thus, unfort
* mand the Se of the greatest navigator of modern times. much as 3 X 6 X 5 X 9, the common multiple of 3, 6, 5, and
prus CtA who was sooond in command, took charge of 9, which we have taken, is not the least common multiple. h o n and sailed to the north-east in search of the 12. We are enabled by this means to find which of two JUILLET * Atlantic ; but the same obstacles compelled him fractions is the greater. For instance, if we wished to know
c. the enterprise, and he died on the voyage home. which of the four fractions given in Art. 11 is the greatest, Stop to describe all the benefits which the discoveries having reduced them to a common denominator, 810, we are geze cook have conferred on the sciences of geography and able to say that the second fraction, , is the greatest, becanse
a r, is more than can be done in this historical sketch it contains the greatest number of the 810 parts into which the Eibase memorable expeditions. The accuracy with which unit is divided, viz., 675; and in the same way we see that the n ostrious navigator determined the geographical positions order of magnitude of the four fractions is , , , ,
räte places which he discovered or visited, rectified numerous aces in the maps and charts of the century in which he
EXERCISE 24. focisbed, and accelerated the progress of the science to which Place in order of magnitude the following sets of fractions:ase remarks form our introduction, in a degree hitherto un. 1. £, , 3, 1. i 3. $, , , li
5. , }}, , . bow. Mathematical geography has, since this time, taken 2. $, 3, , 5. 1 4. 18, 186, 1. 1 6. ful!, H.H. ber place among the exact sciences.
13. Addition of Fractions. In concluding this lesson, we may remark that Cook lifted
Required to add ; and together. Reducing the fractions to the veil of darkness which hung over the extremities of the Pacific Ocean, and the junction of the continents of Asia and
a common denominator, j = 18 , and } = is : America. His last voyage, by disclosing the vast breadth of
Therefore 3 + 1 = 1: +1 = 1; America at the latitude of Behring Strait, made the hopes of discovering the north-western passage darker than ever. Thąt
or, as it could be written, 14 (Art. 8). We have here effected
the addition, i.e., found a single fraction which is equal to the continent had, previous to the time of the English navigator,
sum of the two given ones, by reducing the fractions to a combeen considered as terminating to the north in a point or cape,
mon denominator, 15. after passing which, the navigator would find himself at once in the South Seas, and in full sail to China or Japan. But the
The same method will apply to any other two or more fracdiscovery of Cook showed that there was found intervening a
tions. Hence we are able to enunciate the following
Rule for the Addition of Fractions. space of land of nearly three thousand miles in breadth, a very
| Reduce the fractions to a common denominator, add the new large portion of the circumference of the globe. Hence, geo
numerators so formed for a numerator, and take the common graphers viewing the coast running northward from Behring Strait, Hudson Bay, and Baffin Bay, all enclosed by land,
denominator for a denominator. The single fraction so formed
will be the sum of the given fractions. Pereived the impression, and constructed their maps accordingly, that an unbroken mass of land reached onwards to the pole,
Obs.-It will generally be most convenient to reduce each and that all these boundaries were for ever barred against the
fraction, before commencing the operation, to its lowest terms,
if it is not already in them, and then to take the least common enterprising navigator.
Add together the following sets of fractions :-
1. 1 and . 1 6. &, £, it is.
11. To se
12. 1, 11, 1. 19. To reduce fractions to equivalent fractions having the same 3. 1, 3, .
& 4, 81, 2, 61, s. 13. #, #, 11, 18. dennnánator,
9. 211, 351, 1, 1. 14. 13, 4, HULE,- Find the least oommon multiple of all the denomina
5. 3, , 1, 1 10. zást,
15. 34, 13, 1, 101 ma Multiply the numorator and denominator of each fraction by the quotient obtained from dividing the least common mul.
14. Subtraction of fractions.
The operation of subtracting one fraction from another will teple boy that denominator,
Thus, to subtract DXAMPLEReduco ... ... Ito a common denominator. | evidently be effected in the same manner. 12ey in the least common multiple of 9, 7, 10, 12 (see page 134), / from 3, wo have, as above, A tha quotients of 1260 by theso respectively are 140, 180,
1 - f = if-, 124, 195, Multiplying each numerator and each denominator and 9 fifteenths subtracted from 10 fifteenths is 1 fifteenth, bry pak tumbers respectively, we get 1180, POTEM 230, which i.e., te. *** town eynivalent to the given ones, and all of which have
Hence j -f=ts tode , Arnominator.
Hence the following It way be olmerved that the common denominator found in Rule for the Subtraction of Fractions. 1. Kan is the least. Any common multiple of the denominator Roduce the two fractions to a common denominator, subtract
la inal fractions would have given fractions with the the less numerator from the greater for a numerator, and take ** Imun denominator; but the least common multiple gives, the common denominator for a denominator. The fraction so MAX , the least common denominator.
formed will be the difference of the given fractions. II Wruptions may also often conveniently be made to have | The same observation with respect to the least common denoa la denominator by the following method :-Multiply each minator, which was made with reference to the rule for AddiA m it into all the denominators except its own for a new tion, evidently applies equally to that for Subtraction. AS I , and all the denominators together for a common N.B.--In all cases a whole number must be treated as & A n tor. The reason of this will be clearly seen from an fraction having a denominator unity. For instance, to subtract
RAM Reduce 3, 4, 3, 2, to fractions having the same 1 from 2. 2 = * = g.
Therefore 2 – f = f - f = $ = 13.
1. Find the difference betweenwhun wa bwana multiplied the numerator 2, and denominator 3, 1. and
5. 3! and is
9, 837, and Pre , the product of the denominators of the other 2. and 1 6. " and 73.
10. 230.4 and 160
3. s fruitions will therefore be
7. H and 15. 11 1 and 11
12. 5 and 3.
2. Simplify the following expressions :
2. Simplify the following expressions :
1. 3 - +$- *.
3. 127/4 - 3104 + 578671 + 14284-
4. 414 - 1 + 1053 - 1 + 3001 + 414 + 472 - 2301.
“We are little airy creatures,
All of different voice and features;
One of us in glass is set, 1. Reduce the following given fractions to fractions of the
One of us you'll find in jet; sazne value, and having a common denominator :
Tother you may see in tin, 1. j and 6. }, }, , , and
And a fourth a box within ; 1, and 7. 1. and #.
If the fifth you should pursue,
It can never fly from you." 31,1, , 1's, and the
8. 11, Tou, and to 4. 1'5, 18. 3's, and is
9. $, d, a', si, and is
An excellent practice in composition is letter-writing. I shall 5. }, }, , and it
10. _, , , to g's, and on therefore give, in this lesson, some specimens of epistolary corre2. Which of the two fractions and is the greater ; what spondence. And I advise my pupils to accustom themselves to is the difference between them; and what is their sum ?
express their thoughts in the form of letters. Let the letters 3. Two persons, A and B, are shareholders in different com. | be real ; I mean, let them be written, not as exercises in com. panies; A has £320,000 of stock in a company worth £560,000; position, but on some business, and to some friend or acquaintand B has £480,000 of stock in a company worth £840,000: ance. Your chief want at first, as I have before intimated, which of them has the largest fraction of the concern to which is the want of matter. “I don't know what to say,” is a he belongs ?
complaint with young composers no less true than embarrassing. 4. Find the integral or mixed value of the following fractions :
You will find something to say if you take your pen in hand, -4 , 5, 9, and 142:
and sit down to address a few lines to an absent friend. Only 5. Find the integral or mixed value of the fractions 3, 4, 197, do not attempt anything great or fine. Be simple. Consult S3, 5, and
your heart, if your head is silent. Just say what occurs to you, 6. Reduce the whole numbers 25, 48, 301, 4000, and 5876934 without being anxious whether it is very wise or very foolish; to improper fractions.
whether it is trivial or important. Specially would I advise my 7. Reduce the preceding whole numbers to improper fractions | pupils to correspond one with another. For instance, say that whose denominators shall be 12, 6, 5, 4, and 2 respectively. a young man in Exeter writes a letter to a former companion 8. Reduce the following mixed numbers to improper frac
who has gone to reside at Bristol. B., living at Bristol, replies tions :-51, 73, 123, 189, 101%, and 1234135.
to his friend A. at Exeter. The two continue to interchange 9. Reduce the following mixed numbers to improper fractions :
| letters. If they have nothing else to write about, they may -15, 174, 253, 49, 34, and 21847.
write about these lessons. Let them endeavour to give each 10. Reduce the following compound fractions to simple frac
te simple from other aid in their study of the English language. Let them tions : of of f of j; of of, of it; and of Lo of 4 of 48.
freely and kindly criticise each other's letters. Let them ask 11. Reduce the following compound fractions to simple frac
and give explanations. Let A. correct B.'s exercises, and let B. tions :
do the same for A. Let them agree on some book which they
will both read, with a view to make in writing and submit to 1 of 4 of of.
4. } of of 1 of of .
each other remarks on the composition. For this purpose I 2 of of of of .
5. šof of 4 of . 3. ? of of off.
6. z of of 11, of 128.
would suggest to them the Spectator, in which they will find
many papers by Addison and other eminent writers. 12. Find the sum of the following fractions and mixed In this counsel I have mentioned young men, by no means numbers:
intending to exclude young women. Most desirous am I that 1. VJ, a, b, and 3.
4. 53, 63, 73, and 213. | young women should receive a good education. Most necessary 23 tk, and y.
5. 113, 183, 194, and 116. to them, as being the future mothers of our land, is a good 3 $. I tu, and 1.
6. 6351, 427, and 1625). education. A far better education ought they to receive than
the best which they do receive. But to be well-educated they 13. Find the difference of the following fractions and mixed
must be self-educated. Let young women then consider them. munbers:
selves specially addressed in the lessons I supply, and the advice 1 Between it and yo 4. Between 41 and 27.
I give. 2 Between and , 5. Between 1906, and 70876
LETTER I. 3. Between 1 anda. 6. Between 49147 and 24,141
FROM DEAN SWIFT TO THE REV. WILLIAM DRAPER,
To the Rev. Mr. William Draper,
Dean, near Basingstoke, Hampshire.
London, April 13, 1713. HAVING thus furnished you with some criteria or means of SIR, I am ashamed to tell you how ill a philosopher I am, and that ascertaining what words have their origin in Saxon, or, as it a very ill situation of my affairs for three weeks past made me utterly is more correctly called, the Teutonic branch of our language, incapable of answering your obliging letter, and thanking you for your I must now request, that in all your studies you will constantly most agreeable copy of verses. The prints will tell you that I am ask yourself, whether each word you meet with, is, or is not, of
condemned again to live in Ireland; and all that the court and minisSalon derivation ? Among English writers, no one has a larger
try did for me, was to let me choose my situation in the country
where I am banished. I could not forbear showing both your letter portion of Saxon in his compositions than Dean Swift; and no
and verses to our great men, as well as to the men of wit of my one writes the language more correctly. I shall therefore make
e acquaintance: and they were highly approved of by all. I am altotise of his writings in this part of my task. William Cobbett's
gether a stranger to your friend Oppian; and am a little angry when Forks may be advantageously studied for the Saxon treasures those who have a genius lay it out in translations. I question which they contain.
whether "Res angusta domi” (narrow means) be not one of your
motives. Perhaps you want such a bridle as translation, for your EXERCISES IN PARSING.
genius is too fruitful, as appears by the frequency of your similes; and It is a miserable thing to live in suspense. To live in suspense, is this employment may teach you to write like a modest man, as to live the life of a spider. No wise man ever wished to be younger. Shakespeare expresses it. An idle reason lessens the weight of good reasons. Complaint is the I have been minding my Lord Bolingbroke, Mr. Harcourt, and Sir largest tribute paid to heaven. Complaint is the sincerest part of our William Windham, to give you a living; as a business which belongs to devotion Praige is the daughter of present power. Every man
our society, who assume the title of awarders of merit. They are very desires to live long. No man is willing to be old. Kings are said to well disposed, and I shall not fail to negotiate for you while I stay in have long hands. Kings ought to have long ears. Vision is the art England, which will not be above six weeks; but I hope to return in of seeing things invisible. Good manners is the art of making asso October, and if you are not then provided for, I will move heaven and cates easy. Flattery is the worst and falsest way of showing our earth that something may be done for you. Our society has not met esteem. A fine gentleman has both wit and learning. Come into of late, else I would have moved to have two of us sent in form to the garden, Maud. He gave me half-a-crown for my trouble. The request a living for you from my lord chancellor ; and if you have any king's crown is made of solid gold.
way to employ my services, I desire you will let me know it; and
believe me to be very sincerely, The reader may exeroise his ingenuity, as well as his gram
Sir, mar, while he discovers the explanation of a riddle of the
Your most faithful, humble servant, learned Dean, which is appropriate to my subject :
This town, which has the honour of being the Emperor's residence,
did not at all answer my idea of it, being much less than I expected to FROM CHARLES LAMB TO SAMUEL TAYLOR COLERIDGE.
find it; the streets are very close, and so narrow one cannot observe the [Giving a detailed account of tho death of his mother, who was stabbed by
fine fronts of the palaces, though many of them very well deserve
observation, being truly magnificent, all built of fine white stone, and his sister, in a fit of delirium.]
excessively high. The town being so much too little for the number of October 3rd, 1796.
people that desire to live in it, the buildings seem to have been projected
peo MY DEAREST FRIEND.-Your letter was an inestimable treasure to to repair that misfortune by clapping one town on the top of another, me. It will be a comfort to you, I know, to know that our prospects most of the houses being of five, and some of them of six storeys. are somewhat brighter. My poor dear, dearest sister, the unhappy
You may easily imagine that the streets being so narrow, the lower and unconscious instrument of the Almighty's judgments on our
rooms are extremely dark, and what is an inconvenience much more house, is restored to her senses; to a dreadful sense and recollection
intolerable, in my opinion, there is no house that has so few as five or of what has passed, awful to her mind and impressive (as it must
six families in it. The apartments of the greatest ladies, and even of be to the end of life), but tempered with religious resignatioa, and
cers of state, are divided but by & partition from that of a the reasonings of a sound judgment, which, in this early stage, knows
tailor or a shoemaker; and I know nobody that has above two floors how to distinguish between a deed committed in a transient fit of
in any house, one for their own use, and one higher for their servants. frenzy, and the terrible guilt of a mother's murder. I have seen her.
Those who have houses of their own, let out the rest of them to whoI found her, this morning, calm and serene; far, very far from an
ever will take them; thus the great stairs (which are allatone) are indecent forgetful serenity; she has a most affectionate tender concern
as common and as dirty as the street. 'Tis true, when you have once for what has happened. Indeed, from the beginning, frightful and travelled through them, nothing can be more surprisingly magnificent hopeless as her disorder seemed, I had confidence enough in her
than the apartments. They are commonly & suite of eight or ten strength of mind and religious principle, to look forward to a time
large rooms, all inlaid, the doors and windows richly carved and gilt, when even sho might recover tranquillity.
and the furniture such as is seldom seen in the palaces of sovereign God be praised, Coleridge, wonderful as it is to tell, I have never princes in other countries—the hangings the finest tapestry of Brussels, once been otherwise than collected and calm ; even on the dreadful prodigious large looking-glasses in silver frames, fine Japan tables, day, and in the midst of the terrible scene, I preserved a tranquillity
beds, chairs, canopies, and window curtains of the richest Genoa which bystanders may have construed into indifference--a tranquillity
damask or velvet, almost covered with gold lace or embroidery, the not of despair. Is it folly or sin in me to say that it was a religious
whole made kay by pictures and vast jarg of Japan china, and almost principle that most supported me? I allow much to other favourable in every room large lustres of rock crystal circumstances. I felt that I had something else to do than to regret.
I have already had the honour of being invited to dinner by several On the first evening (September 22nd). my aunt was lying insensible. of the first people of quality, and I must do them the justice to say to all appearances like one dying,--my father, with his poor forehead
one dying.my father, with his poor forehead the good taste and magnificence of their tables very well answers to plaistered over, from a wound he had received from a daughter dearly
that of their furniture. I have been more than once entertained with loved by him, and who loved him no less dearly,--my mother, a dead fifty dishes of meat, all served in silver, and well dressed, the dessert and murdered corpse in the next room-yet I was wonderfully sup. proportionable, served in the finest china. But the variety and richported. I closed not my eyes in sleep that night, but lay without ness of their wines is what appears the most surprising. The conterrors and without despair. I have lost no sleep since. I had been
stant way is, to lay a list of their names upon the plates of their long used not to rest in things of sense,-had endeavoured after a guests, along with the napkins; and I have counted several times to comprehension of mind, unsatisfied with the "ignorant present time,"
the number of eighteen different sorts, all exquisite in their kinds. and this kept me up. I had the whole weight of the family thrown on I was yesterday at Count Schönbrunn, the vice-chancellor's garden, ine; for my brother, little disposed (I speak not without tenderness where I was invited to dinner, and I must own that I never saw a for him) at any time to take care of old age and infirmities, had now, pla se so perfectly delightful as the Fauxbourgs of Vienna. It is very with his bad leg, an exemption from such duties, and I was now left large, and almost wholly composed of delicious palaces; and if the alone. . . . .
emperor found it proper to permit the gates of the town to be laid I mention these things because I hate concealment, and love to give
open, that the Fauxbourgs might be joined to it, he would have one of & faithful journal of what passes within me. Our friends are very
the largest and best-built cities of Europe. Count Schönbrunn's villa good. Sam Le Grice, who was then in town, was with me the first
is one of the most magnificent; the furniture, all rich brocades, 80 three or four days, and was as a brother to me. He gave up every
well fancied and fitted up, nothing can look more gay or splendid; hour of his time, to the very hurting of his health and spirits, in con
not to speak of a gallery, full of rarities of coral, mother-of-pearl, etc., stant attendance and humouring my poor father ; talked with him, and, throughout the whole house, a profusion of gilding, carving, fine read to him, played at cribbnge with him (for so short is the old man's paintings, the most beautiful porcelain, statues of alabaster and ivory,
collection that he was playing at cards as though nothing had and vast orange and lemon trees in gilt pots. The dinner was per happened, while the coroner's inquest was sitting over the way)!
fectly fine and well ordered, and made still more agreeable by the good ... Of all the people I ever saw in the world, my poor sister
humour of the count. was most and thoroughly devoid of the least tincture of selfishness.
I have not yet been to court, being forced to stay for my gown, I will enlarge upon her qualities, poor dear, dear soul, in a future
without which there is no waiting on the empress ; thongh I am not letter, for my own comfort, for I understand her thoroughly; and, if
without a great impatience to see a beauty that has been the admiraI mistake not, in the most trying situation that a human being cantion of so many different nations. When I have had that honour, be found in, she will be found (I speak not with sufficient humility, I will not fail to let you know my real thoughts, always taking a partifear, but humanly and foolishly speaking), she will be found, I trust, | cular pleasure in communicating them to my dear sister. uniformly great and amiable. God keep her in her present mind, to
EXERCISES IN COMPOSITION. whom be thanks and praise for all His dispensations to mankind !
1. Form sentences, each having in it one of the following LETTER III.
words :FROM LADY MARY WORTLEY MONTAGU TO HER SISTER, THE COUNTESS
Debts; light; sing ; come; health ; water; sky; home; day; night; OF MAR.
lark; rose ; Victoria; Mary; Henry; mother; bread; England;
wife; buttercup ; linnet; daisy ; stone. [Giving a brief description of her journey from Ratisbon to Vienna, and 2. Give brief descriptions of the following objects and some account of the last-named city.]
places : Vienna, September 8th, 1716.
A chair ; a wheel of a coach ; a kite; a waterpot; an oak-tree; the I am now, my dear sister, safely arrived at Vienna; and, I thank
room in which you write; and the place where you work. God, have not at all suffered in my health, nor (what is dearer to me) in that of my child, by all our fatigues.
3. Write historical themes on the following subjects :We travelled by water from Ratisbon, a journey perfectly agreeable, 1. The patriarch Abraham's visit to Egypt. down the Danube, in one of those little vessels, that they very pro 2. The battle of Hastings. perly call wooden houses, having in them almost all the conveniences 3. The conversion of St. Paul. of a palace-stoves in the chambers, kitchens, etc. They are rowed 4. The murder of Thomas à Becket, by twelve men each, and move with an incredible swiftness, that in | the same day you have the pleasure of a vast variety of prospects;
4. Write letters on the following subjects :and, within a few hours' space of time, one has the different diversion
& space of time, one has the different diversion 1. A letter of condolence to an intimate friend on the death of 2 of seeing a populous city adorned with magnificent palaces, and the near relation. most romantic solitudes, which appear distant from the commerce of 2. A letter to a friend in town, inviting him to pay you a visit in mankind, the banks of the Danube being charmingly diversified with the country, and describing the scenery of the neighbourhood in which woods, rocks, mountains covered with vines, large cities, and ruins of you live. ancient castles. I saw the great towns of Passau and Lintz, famous 3. A letter of thanks to a gentleman who has enabled you to obtain for the retreat of the Imperial Court when Vienna was besieged. Ta situation in a house of business by his recommendation.
LESSONS IN PENMANSHIP.—XI.
present it will be sufficient to deal with those into whose forma
tion it enters without any alteration or modification whatever. DUE attention to the instructions that have been given in the The letter o is purely a curved letter, for no portion of it preceding lessons in the art of Penmanship, and assiduous consists of a perfectly straight stroke, as the other letters which practice for about an hour a day, will have rendered any one, have already been brought under the reader's notice. It may who is endeavouring to learn to write from our copy-slips, a be commenced on the straight line cc, but it is better to begin tolerable proficient in making letters, composed of right or and end the letter at the point «, a little above the line, as it is straight lines, or lines that are commenced, or finished, or from this point that a fine hair-line is carried to the right, when commenced and finished, as in the case of the top-and-bottom- it is necessary to connect the letter o with any letter that may turn, with a hook or turn.
follow it, as the learner will see in Copy-slip No. 40. CommencA great number of copies, consisting of letters of this kind, ing, then, at the point «, the hair-line, of which the right side of have been supplied to give the learner a sufficient variety in the the letter consists, is carried upwards to the line a a, and then Fords or combinations of letters that he is copying, and to give turned to the left and brought downwards. By a gradual preshim confidence in his power to make the four strokes which enter sure on the pen the hair-line is now turned into a thick stroke, into the formation of by far the greater part of the letters of which attains its broadest part at the line cc, when the pressure
the writing alphabet, before he begins to make the remaining of the pen is relaxed, and the thick down-stroke is gradually elementary strokes, which are of less frequent occurrence. The narrowed again into a hair-line, which is turned upwards topractice that he has now had, and the knowledge and amount of wards the right and joined to the hair-line with which the letter skill in writing that he has already acquired, will enable him to was commenced at the point. The learner will notice that the advance more rapidly, and we shall proceed as quickly as pos- upper part of the letter o, which lies above the line c c, is the sible to the end of our elementary lessons in the formation of only portion of the letter that is really new to him, for the lower the small letters of the writing alphabet, as exhibited in large part of the letter is very nearly the same as that portion of the tert, giving fewer copies than we have hitherto done, for the bottom-turn or top-and-bottom-turn which is below the line c c. sake of affording practice in the formation of each particular In Copy-slip No. 36 the letter o and the bottom-turn are letter in combination with others.
given. These strokes, in combination from the letter a, as in In Copy-slip No. 35 the learner's attention is directed to the Copy-slip 37, the bottom-turn being appended to the letter o in letter 0, which is a complete and perfect letter in itself, while, such a manner that the point where the hair-line forming the at the same time, it may be considered as a simple elementary right side of the letter cuts the line c c lies in a line passing form, since it enters into the composition of the letters a, d, along the centre of the thick down-stroke of the bottom-turn. and q. It also influences the formation of many other letters The letters d and q are formed by adding modifications of the of the alphabet, as the learner will see hereafter ; but for the bottom-turn to the letter o, as shown in Copy-slips 38 and 39.