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EXAMPLE.-What is the least common multiple of 24, 16, and

12?

SOLUTION.-By inspection, we find the greatest common divisor of 24 and 16, is 8. Now, 24-9=3; and 3x16-18. Again, the greatest common divisor of 48 and 12, is 12. Now, 48-12

4; and 4X12-13. Ans.

PROOF.-Resolving the given numbers into their prime factors, 24 2×2×2×3; 16=2x2x2x2; and 12-2X2X3; consequently, 2×2×2×2×3=48, the least common multiple.

The reason of this rule depends upon the principle, that if the product of any two numbers be divided by any factor which is common to both, the quotient will be a common multiple of the two numbers. Thus, if 48, the product of 6 and 8, be divided by 2, a factor of both, the quotient 24, will be a multiple of each, since it may be regarded either as 8 multiplied by the quotient of 6 by the factor 2, or as 6 multiplied by the quotient of 8 by the same factor. Hence, it is obvious, that the greater the common measure is, the less will be the multiple; and, consequently, the greatest common measure will produce the least common multiple.

When the common multiple of the first two numbers is found, it is evident, that any number which is a common multiple of it and the third number, will be a multiple of the first, second, and third numbers.

EXERCISES.

1. What is the least common multiple of 75, 120, and 300 ?
2. What is the least common multiple of 96, 141, and 720?
3. What is the least common multiple of 256, 512, and 1728?
4. What is the last common multiple of 375, 850, and 3400?

LESSONS IN GERMAN.--No. XIX.
SECTION XXXIII.

Beite (plural) is declined like an adjective, and, unlike its equivalent, (both) comes after the article, or pronoun with which it is used. Ex.: Die beiten Ste; both the hands: mine beiden Sante; both my hands. Atte (all) is sometimes, for the sake of emphasis, placed before beite, and, may together be transinted, both of them," or simply, "both" as, alle beite; both of them; both.

44

VIII. Anter, with a noun denoting time, may be employed to designate as well a future as a past period; but never, like the word "other," as in the phrase "the other day," to denote indefinite past time. Ex. Den antern Tag nach seiner Ankunft verlee er seinen Vater; the "next" day after his arrival, he lost his father. Morgen gehe ich nach Rem, und ten antern Tag nach Neavel; to-morrow I go to Rome, and the "nert" day to Naples. As in the above examples, anter, when similarly employed, is rendered by "next."

IX. The neuter anteres, preceded by etwas," (in conver sation usually contracted to was) is rendered by the phrase "another thing" Das ist etwas Anteres, or, tas ist was Anteris; that is "another thing."

X. The adverb anders is readily distinguished by its ferm, and is rendered by "otherwise, differently," &c. Ex.: Er spricht anders als er denft; he speaks otherwise than he thinks.

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Mittel, n. means;
Muster, n pattern;
Pennsylva'nien,

(there);

Damesschiff, n. steam- Pennsylvania;
ship:
Pflaume, f plum;
G'benfe, just as (IV.); Recht, n. right;
Gi'nige, some, several; Meten, to speak, talk:
Mühren, to move, af-
life, f. Elisa;
fect;
Erlau'ben to allow;
Freu'tenthräne f. tears ae, f. thing, affair;
of joy;
Sem'merreck, m. sum- Zweck, m. aim, purpose.
mer-coat;
Geleert, vacant, empty;
Er hat zwei Söhne, aber beite sind
taubftumm

Der Riese faßte die Keule mit bei.
den Händen.

Hat ter Kaufmann ein Vert eder
einen Wagen?
Er hat Beides.
Die Wahrheit und die Rose find
sehr schön, aber Beite haben Dor.

nen.

razie rengeben, to take a walk; Stoat, m. state; Thaler, thaler (a Ger

man coin); Trennen, to separate; Un'angebaut, uncultivated; Unmöglich, impossible; Unrecht, wrong; Verstän'vig, intelligent; n. Waare, f. ware, goods; Weg nehmen, to take away: Winterred, n. wintercoat; Weblfeil, cheap; Zuschauer, m. specta tor;

Gin auf'richtiger Mann verabscheut
eine Lüge.

I. Veites, (neuter singular) is frequently employed to couple fro things different in kind, whether designated by nouns alike or different in gender. Ex.: 25cm ist ($ 129. 2.) tiefes Messer und riefes Schwert? Veites gehört meinem Frenate; bb belong to my friend. Hat 3baen ter madee nur tie lor et auch in Ring gemacht? Er hat Bates gemacht; or, Vei e gema. t Sind Sie mit ter Uhr und dem Ring zuirieren? Nein ich bin mit tem unguicieten, benn Beites ist nicht nach meinem Wunsie; no, I am dissatisfied with both, for both are not according to my wish.

II. For the pronoun "neither" the phrase feines or feins von feiten" is used. Ex.: Haben Sie das neue ever tas alte Vuch? Ich habe keine von Beiten; I have neither (of the two).

III. Rect and intet like the words "right" and “wrong' are nous, adjectives, and adverbs. The phrases, however, "to be right, to be wrong," are expressed in German by the noun, with the transitive verb baben. Ex.: Gr hat Rect; he (has) is right. Sie haben nicht Unreat; you (have) are not wrong.

""

IV. Gbenfo, before an adjective, signifies, "just as. Ex.: Dieses Kind ist eben se alt wie jenes; this child is just as old as that. Diefer Mann bat even so viel Klugheit wie Verstant; this man has just as much prudence as understanding.

1. Wollen Sie ein Muster von diesem oder jenem Tuche baben? 2. 3ch will keines ven beiten haben. 3. Wir geben im einen Tater für jeten ter beiten Männer. 4. Trinken Sie Wein eter Vier? 5. Sch trinke weter Wein noch Vier (or ich trinke feines ven beiten). 6. Eie haben Recht, daß Sie das gethan haben. 7. Hat Johann Necht, daß er se tange ausbleibt ? 8. Nein, er hat Unredt, ta er seine Aufgaben zu lernen V. Ganz wie," with a verb, siguities "precisely" or "just as" hat. 9. Wie viel Tuch braucht der kleine Friedrich zu (Sec. 74. 1) einem or like " Ex.: Gr ist ganz wie ich; he is just as I (am), he is just. Sommerrede? 10. Gr braucht ebensoviel, wie zu einem Winterrocke. 11. like me. Sie tenkt ganz wie er; she thinks precisely as he Der Staat Pennsylvanien liefert ebensoviel Koblen, als ganz England. 12, (thinks), she thinks precisely like him. Arbeitet Gustav nicht ebenseviel, wie sein Bruter Hermann? 13. e kleine Elise gab ihrer Schwester Vauline ebensoviel Pflaumen, wie ihrer Freuntin Emma. 14. Haben unsere Nachbarn noch keinen Garten? 15 Nein, fie haben noch keinen. 16. Bleiben sie noch lange auf dem Lande ? 17. 3ch bleibe noch eine kurze Zeit da, und auch meine steunte 18. Gelca Sie heute noch frazieren? (Sect. 65. 1) 19. Nein, renn ich mus Re✩ arbeiten. 20 Die Freurenthränen ter lang getrennten Freunde rührten vie erzen aller Zuschauer. 21. Können sie die Waaren nicht billiger vers faufen? 22. Es ist rein unmöglich. 23. Sie müssen dieses anders mecca 28 Was fann ich anters thun? 24. Du kannst anters reten und

VI. Nech, besides its signification as disjunction, (Sect. 12.) is variously rendered by "still, some or yet more, another, besides," &c. Ex.: Gr schläft nech; he sleeps still. (ich dem Kinte noch Bred; give the child some more bread. Wann bat er noch ein Pferd gefaust? when did he buy another horse? Ginen Apfel hat das Kind gegessen, aber es hat noch einen; the child has eaten apple, but it has one besiles (or another).

"

Wicht, connected with a negative word, is used like its

lent "more. Ex.: Ich habe feins mehr; I have no more. ne nicht viel mehr; I have not much more. Used with a he adverb follows, while in English, it precedes the noun

Fast jeder Mensch hat e'ben so viel
Kummer als Freute.

He has two sons, but both are deaf and dumb

The giant seized the club with

both hands.

Has this merchant a horse or
a wagon?
He has both?

The truth and the rose are
very beautiful, but both have
thorns.

An upright man abhors a lie.

Nearly every human being has quite as much sorrow as joy

Hanteln. 25. Ich wette Sie besuchen, wenn Sie es erlauben. 25. Er erzählte die Suche ganz auters. 26. Es ist etwas anderes, ob ich schreibe: er in gelehrt," eter „geleert."

1. Has the teacher taken away the paper or the book? 2. He has taken away both; then both belong to him. 3. Both towns are situated on navigable rivers. 4. They may take either way, as they have proceeded so far. 5. A great part of the land in America is still uncultivated. 6. He who wants the purpose. must will the means. 7. The Rhine steamboat has just set sail for Holland. 8. You err altogether when you say that you have quite surmounted every difficulty, otherwise all that you have stated would be correct. 9. Which of us is right, I or he? 10. You are both wrong. 11. It is quite another thing to say that he was not well, and could not come in consequence of it. 12. I shall speak no more about it; because I have found upon closer investigation, that he is neither covetous, nor prodigal. 13. They do not think themselves better than others. 14. Emma is just as intelligent as Elisa.

SECTION XXXIV.

noch zu überreden.

15. Sein Betragen ist gar nicht zu verzeihen. 16. Wie heißt Ihr Freund? 17. Er heißt Jafeb. 18. Wie heißt das auf Deutsch? 19. Es heißt eine Brille. 20. Ein Kunstwerk ist defto schöner, je vollkommener es ist, das heißt, je mehr Theile es hat und je mehr alle diese Theile zum Zwecke beitragen.

Die Rose heißt die Königin der
Blumen.

LESSONS IN ENGLISH.-No. XX.
By JOHN R. BEARD, D.D.
SUFFIXES (continued).

VERBS ACTIVE IN FORM WITH PASSIVE SIGNIFICATION.

I. The infinitive of the active voice, in certain phrases, is, THERE is nothing that will more help to form an English heart in ourselves and in others than the study of the English language. especially after the verb in, often employed in a passive sig-We could scarcely receive a single lesson on the growth of our English nification. Ex.: Er ist zu ehren; he is to be honored. Gr ift 3 tongue, we could scarcely follow up one of its significant words, leben; he is to be praised. Lay ihn rufen: let him be called. without having unawares a lesson in English history as well; withThis use of the infinitive prevails to some extent in English out not merely falling on some curious fact illustrative of our Thus, we may translate literally the following examples: national life, but learning also how the great heart which is beating Dieses Haus ist zu vermiethen; this house is to let. Sind diese erfel at the centre of that life was gradually shaped and moulded. We zu effen? are these apples to eat? Dieses Wasser ist zu trinken; this should thus grow, too, in our feeling of connexion with the past, water is to drink. Dieser Knabe ist zu tareln; this boy is to blame of gratitude and reverence to it; we should estimate more truly, II. Heißen, signifies, to name, to call; also sometimes to and therefore more highly, what it has done for us, all that it has command. In the sense of naming or calling, it is most gene-bequeathed us, all that it has made ready to our hands. It was rally used in a passive signification. Ex.: Wie heißen Sie? How something for the children of Israel when they came into Canaan, are you called? or, what is your name? Ich heiße Rutely; my to enter upon the wells which they digged not, and vineyards which name is Ralph. they had not planted, fields which they had not sowed, and houses which they had not built; but how much greater a boon, how much more glorious a prerogative, for any one generation to enter upon the inheritance of a language which other generations by their truth and toil have made already a receptacle of choicest treasures, a storehouse of so much unconscious wisdom, a fit organ for exover-pressing the most subtle distinctions, the most tender sentiments, the largest thoughts, and the loftiest imaginations, which at any time the heart of man can conceive.*

llebung, f. practice,

use;

per

EXERCISE 38.
Aussprache, f. pronun- Heißen, to name (See
ciation;
II.);
Vei tragen, to contri- Herstellen, to restore, leberre'ten,
bute;
re-establish;
suade;
Braunschweig, n. Himmel, 772. (the) Ur'berschuh, m.
Brunswick;
heavens, sky;
shoe;
Durch, through, by Jafob, m. James; Ueberzeu'gen, to
Je desto, or je je, the-
vince;
the (Sect. 31. VI.); Vermie'then, to let;
Kunstwerk, n. work of Verzeihen, to pardon,

means of;
Ginzig, single, only;
Grflim'men, to elimb;
Grier'nen, to learn;
Gewinnen, to win,

art;
Mühe, f pains, toil;
gain;
Ohne, without;
Glückseligkeit, f. feli- Schnell, quick, rapid-
city i
ly;
Ein böses Gewis'sen ist nicht zu be.
ruhigen.
Ein Gelehr'ter ist leichter zu über.
zen'gen, als ein Dummer.
Weisheit, ist nicht wie eine Waare
zu kaufen.

to

con

excuse;

Bellfom'men, perfect;
Werthvoll. valuable.

An evil conscience is not to be
quieted.

A learned man is easier to

vince, than a stupid (one). Wisdom is not to be bought

like wares.

Etiquette is the same word as our ticket, and originally denoted the short inscriptions, or tickets put on packages of goods to point out what they contained. But similar etiquetts or tickets were con-employed to declare certain observances required in a public assembly; and so the word came to signify forms and formalities, a strict regard to custom, and in general, social conventionalism, particularly in relation to deportment.

The rose is called the queen of
flowers.

1. The pronunciation of foreign words is only to be acquired through practice. 2 Nothing is to be learned without pains. 3. Perfect felicity is not to be found in this world. 4. You speak so quick, that you are not to be understood. 5. Health is not to be bought with money. 6. The peace of the town was not to be restored through severe orders. 7. How do you call these flowers? 8. They are called tulips. 9. The intelligent scholar is to be praised. 10. The difference between to buy and to sell, must, by this time, be known to the scholar. This book is to be had of the bookseller C. in London.

11.

Ette, of French origin, is found in words taken from the French; as, coquette, etiquette. Coquette is, with us, applied to a female who employs her personal attractions to gain attentions from males. In French, there is the word coquet, a male coquette. Coquet seems to come from cog, a cock, a showy and uxorius animal; and accordingly, it signifies a man who resembles a cock in his attention to woman. By a natural step, in the progress of language, the term was applied to females.

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Coquet and coy at once her air,

Der Löwe heißt der König der
Thiere.

The lion is called the king of
the beasts.

1. Diese greßen schönen Häuser find alle zu vermiethen. 2. Das eine Haus ist zu vermiethen, das audere zu verkaufen. 3. Es ist nicht zu glau ben, daß er uns verlassen hat. 4. Dieses Buch ist bei Herrn Westermann in Braunschweig zu haben. 5. Kein einziger Stern war am ganzen Him mel zu sehen. 6. Wie ist dieses lange Wert auszusprechen? 7. Wo find die besten Stiefel, Schuhe und Ueberschuhe zu finden? 8. Die beften, bie ich gesehen habe, sind bei meinem alten Nachbar N. zu finden. 9. Das Feuce brannte so schnell, daß nichts im Schlosse zu retten war. 10. Nichte Werthvelles ist ohne Müße zu gewinnen. 11. Dieser hohe Felsen ist nicht zu erklimmen. 12. Dieses alte Haus ist nicht mehr herzustellen. 13. Durch diesen Walt ist nicht zu kommen. 14. Er ist weter zu überzeugen,

Both study'd, though both seem neglected;
Careless she is with artful care,

Affecting to seem unaffected,"

Congreve. Eur, a French termination, from the Latin or; thus vendeur (a seller), is from the Latin venditor; proditeur, a betrayer, from Latin proditor. It is similar in import to our ending er, and denotes an actor; e. g., producteur, Fr. a producer. Of old many English words, now terminating in or, terminated in eur; as autheur for author. The termination is still retained in certain nouns denoting abstract qualities; for instance, grandeur (Lat. grandis, great); hauteur (Fr. haut, high), derived immediately from the French. The notion of the actor is retained in the French douceur (from doux, sweet), a sweetener; a fee, or bribe.

Ever, connected in origin with the Latin aevum, age; and the Greek aion, age, come to us directly from the Anglo-Saxon aefre,

French "On the Study of Words," p. 25-6.

and signifies always, an enduring reality, either in time past (Ps.

ANSWERS TO CORRESPONDENTS. XXV. 6; xc. 2), time present (Ps. cxix. 98), or time to come (Ps. csi. 5). Ever, as a suffix, strengthens the word to which it is ap- therefore agree with gender, number, and case. Your statement under

LATIN.-J. R.: In Lesson IX., "norse" qualifies " nothing," and must pended, thus : " whatever you do " has more force than what - 2nd ” is incorrect; consult the Lesson, and do not make unnecessary inyou do." Ever is found in other compounds ; e. g., whoever, quiries : your letter has other proofs of haste or want of care. The specimen however, wherever, whenever. Additional force is given by the in- of your Latin is pretty well; consult the Key.-VINCIo will act foolishly it sertion of the particle so; as, whosoever, whencesoever, whither. By running from one thing to another, he will become master of nothing. soever. This so used to stand where ever is now placed; as, whoso, Every aid that marks of accentuation can give, is given in the Lessons; only howso, whatso.

from a living tongue can complete accuracy be obtained.

T. R. N.: We do not reniember receiving his cominunications, and we "Her cursed tongue (full sharp and short)

have a tolerably good memory. Can he kindly suppose, not to say charitably Appeared like aspis' sting, that closely kills,

beliere, that we, THE Editor, never received thein ?-W.0, M. (London): Or cruelly does wound whomso she wills."

We are not aware that there is at present any professed teachers of artificial Spenser, “Faerie Queen e.” memory going about town or country.-J. M.: In the sentence alluded to

that is used for the relative which, the antecedent being years, and is there. Full, of Saxon origin, obviously the same as the adjective full, fore the nominative to the verb have.- Amicus : See the regulations for the gives an instance of the origin of these particles in words which degree of M.A. in the "London University Almanac.". Your solution of the originally had a definite form and signification. According to its snail query is wrong.-W. Moore (Chelsea): If he will send a list of words root-meaning, full (now in combination written ful) denotes a large correct copy of the inscription : there is an error in it. - Correct answers to portion of the quality indicated by the word to which it is affixed; the snail query have been received from J.8.(Woodhali Colliery); A YOUTH as, hate, hateful; thank, thankful; grateful, delightful. Full has TEN YEARS OF AGE (Easington-lane), beautifully done; Isak (Leicester). for its opposite less ; e. g., merciful, merciless. In the employ: (Portobello); and others.-A SUBSCRIBER (Piccadilly) should by all means ment of words, you cannot follow analogy alone, but must consult study the Lessons in English first.-Constant RBADRR (Dartınouth). and authority, thus : you may say penniless, but cannot say penniful; J. 0. N. (Liverpool) have not come up to the requirements of the nine-digityet pitiful is as good as pitiless.

square query.- INQUIRER (Wakefield): The Lessons will ultimately be pube

lished as he wishes; in the meantime, we recommend the P. E.or Dr. Beard's " How oft, my slice of pocket store consum'd

"Latin Made Easy," see note, col. 2, page 72, vol. I. P. E.-B. A. S. 6.: Still hungering, pennyless, and far from home,

Apply to the Rev. J. Curwen, Plaistow, by letter.-HENRICUS : Go on and I fed on scarlet hips and stony haws." Cowper, “ Task.”

prosper; study the Lessons in Penmanship in the P. E. and Cassell's Arith

inetic and Euclid, with the Lessons on the same in the P.E., and then apply to Fy, is from the Latin facio, I make. Facio, in combination, be- the Normal school nearest to your residence.-J. GOUGH (Liverpool): Thanks comes ficio; as in efficio. The fi in this word, written fy, is the for his suggestion; as to eyes, ours are not the best, but we advise him to particle under consideration. It is seen in fructify, literally, to let doctoring them alone; ibe iinprovement of the general health will do au

that is required. You know "if one member suffer all the members suffer inake fruit; that is, to make fruitful.

with it," 80, if all the members improve by health so will the eyes.-R. “Calling druv kenness, good-fellowship; pride, comeliness; rage, Tucker (Cheapaide): The P. E. Lessons, of course, for the Germán; and valour; bribery, gratification.Bishop Morton.

the same for the Spanish when they come out.-J. THURLOW (Minories):

We stated repeatedly that this office supplies covers for the P. E. only at the Head or hood, from the Saxon had, head, in composition, denotes prices ls for the common edition, and 15. 61. for the fine edition. If it is the essence of any person or thing; its essential condition, viewed wanted to be bound in any other style, application must be made to regular as a whole ; thus, in Anglo-Saxon and English, manhad, manhood; bookbinders:-J. G.jun. (Kelso): As his answer to the snail query is wrong.

we do not insert his proposed query ; besides we cannot read the word of wifhad, wifehood, or womanhood ; cildhad, childhood; brotherhad, whose spelling he is doubtful. In the German words the f and the s are brotherhood ; preosthad, priesthoud.

pronounced, and not the p.-G. A. jun. (Liverpool): It is now too late to “Can'st thou, by reason, more of golhead know,

alter our plan; but the two volumes can still be bound together, the

title-pages and indexes retained. There is an Illustrated Edition Unci Than Plutarch, Seneca, or Cicero."

Tom's Cabin, issued by Mr. Cassell, price 1s., in boards; and George Dryden, “Religio Laici."

Cruikshank, Esq., has undertaken to illustrate this surprising tale by 37 Head is sometimes employed with a more direct reference to drawings from his inimitable pencil, to be published in Weekly Numbers, the meaning, which it has in current use; as in wronghead and price 2d: each, the first of which is issued this day.

AMICUS (Liverpool): Whateley's.-1. J. (Beliast) surprises us; here we wrongheaded.

have four important languages, carrying on from week to week in our “ Much do I suffer, much to keep in peace,

penny numbers, besides other important, useful, and varied informatioa, This jealous, waspish, wronghead, rhyming race." Pope.

and yet he wants a Fifth language put in, and all for a penny! Greek

SHALL be given; but we MUST take our own time; reason's reason. Be “Whether we (the Irish) can propose to thrive so long as we enter

cause He Finds a difficulty in learning Greek nouns, probably in some bad taiu a wrongheuded distrust of England ?''-- Bishop Berkeley.

Grammar, this is no reason why we should throw all our numerous students After a similar manner we use both heart and head, in fainthearted, of other subjects overboard, in order to serve him! And he is not alone ;

we have numerous correspondents like him every day; to satisfy all of lighthearted, hotheaded, lightheaded, &c.

whom, would require a book as large as the Bible to be given to thein every Ible, see able formerly explained under suffixes.

week for a penny. We hope some of our readers will take this friendly hiot, Ic, ick, ich, have counterparts in the Latin termination icus, and and be more considerate in future. We shall do all in our power to piease the German ich, isch; as soporificus (sopor, Lat. sleepiness), he can Matriculate at the London University,

without going under the wing

but we cannot do impossibilities.-W. M. R. W.: We are doubiulit soporific, rusticus (rus, Lat. the country), rustic, cildisc in Anglo- of some tutor, but we advise him to try : we have sometimes seen attached Saxon, childish in English ; bookish.

to the name of one who passed the Matriculation examination successfully, “The sweet showers of heaven that fall into the sea are turned into

the words privale tuition - A. S. W.: The words Russia and Prussia, are

pronounced exactly as they are spelt. its brackish taste."- Bates. Ical, an adjective-ending, from the Latin icalis; e. g., amicalis,

LITERARY NOTICES. amical (friendly), grammaticalis, grammatical, so critical (krino, Gr. I judge), which passes into a noun by dropping al, as critic;

JOHN CASSELL'S ALMANACKS FOR 1853. so musical, music, mystical, mystic.

THE UNCLE Tom's CABIN ALMANACK; or, THE ABOLITIONIST MEMENTO " Fool, thou didst rot understand

FOR 1853, splendidly Illustrated by George Cruikshank, Gilbert, Harvey, The mystic language of the eye nor hand."

• Phiz," and other eminent Artists, price ls. Donne.

Price Sixpence, THE ILLUSTRATED EXHIBITOR ALMANACK for 1853, Te, from the Latin adjective termination ilis, to be seen in containing upwards of Thirty beautiful Engravings. docilis (doceo, Lat. I teach), docile, teachable ; fragilis (frango, Price Twopener, THE POPULAR EDUCATOR ALMANACK for 1813, conLat. 1 break), fragile, easily broken. Some Latin adjectives in ilis taining Forty-eight Pages of most interesting and valuable Educaticna! are represented by adjectives in ful in our tongue, as utilis, useful. Statistics, including a comparative View of Education at Home and abroad; In, ine is from the Latin termination inus, which denotes some position of Technical Terms ; &c. &c.

Essays on the Leading Sciences; Brief Notices of Eminent Scholars; Ex. times a name, as Tarentine, an inhabitant of Tarentum, but in Price Twopence, THE TEXPERANCB ALMANACK for 1863, much improved English more often a quality, as genuinus (genus, Lat, a kind or and enlarged, and in which will be inserted a Tale of thrilling interest, from race), genuine ; that is, that which possesses the qualities belonging Tom's Cabin," entitled, " THE PLEDGE TAKEN ; or, The Husband Saved,

the inimitable pen cf Mrs. Harriet Beecher Stowe, authorese of "Uncle to its kind, in opposition to spurious, which, in its Latin meaning, and a Family' made Happy;” with valuable details of the great Temperance signified a bastard.

Movement, Statistics, &c. With several Engravings. "We use

Price Sixpence, THE PROTESTANT DISSENTEKS' ALMANACK, for 1853, No foreign gums, por essence fetch'd from far,

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In our last lesson, we explained the nature of Bode's law of to be censured; the greatest men of all periods have been fond the distances of the planets so far as to show that, in the series of such lusus ingenii," jeux d'esprit, or plays of the understanding, of numbers which represented this law, there was a gap or Another fine specimen of the lusus ingenii was given out by chasm between the numbers 16 and 52, which required to be Dr. Olberg. On the discovery of the first three telescopic filied up in the following manner, to render the series complete; planets, he conjectured that they were the fragments of one thus,

large planet, our supposed Pluto, which had formerly existed 28=4+3X2X2X2.

and revolved in the space between Mars and Jupiter, at a The discovery of the planet Uranus by Sir W. Herschell, distance corresponding exactly, or nearly so, to the law of about nine years after the announcement of this law by Bode, Titius or Bode; and which had been burst asunder by some

He concluded also, that, confirmed the truth of the series, by showing its applicability tremendous convulsion of nature. to the remotest known planet in the solar system. Had there although the orbits of these planets, were differently inclined however, been a planet revolving in the space between Mars to the ecliptic, yet, as they must all have diverged from the and Jupiter, and had it been called Pluto, and another called same point, they ought to have two common points of union, Neptune beyond Uranus, then the series would have been so far or two nodes (points of intersection) in opposite regions of the complete, and the law would have been completely verified. heavens through which all these planetary fragments must The series would then have stood as follows, with the names sooner or later pass. One of these nodes he found to be in the of the planets in the order of their distances from the Sun, constellation Virgo, and the other in the Whale, in the latter and the proportionate numbers representing those distances : of which Mr. Harding actually discovered Juno. With the

intention, therefore, of detecting other fragments of this supposed Mercury, 4=4

planet, Dr. Olbers examined thrice every year all the little Venus, 7=1+3

stars in these constellations, when his labours were rewarded The Earth, 10=4+3X2

by the discovery of Vesta in the constellation Virgo ! NotwithMars, 16=4+3x2x2

standing this singular fact, we find Sir John Herschell writing Pluto, 28=4+3x2x2x2

as follows so late as 1834 :—“It has been conjectured that the Jupiter, 52=1+3x2x2x2x2

ultra-zodiacal planets are fraginents of some greater planet, Saturn, 100=1+3x2x2x2x2x2

which formerly circulated in that interval [between Mars and Uranus, 196=1+3x2x2x2x2x2x2

Jupiter], but has been blown to atoms by an explosion; and that Neptune, 388=1+3x2x2x2x2x2x2x2

more such fragments erist, and may hereafter be discovered. This With this singular empirical ( the result of trial) law before them, may serve as a specimen of the dreams in which astronomers, astronomers, still harping upon the numerical analogies of likeother speeulators, occasionally and harmlessly indulge!"Dr. nature from the time of Kepler, and even from that of Pytha- | Olbers did say that “we might expect to discover in the same goras till now, were surprised, on the first day of the present region more such fragments describing an elliptic orbit round century, by the discovery of a planet nearly in the place where the sun ;'' but the ridicule, not to say the supposed profanity, our supposed Pluto should have been found, namely Ceres; and which was attached to such a conjecture, no doubt prevented within seven years thereafter, by the discovery of other three, other astronomers from attempting to verify it by new disrevolving nearly at the same distance, but in different orbits, coveries ; for a period of no less than thirty-eight years elapsed all intersecting each other. The original remarks of Tirius on before any addition was made to these fragmentary planets the subject of the law thus so singular'y veritied will not be in the solar system. At last the idea was again revived unacceptable to some of our readers; we extract them from by the discovery of Astræa, on the 8th of December, 1845; and Humboldt's “Cosmos:"_." "If” says ne, “we exainine the from that period to the moment at which we now write, 18th distances of the planeis we find in almost all a proportion of October, 1852, no less than TWELVE NEW PLANETS, fragments be:ween their distances apart and the increase of their of our supposed Pluto, hare been discovered revolving all in the corporeal magnitudes. If the distance from the Sun to same region of space, and having their orbits all intersecting Sarurn gives (be divided into] 100 parts, then Mercury is one another, nearly at the same distances from the sun. We distant 4 such parts from the Sun, Venus 4+3=7 parts from say twelve new planets, for although we inserted only eleven in the Sun, the Earth 4+0=10, Mars 4+12=16. But from Mars the table of the solar system in our last lesson, we have since to Jupiter we come to a departure from this progression pre- found that Mr. Hind has discovered in the same region a new viously so exact. Beyond Mars there follows a space of 47 24 planet, which he calls Fortuna, and which is supposed by some =28 such paris ; but here we find neither primary planet v.or to be the same with a new planet, said to be very recently dissatellite. Can we suppose that the Great Architect has eft covered at Marseilles, and hence called Massilia. Attempts, this space void: We must not doubt that it is occupied; it indeed, have been made to prove the truth of the hypothesis of may be by the hitherto undiscovered satellites of Mars, or Dr. Olbers regarding the origin of these planets by a Mr. Jupiter may have additional satellites that have never yet been Kirkwood, in America, who has imagined it possible to underseen by any telescope. From this unknown interval (unknown take the restoration of the original shattered planet from the as to that which occupies it) the space to Jupiter is 4+48–52. surviving fragments, after the manner followed in regard to Then follows Saturn at the solar distance 4+96= 100 parts-an the remains of extinct animals. He assigns to the planet-our admirable proportion !" Titius therefore, imagined the interval supposed Plutoa diameter larger than Mars (about 4,320 between Mars and Jupiter to be occupied with several bodies miles), and a rotation slower than that of any other planet, belonging to our system; but he conjectured them to be making the length of its day 57 hours and a half. Thus we satellites and not planets. And as far, indeed, as their mag- see that, both in earth and in heaven, both underground and nitudes are concerned, they partake more of the nature of the above it, there are phencmena daily and hourly taking place, if former than of the latter, being all so small that none of them we would but observe them, which are calculated to strike the can be seen without the aid of a telescope. Hence they are mind with awe, and even with fear, at the wonderful arrangefrequently called telescopic planets.

ments of the Great Creator. Geology teaches us that underThe failure of the law of Titius in the case of the first planet ground there is a great central fire which occasions frequent in the solar system, was clearly pointed out by Gauss, in words disruptions of the carth's crust in different parts of the world; to the following purport, on the occasion of the discovery of and we know that the power of this fire or central heat is only Pallas by Dr. Olbers, in 1802:—"Contrary to the nature of all restrained by His word from producing effects of the most distruths which deserve the name of laws, that of Titius astrous kind to the numerous tribes of living creatures which applies only in a very cursory manner to most of the planets, dwell on the surface of the globe, and to man himself, the lord and (which does not appear to have been before remarked) not of the lower creation. Astronomy teaches us that such erents at all to Mercury. It is clear t' at the series 4,4+3, 4+6,4+12, have taken place above ground in the regions of the solar 4+24, 4+48, 4796, 4+192, wito which the distances should system ; and that there some vast central fire has created an agree, is not a continuous series. The number preceding 4+3, explosion which shattered in pieces a planet like our earth, and ought not to be 4, that is 4+ , but 4+1); for in the general sent the fragments revolving in space around the sun, a series expression, which includes all the terms, namely 4+3X 21~2, of shapeless messes, telling their tale of disaster to all the other when 51, the result is not 4 but 5! Attempts to discover planets which revolve like them around that great centra such proximate agreements in nature are, however, by no means' luminary.

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