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LESSONS IN FRENCH.-XXVIII. soldat? 24. Je ne lui ai rien donné. 25. Pendant son séjour à

B., nous lui donnâmes tout ce qu'il voulut. SECTION L.-THE PAST DEFINITE (S 120]. 1. Tur past definite may be called the narrative or historical

EXERCISE 96. tense of the French. It is used to express an action entirely 1. What did you receive last week ? 2. We received fifty past, definite and complete in itself. The time must be specified, francs from your friend, and twenty-five from your brother. 3. and every portion of it must be elapsed. Some time at least Did you take your son to church with you yesterday 4. I should have occurred since the action took place.

did not take him thero (y). 5. What did you lose last year? Mon frère partit hier pour Paris, My brother left yesterday for Paris.

6. We lost our money, our clothes, and our horses. 7. Have 2. The student will bear in mind that the past indefinite not find them. 9. Did they speak of your brother yesterday ?

you looked (cherchés) for them ? 8. I looked for them, but did [Sect. XL.) may be used for the past definite. The past definite,

10. They spoke of him and of you. 11. What did the physician however, may never be used for the indefinite. In conversation

give you ? 12. He gave me nothing. 13. At what hour did the indefinite is often preferred to the definite, as the latter

your sister rise yesterday? 14. She rose at five o'clock. 15. would at times appear too formal ($ 121 (3)].

Did you rise early this morning ? 16. We rose at half-past 3. The past definite may generally bo rendered in English by the simple form of the imperfect, or by the same tense conju- not sold it, he has given it to his eldest sister. 19. Has the

six. 17. Has your cousin sold all his property? 18. He has gated with did. The past definite can never be rendered in

traveller related his adventures to you? 20, He related them English by the participle present of the verb preceded by was.

21. Did that man try (cherché) to speak to your father? J'allai à l'église hier matin, I went or did go to church yesterday 22. He tried to speak to him. 23. Did the professor speak of

morning.

your brother during his stay at your house ? 24. He spoke of 4. TERMINATIONS OF THE PAST DEFINITE OF THE FOUR him. 25. Has your friend worn his new coat? 26. He has CONJUGATIONS. (See Sect. XXII., and $ 60.]

not worn it yet. 27. Have you thanked your brother ? 28. I Jo chant ai fin .is

have thanked him.
rend
rec
is.

29. What have you given to your eldest
sang
finished received

rendered,

sister? 30. I have given her nothing, I have nothing to give Tu parl

chér -is

aperç -us vend .is, her. 31. When your brother gave you a book last year, did spokest cherishedst perceivedst soldest.

you thank him ? 32. I did not thank him. 33. Is it late? Il donn fourn it

tend

34. It is not late, it is only six. 35. Is it fine weather or bad gavo furnished gathered

tended.

weather 36. It is very fine weather. Nous cherch -ames

pun
-imes
conç -ûmes

entend imes,
sought
punished conceived heard.

SECTION LI.-THE PAST DEFINITE OF IRREGULAR Vous port -âtes sais -ites

-ûtes
perd
-ites.

VERBS.
carricd
seized
owed
lost.

1. The terminations of the past definite of irregular verbs Ilg aim -èrent

-irent déç -urent mord -irent. loved, liked united

are seldom arbitrary,* but an irregular verb of one conjugation deceived bit.

will sometimes, in this tense, assume the terminations of another 5. It will be seen that the terminations of the second and fourth conjugation. In a few instances the stem (Sect. XXII.] of the conjugations are alike.

verb is entirely changed.
RÉSUMÉ OF EXAMPLES.
Avoir, to have. ETRE, to be. VOIR, to see,

LIRE, to read. On nous parla de vous hier. They spoke to us of you yesterday.

J'

f -as
vis

1-us. Le banquier nous donna de l'argent The banker gave

money last

Tu
e -us
f-us
V.is

1 -us. l'année dernière.

Il e-ut
f -ut

1 -ut. Le banquier nous a donné de l'ar. The banker has given us money.

Nous e-ûmes

f -ûmes
v -imes

1 - umes. gent.

Vous e-utes

f -ûtes
v-ites

1 -utes. Le professeur nous parla de vous The professor spoke to us about you

Ils e-urent

f -urent
virent

1 -urent. l'année dernière. Il nous a parlé de ses amis et des He spoke to us of his friends and of new stem, e-us, f-us; être and lire, though belonging to the fourth

2. Avoir and être, it will be perceived, take in this tenso a pôtres. Pendant notre voyage il nous ra. During our journey he related to us

conjugation, take the terminations of the third; and voir, a verb conta ses aventures.

his adventures.

of the third, takes the terminations of the fourth. Il nous a raconté l'histoire de sa He related to us the history of his 3. In other instances, the stem of the verb drops some of its vie.

lifo.

letters, and sometimes adopts others. This may be seen in the VOCABULARY.

verbs Alné, -e, elder, eldost. Se lev-er, 1, ref., to Propriétés, f. pl., pro

VENIR, PRENDRE, CRAINDRE, CONNAÎTRE, COXDUIRE, Avec, with.

rise.
perty.

to come.
to take.
to fear.

to knor. to conduct. So couch-er, 1, ref., to Lorsque, when.

Remerci-er, 1, to thank.
Je vins
craign -is

conduis -is. go to bed. Neuf, -ve, now. Séjour, m., stay. Tu V -ins craign -is

conduis -is. Dernier, -e, last. Ordinairement, gene- Semaine, 1., week.

Il v int

craign .it conn -ut conduis -it. s'échapp-er, 1, ref., to rally.

Soldat, m.,
soldier.
Nous v inmeg

craign -imes conn -ûmes conduig -imes. escape. Pendant, during. Tard, late.

Vous v -intes

craign -ites conn -ûtes conduis -ites. Habillement, m., dress. Pri-er, 1, to beg. Trop tôt, too soon.

Ils V -inrent pr-irent craign -irent conn -urent conduis -irent. EXERCISE 95.

4. Like venir, are conjugated all verbs ending in enir; like 1. Le banquier reçut-il beaucoup d'argent la semaine dernière? and uire; and like prendre, those composed of this verb and a

craindre, connaître, and conduire, those ending in indre, attre, 2. Il en reçut beaucoup. 3. Aussitôt que vous aperçûtes votre frère, no lui parlâtes-vous pas ? 4. Dès que jo l'aperçus, je lui prefix, as comprendre, surprendre, etc. parlai. 5. Avez-vous déjà porté vos habillements neufs ? 6. irregular verbs, $ 62, for those tenses of the irregular verbs

5. We would at all times refer the student to the table of Je ne les ai pas encore portés. 7. Quand il vous donna de l'argent hier, le remerciâtes-vous ? 8. Je le remerciai et je le with which he is not familiar. priai de vous remercier. 9. Avez-vous trouvé vos livres ?

RÉSUMÉ OF EXAMPLES. Je ne les ai pas encore trouvés. 11. Lorsque vous vîntes nous Ne conduisîtes-vous point votre Did you not take your son to Spain voir ne finites-vous pas vos affaires avec mon père ? 12. Je les fils en Espagne l'année dernière ?

last year? finis alors et je le payai. 13. N'avez-vous pas vu votre s@ur Je l'y conduisis et je l'y laissai. I took him there, and left him there. ainée pendant votre séjour à Lyon ? 14. Je ne l'ai pas vue.

Aussitôt que vous vites votre frère, As soon as you saw your brother, did 15. Ne vous couchâtes-vous pas trop tôt hier au soir ? 16. Je

ne le reconnûtes-vous pas?

you not recognise him! me couchai tard. 17. À quelle heure vous êtes-vous levé ce

Je le reconnus aussitôt que je I recognised him as soon as I pepe matin ? 18. Je me suis levé à cinq heures ; je me lève ordi

l'aperçus.

ceived him, Dairement de bonne heure. 19. Ne cherchâtes-vons pas à vous

Le pharmacien ne vint-il pas vous Did not the apothecary come to so

voir ? échapper de votre prison l'année dernière ? 20. Je n'ai jamais

you? cherché à m'échapper. 21. Avez-vous venda vos propriétés ? This termination is arbitrary only in verbs ending in enir, in which 22. Je ne les ai pas vendues. 23. Qu'avez-vous donné au an n comes after the i of the terminution; vinmes, tinmes, etc.

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Il vint ine voir ; il fat bien étonné He came to see me; he was much d'argent et le porte-crayon d'or. 12. A-t-elle la robo de satin ? 13.

de trouver chez moi un de ses astonished to find one of his old La scur du médeciu a la robe de satin. 14. Qui a le bois ? 15. Lo anciens amis. friends at my house.

frère du charpentier a le bois. 16. Avez-vous les bas de laine ? Ne prites-vous pas congé de vos Did you not take leave of your friends 17. Nou, Monsieur, j'ai les bas de coton, 18. Qui a le pain du anis hier? yesterday?

boulanger? 19. Nous avons le pain du boulanger et la farine du Je nris congé d'eux, et je les prini I took leave of them, and begged them meuuier. 20. Avons-nous le foin du cheval ? 21. Vous avez l'avoine de in'écrire. to write to me.

du cheval. 22. Avons-nous le chapeau de soie du tailleur ? 23. Oui,

Monsieur, vous avez lo chapeau de soie du tailleur et le soulier de VOCABULARY.

cuir du cordonnier, 24. Avez-vous le soulier de drap de la seur du Accompagn-er, i, to De mon mieux, as well | Histoire, f., history, médecin ? 95, Non, Madame, j'ai la robe de soie de la dame. accompany. as I could. Inform-er, 1, to inform.

EXERCISE 5 (Vol. I., page 20).
À la fin, at last. Se dépèch-er, 1, ref., to Lu, from lire, 4, ir., to
Amicalement, kindly. make haste.

read.

1. Have you some (or any) meat? 2. Yes, Sir, I have a pound of Arrivée, f., arriral, Dès que, as soon as. Notaire, m., notary. meat. 3. Has your son a piece of bread? 4. Yes, Madam, he has a Attend-re, 4, to wait for. Ecolier, m., scholar, Peintre, m., painter.

piece of bread. 5. Has the bookseller a book? 6. He has ink and An secours, to the as- S'ennuy-er, 1, poc., to Sans, without,

paper. 7. Has your sister a gold watch? 8. She has a gold watch sistance.

become weary.

Secour-ir, 2, ir., to suc- and a silver thimble. 9. Has the baker wine or beer? 10. The baker Congé, m., leave. Se hát-er, 1, ref., to cour.

has tea and coffee. 11. Has your brother cheese? 12. Ho has cheese Cour-ir, 2, ir., to run. haston.

and butter. 13. Has the lady a silver spoon 14. The lady has a

fork and silver spoon. 15. Has the butcher any meat to-day? 16. EXERCISE 97.

Yes, Sir, he has a piece of beef. 17. Has the carpenter a table ? 18.

19. Have you the physician's 1. Nos écoliers s'ennuyèrent-ils hier d'attendre si longtemps ? Yes, Sir, he has a mahogany table.

book ? 2. Ils furent obligés d'attendre si longtemps, qu'à la fin ils per coffee and sugar? 22. The grocer has coffee and sugar.

20. No, Madam, but I have your sister's book. 21. Who has

23, Has the dirent patience. 3. Ne roçûtes-vous point votre parent amieale- bookseller's sister a glove? 24. No, Sir, but she has a book. 25. Has ment lorsqu'il vint vous voir ? 4. Je le reçus de mon mieux. she a steel pen? 26. No, Sir, she has a gold pen. 27. You have the 5. Ne lûtes-vous pas la lettre de votre frère avant-hier ?

6. Je

physician's pencil-case. la lus et je l'envoyai à mon oncle. 7. Ne courûtes-vous pas au

EXERCISE 6 (Vol. I., page 20). secours de votre frère aussitôt que vous le vites en danger ? 8. Je me hâtai de le secourir. 9. Ne vous êtes-vous pas dépêchés 1. Avez-vous du thé ? 2. Oui, Madame, j'ai une livre de thé. 2. de venir ? 10. Nous nous sommes dépêchés. 11. Aussitôt que Qui a du pain? 4. Le boulanger a du pain, du beurre, et du fromnge. vous eûtes aperçu mon frère, ne m'informâtes-vous pas de son

5. Le tailleur a-t-il du drap? 6. Le tailleur a un morceau de drap. arrivée ? 12. Je vous en informai. 13. À quelle heure votre 7. Le médecin a-t-il de l'or? 8. Oui, Monsieur, le médecin a de l'or

et de l'argent. scur est-elle venue aujourd'hui ? 14. Elle est venue à midi. Mademoiselle, la dame a une montre d'argent et une plume d'or. 11.

9. La dame a-t-elle une montre d'argent? 10. Oui, 15. Vos compagnons vinrent-ils hier vous prier de les accom

Votre scur a-t-elle de la soie ? 12. Oui, Monsieur, elle a de la soie pagner ? 16. Ils vinrent me voir, mais ils me quittèrent sans et du coton. 13. Avez-vous un couteau ? 14. Oui, Monsieur, j'ai un me parler de leur voyage. 17. Ne peignîtes-vous pas un tableau couteau d'acier et un fourchette d'argent. 15. Avez-vous de la viande l'année dernière ? 18. Je peignis un tableau d'histoire. 19. aujourd'hui, Monsieur ? 16. Oui, Monsieur, j'ai un morceau de bæuf. Le peintre italien a-t-il fini son portrait ? 20. n le finit hier. 17. Votre charpentier a-t-il une table d'acajou ? 18. Oui, Monsieur, 21. n l'a fini ce matin. 22. Dès que j'ous reçu cette nouvelle, il a une table d'acajou ? 19. Votre sour a-t-elle un gant? 20. Oui,

21. Le fils du libraire a-t-il un j'envoyai chercher le notaire. 23. Ce jeune homme a-t-il pris Monsieur, ma sour a un gant de soie. congé de son père? 24. Il a pris congé de lui. 25. Il prit congé porte-crayon d'or? 22. Oui, Monsieur, il a un porte-crayon d'or et

une plume d'acier, 23. Qui a la montre de votre scur? 24. Votre de lui hier.

frère a la montre d'or et le chapeau de soio. 25. Nous avons de l'or, EXERCISE 98.

de l'argent, et de l'acier. 1. Did the notary accompany you yesterday? 2. He accom.

EXERCISE 7 (Vol. I., pago 20). panied me as far as (jusque chex) your brother's. 3. Did your

1. Has the hatter silk ! 2. The hatter has no silk, but he has velvet, companion take leave of you yesterday ? 4. He took leave of

3. Has he cotton velvet? 4. No, Sir, he has no cotton velvet, he has me this morning. 5. Did you read yesterday the book which

silk velvet. 5. Have you ment? 6. Yes, Sir, I have meat. 7. The I have lent you? 6. I read it the day before yesterday (avant. physician has do monoy. 8. Who has money? 9. The merchant has hier). 7. At what time did the painter come this morning ? no money, but he has cloth, velvet, and silk. 10. Have you anything? 8. He came at half-past nine. 9. Has he finished your father's 11, No, Sir, I have nothing at all. 12. Has the tailor two silver butportrait? 10. He painted all day yesterday, but the portrait tons ? 13. No, sir, he has two silk buttons. 14. Who has your dog? is not yet finished. 11. Did you not run to your father's relief 15. The neighbour has my cousin's dog. 16. Has he not your horse

also ? when you saw him in danger ? 12. I hastened to succour him.

17. No, Sir, he has your friend's horse. 18. Have you the 13. What did you do when you came ? 14. As soon as I came

history of France! 19. No. Madam, I have neither the history of

France nor the history of England. 20. Have you peither the book I sent for my brother. 15. Did you take your sister to Germany

por the paper? 21. No, Miss, I have neither the one nor the other. last year? 16. I took her there this year. 17. Did you take 22. Who has paper? 23. The bookseller has no paper. 24. Has any your children to sehool yesterday?

18. I took them to my one a book ? 25. No one has a book. brother's. 19. Do you paint an historical picture ? 20. I painted last year an historical picture. 21. Did your sister beg

EXERCISE 8 (Vol. I., page 21). you to accompany her? 22. She begged me to accompany her. 1. Le boulangor a-t-il du velours ? 2. Non, Monsieur, le boulanger 23. Did you send for the notary as soon as you heard from your n'a pas de velours. 3. Qui a du velours de soie ? 4. Le chapelier a father? 24. I sont for him. 25. When did the notary take du velours de soie et un chapeau de soie. 5, Avez-vous deux boutons leave of yon ? 26. He took leave of me this morning at nine.

d'argent? 6. Non, Monsieur, j'ai un habit de drap, un chapeau de 27. Has the apothecary finished his letter? 28. He has not yet 8. Oui, Monsieur, il a une table d'acajou. 9. Votre cousin a-t-il une

soio, et un soulier de velours. 7. Votre voisin a-t-il uno table de bois ? finished it. 29. Were you not astonished yesterday to see that histoire d'Angleterre ! 10. Non, Monsieur, il a une histoire de France. lady? 30. I was not astonished to see her. 31. Did you make

11. Je n'ai ni le drap, ni le velours. 12. Nous n'avons ni la viande ni haste to read your book last night (hier au soir) ? 32. I made le café. 13. Quelqu'un a-t-il un livre ? 14. Votre cousin a un livre, baste to read it. 33. Have you finished it ? 34. I have not un babit de velours, et un chapeau de soie. 15. Avez-vous le livre yet finished it.

du médecin ? 16. Oui, Madame, j'ai le livre du médecin, et la plume d'or de la dame. 17. Le marchand a-t-il du drap? 18. Le marchand

n'a pas de drap, mais il a de l'argent. 19. Qui a le chien de votre KEY TO EXERCISES IN LESSONS IN FRENCH.

voisin? 20. Personne n'a le chien de mon voisin. 21. Quelqu'un a-t-il

mon livre? 22. Personne n'a votre livre, 23. Le frère de votre cousin EXERCISE 4 (Vol. I., page 3).

a-t-il quelque chose ? 24. Non, Monsieur, il n'a rien. 25. Qui a le 1. Avez-vous le livre du tailleur ? 2. Non, Monsieur, j'ai la montre

livre de votre ami? 26. Votre frère a le livre de mon cousin. 27. A-t-il da médecin. 3. Qui a la montre d'or? 4. La dame a la montre d'or l'habit du tailleur? 28. Il n'a pas l'habit du tailleur. 29. Nous n'avons et le porte-crayon d'argent. 5. Avez-vous le soulier du tailleur ? 6.

ni le drap ni la soie. J'ai le soulier de drap du tailleur. 7. Avons-nous la table de bois ?

EXERCISE 9 (Vol. I., page 43). 8. Oai, Monsieur, vous avez la table de bois. 9. Ont-ils le couteau d'argent? 10. Ils ont le couteau d'argent. 11. La dame a le couteau 1. Who is sleepy? 2. My brother is hungry, but he is not aleepy.

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3. Are you right or wrong? 4. I am right, I am not wrong. 5. Have called the square of that number. But the numbers 1, 4, 9, 16, Fou my brother's good gun? 6. I have not the gun. 7. Are you cold | 25, 36, 49, 64, 81, etc., are the squares of the numbers 1, 2, 3, 4, to-day? 8. I am not cold; on the contrary, I am warm. 9. Have you 5, 6, 7, 8, 9, etc., because they are found by multiplying the good bread? 10. I have no bread. 11. Are you not hungry? 12. I am neither hungry nor thirsty. 13. Are you ashamed ? 14. I am

latter numbers each by itself; and the fractions , , , bet tas neither ashamed nor afraid. 15. Have we pepper or salt? 16. You to teto., are called the reciprocals or inverses of the squares; have neither pepper nor salt. 17. What book have you ? 18. I have

and ratio means the rate at which anything increases or demy cousin's book. 19. Have you the iron hammer or the silver creases; hence, the force of heat, or quantity of heat received bammer? 20. I have neither the iron hammer nor the silver ham. from a common fire, is in the ratio of the inverses of the squares mer, I have the tinman's wooden hammer. 21. Iş anything the of the distances; or more shortly, in the inverse ratio of the matter with you? 22. Nothing is the matter with me. 23. Have

squares of the distances. you the bookseller's large book ? 21. I have neither the book

This may be explained in another way still. Suppose A seller's large book, nor the joiner's small book; I have the captain's to be placed at 2 feet distance from the fire, and B at 3 feet good book.

distance; then B will receive less heat than A, not in the

ratio of 2 to 3, the numbers which represent their distances, LESSONS IN GEOGRAPHY.—XV. but in the ratio of 2 times 2 to 3 times 3, that is, of 4 to 9: in

other words, as 4 is contained 2 times in 9, 80 A will ASTRONOMICAL PRINCIPLES OF GEOGRAPHY.

receive 24 times the quantity of heat that B receives ; and this In our last lesson we endeavoured to explain to our geographi. is all that is really meant by the phrase, the inverse ratio of the cal students the nature of the motion of the earth round the squares of the distances. sun, and of its motion round its own axis. We there stated ! Having thus explained the law of the influence of heat upon the principle or law of attrac

two bodies, or any number of bodies tion in the language peculiar to

at different distances from the the science of astronomy, somewhat

source of heat, in the case of a modified and simplified; but as

common fire, we again observe that some of our readers may be entire

this law is equally true of the innovices, and may never have heard

fluence of light and of the influence or understood several of the terms

of attraction upon bodies at different we made use of, we shall in this

distances from the source of light lesson endeavour to make the sub.

and of attraction. Thus we know ject clearer still.

and feel that the sun is the great First, then, as to the said law of

source of light and head to this attraction: let us illustrate this, by

world of ours; and Astronomy a very familiar instance taken from

teaches us that it is also the source the heat of a common fire. Sup

of attraction, or of that power pose two persons, A and B, sitting

which has operated upon the earth at the same distance from the fire,

JUPITER

and the other planets, and which both in front of it—at least, the

continues still to operate upon one as much as the other; it

them, by causing them to revolve is plain that they would both feel

in elliptical orbits or paths round the same degree of heat; for,

ASTEROIDS

that luminary, as explained in our whatever reason may be assigned

last lesson. to show that A received more

From the earliest ages up to the

MARS heat than B, the

time of Kepler, the planets (Greek, might be assigned to show that B

alamtns, pla-ne'-tees, a wanderer), received more heat than A ; there

Moon EARTH

or wandering stars—so called in fore, they must both receive the

opposition to the fixed stars, which same heat.

VENUS

appear always to preserve the same

MERCURY Now, suppose that B removes to

relative distances from each otherdouble the distance that he was at

were reckoned to be in number only when alongside of A, and that A

six; and this number being inaremains in the same place; it might

thematically perfect-that is, equal then be supposed that B would re

to the sum of all its factors, 1, 2, 3 ceive only half as much heat

-it was imagined that no more as he did before; or that A

DIAGRAM ILLUSTRATING THE RELATIVE POSITIONS, planets could exist, or could be exnow enjoying double the

ETC., OF THE SUN, PLANETS, AND PLANETOIDS. pected to be found. Kepler, inheat which B was receiving in his

deed, inquired most earnestly tchy new position. Such is not the case, however; for the degree | they were only six in number ; but Galileo, who first applied of heat does not diminish at the same rate that the distance the telescope to astronomy, opened a new door in the temple of increases, as you might expect at first sight; but it diminishes science, by the discovery four satellites of Jupiter, in at a much greater rate, and the question is how much greater? 1610, and led by this discovery to that of the other planets Now, well-conducted and careful experiments in Natural at a later period, which put to flight all reasons why the Philosophy have proved that the heat received at the dis. number of the planets should be limited to any given number. tances of 2, 3, 4, 5, 6, 7, 8, 9, etc., feet, is not 11,1,1, I, 1, 1. He would be a bold man indeed now-a-days who would try to of the heat received at 1 foot; but it is , , , , , limit the number of the planets, seeing that so many have etc., of the heat received at 1 foot. So that B will receive at been discovered within these few years past. double the distance of A, only one-fourth of the heat which The six planets known from antiquity are the following A receives; at triple the distance, only one-ninth of the heat; Mercury, Venus, the Earth, Mars, Jupiter, and Saturn; no satel. and so on.

lite was known from antiquity but the Moon. The first addiThe law of progression then is as follows:-Let the heat re- tion to the planets of the Solar System was Uranus, at first ceived at the distance of 1 foot be denoted by 1, then the heat called the Georgium Sidus (the Georgian Star), in honour of received at the distance of 2 feet will be represented by 1 King George III., by Sir William Herschel, who discovered it, divided by 2 times 2, or ; the heat received at the distance of March 13th, 1781. It was afterwards called Herschel, in honour 3 feet will be represented by 1 divided by 3 times 3, ord; the of the discoverer ; but it is now called Uranus, because, forheat received at the distance of 4 feet will be represented by 1 sooth, Uranus was in the Greek mythology (the fables of divided by 4 times 4, or id; and so on.

the heathen gods) the father of Saturn! Uranus has eight Now, dividing 1' by any number gives a result which in satellites, of which six were discovered by Sir William Herschel. mathematics is called the reciprocal or inverse of that number; of these, five have since been observed by other astronomers. and multiplying any number by itself gives a result which is The planet Neptune, the third in point of size of those that

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are yet known to form part of our Solar System, was discovered by Dr. Galle, of Berlin, September 23, 1846, in consequence of a letter received from Leverrier, of Paris, stating that he had calculated the position of a planet outside Uranus which would account for certain irregularities in the motion of that planet, hitherto unexplained, and indicating the part of the heavens in which it ought to be found. Neptune has two satel. lites. The credit of the discovery of the planet Neptune belongs to Leverrier and Galle, but it should be said that Mr. J. Couch Adams, of Cambridge, had also gone through a series of calcu. lations establishing the existence of this planet, and would have had the honour of being its discoverer, had the French astro. nomer been a little less prompt in giving publicity to the result of his calculations. By means of the calculations of Mr. Adams, Professor Challis, of Cambridge, also detected the planet simultaneously with Dr. Galle. In 1859 a French physician named Lescarbault asserted that he had discovered a planet, to which he gave the name of Vulcan, moving in an orbit within that of Mercury. Leverrier was satisfied at the time that Lescarbault had really lighted on a fresh member of our Solar System, but as no astronomer has yet been successful in detecting it a second time, it is supposed that Lescarbault was mistaken and that Leverrier gave credit to the supposed discovery because it satisfied an hypothesis he had formed, that a planet existed, moving between Mercury and the sun, and which would be at that time in that part of the heavens in which Lescarbault supposed he had found Vulcan.

At the close of the last century, and for some time prior to this, it was supposed that a planet, which had either escaped discovery or had disappeared from the Solar System, moved in an orbit between those of Mars and Jupiter, for reasons detailed at the close of this lesson. This suspicion was confirmed by the discovery of Ceres by a Sicilian astronomer named Piazzi, at Palermo, January 1, 1801, moving between the orbits of Mars and Jupiter. Further research has resulted in the discovery of nearly one hundred of these small planetary bodies having orbits near that of Ceres. These small planets are called planetoids or asteroids. They were at first supposed to be fragments of a shattered planet which once revolved round the sun between the orbits of Mars and Jupiter ; but this supposition has been proved to be antenable. The following is a list of the planetoids that have been discovered since the finding of Ceres, with the names of their discoverers and the dates and places of their discovery :LIST OF PLANETOIDS REVOLVING BETWEEN THE ORBITS OF

MARS AND JUPITER.

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

a

Pomona Goldschmidt
Polyhymnia Chacornac
Circe

Chacornac
Leucothea Luther
Fides

Luther Atalanta Goldschmidt Leda

Chacornac Lætitia Chacornac Harmonia Goldschmidt Daphne Goldschmidt Isis

Pogson
Ariadne Pogson
Nysa

Goldschmidt
Eugenia Goldschmidt
Hestia Pogson
Melete Goldschmidt
Aglaia Luther
Doris

Goldschmidt
Pales

Goldschmidt Virginia Ferguson Nemausa Laurent Europa Goldschmidt Calypso Luther Alexandra Goldschmidt Pandora Searle Mnemosyne Luther Concordia Luther Danaë

Goldschmidt Olympia Chacornac Erato

Forster Echo

Ferguson Ausonia De Gasparis Angelina Tempel Cybele Tempel Maia

Tuttle Asia

Pogson
Hesperia Schiaparelli
Leto

Luther
Panopea Goldschmidt
Feronia Peters
Niobe

Luther
Clytie Tuttle
Galatea Tempel
Eurydice Peters
Freia

D'Arrest Frigga Peters Diana

Luther Eurynome Watson Sappho Pogson Terpsichore Tempel Alcmena Luther Beatrix De Gasparis Clio

Luther Ιο

Peters Semele Tietjen Sylvia Pogson Thisbe

Peters Julia

Stephan
Antiope Luther
Agina Stephan

Peters
Watson

Watson
Arethusa Luther
Ægle

Coggia Clotho Tempel Ianthe Peters

Paris

Oct. 26, 1854. Paris

Oct. 28, 1854. Paris

April 6, 1855. Bilk

April 19, 1855. Bilk

Oct. 5, 1855. Paris

Oct. 5, 1855. Paris

Jan. 12, 1856. Paris

Feb. 8, 1856. Paris

Mar. 31, 1856. Paris

May 22, 1856. Oxford

May 23, 1856. Oxford

April 15, 1857. Paris

May 27, 1857. Paris

June 28, 1857. Oxford

Aug. 16, 1857. Paris

Sep. 9, 1857. Bilk

Sep. 15, 1857. Paris

Sep. 19, 1857. Paris

Sep. 19, 1857. Washington Oct. 4, 1857. Marseilles

Jan. 22, 1858. Paris

Feb. 6, 1858. Bilk

April 4, 1858. Paris

Sep. 10, 1858. Albany, U.S. Sep. 10, 1858. Bilk

Sep. 22, 1859. Bilk

Mar. 1, 1860. Paris

Sep. 9, 1860. Paris

Sep. 12, 1860. Berlin

Sep. 14, 1860. Washington Sep. 14, 1860. Naples

Feb. 10, 1861. Marseilles

Mar, 4, 1861. Marseilles

Mar. 8, 1861. Cambridge, U.S. | April 9, 1861. Madras, U.S. April 17, 1861. Milan

April 29, 1861. Bilk

April 29, 1861. Paris

May 5, 1861. Clinton, U.S. May 29, 1861. Bilk

June 13, 1861. Cambridge, U.S. April 7, 1862. Marseilles

Aug. 30, 1862. Clinton, U.S. Sep. 22, 1862. Copenhagen Oct. 21, 1862. Clinton, U.S. Nov. 15, 1862 Bilk

Mar, 1, 1863. Ann Arbor, U.S. Sep. 14, 1863. Madras, U.S. May 2, 1864 Marseilles

Sep. 30, 1864. Bilk

Nov. 27, 1864. Naples

April 26, 1865. Bilk

Aug. 25, 1865. Clinton, U.S. Sep. 19, 1865. Berlin

Jan, 4, 1866. Madras, U.S. May 17, 1866. Clinton, U.S. June 15, 1866. Marseilles

Aug. 6, 1866. Bilk

Oct. 1, 1866. Marseilles

Nov. 4, 1866. Clinton, U.S. July 7, 1867. Ann Arbor, U.S. Aug. 24, 1867. Ann Arbor, U.S. Sep. 6, 1867. Bilk

Nov. 23, 1867. Marseilles

Feb. - 1888. Marseilles

Feb. 1868. Clinton, U.S. April 18, 1868. Marseilles

May 29, 1868. Detroit

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1 Ceres

Piazzi 2 Pallas

Olbers 3 Juno

Harding
Vesta

Olbers
5 Astræa Hencke
6
Hebe

Hencke 7 Iris

Hind 8 Flora

Hind 9 Metis

Graham 10

Hygeia De Gasparis 11

Parthenope De Gasparis 12 Victoria Hind 13 Egeria De Gasparis 14 Irene

Hind 15 Eunomia De Gasparis 16 Psyche De Gasparis 17

Thetis Luther 18 Melpomene Hind 19 Fortuna Hind 20 Massalia De Gasparis 21 Lutetia Goldschmidt Calliope

Hind 23 Thalia

Hind 24 Themis De Gasparis 25

Phocea Chacornac 26

Proserpine Luther 27

Euterpe Hind 28 Bellona Luther 29 Amphitrite Marth 30 Urania

Hind 31

Euphrosyne ! Ferguson

Palermo
Bremen
Lilienthal
Bremen
Driesen
Driesen
London
London
Markree
Naples
Naples
London
Naples
London
Naples
Naples
Bilk
London
London
Naples
Paris
London
London
Naples
Marseilles
Bilk
London
Bilk
London
London
Washington

Jan. 1, 1801. Mar. 28, 1802. Sep. 1804. Mar. 29, 1807. Dec. 8, 1815. July 1, 1847. Aug. 13, 1847. Oct. 18, 1847. April 25, 1848. April 12, 1849. May 11, 1850. Sep. 13, 1850, Nov. 2, 1850. May 19, 1851. July 29, 1851. Mar. 17, 1852. April 17, 1852. June 24, 1852. Aug. 22, 1852. Sep. 19, 1852. Nov, 15, 1852. Nov. 16, 1852. Dec. 15, 1852. April 5, 1853. April 6, 1853. May 5, 1853. Nov. 8, 1853. Mar. 1, 1854. Mar. 1, 1854. | July 2, 1851,

Sep. 1, 1854.

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Watson

22

The additions made to the satellites of the planets since the discovery of those of Jupiter and the ring of Saturn by Galileo, are the following :-M. Huygens discovered one of Saturn's satellites in 1665; M. Cassini, four, between 1671 and 1685; Sir W. Herschel, two, between 1787 and 1789; and Messrs. Lassell and Bond, one, September 19th, 1847; making in all eight satellites for Saturn. Mr. Lassell has discovered satellites belonging to Neptune ; it was once supposed that this planet pos. sessed a ring like Saturn. The following is a table of the principal planets of the solar system; their approximate mean

of the

Astronomical

Marks.

Approximate
Mean Dia me.
ters in Miles.

Inclination
of Axes to the

Ecliptic.

Inclination
of Orbits to
the Ecliptic.
Times of Rev.

round the
Sun in Days.

Axes.

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Saturn

distances from the sun; their approximate mean diameters; the RECREATIVE NATURAL HISTORY. inclinations of their axes and orbits to the ecliptic, or path

THE BUTTERFLY. in the heavens in which the sun and planets move; their periodic times, or times of a complete revolution round the sun, as far as “WILL he catch it? Does that thoughtless little imp know what thoy are known; and the axial time of rotation occupied by a creature of beauty he is trying to crush? Well done, bright each planet. Further particulars respecting the planets and fairy of the spring! that last wave of thy sun-tinted wings has their satellites we must reserve for our Lessons on Astronomy, carried thee over that blooming hedge now far away from the otherwise we shall lose sight of those on Geography. We may baffled, puffing, red-cheeked schoolboy.” Such were our reflecremind our readers that the actual existence of Vulcan has not tions as we once watched “my noble English boy" in hot pursuit been confirmed, that to say, it has not been noticed by any of a “Swallow-tail” (Papilio * Machaon) butterfly. (See illusastronomer since its alleged discovery by Lescarbault. For this tration, page 48.) Kill, kill," were the words written on young reason a note of interrogation has been appended to its name, Hodge's face as with determination, worthy of a Briton, he etc., in the subjoined table, in which we have arranged the chased the winged type of beauty. At first it seemed two to one planets in the order of their distances from the sun :

in favour of the boy; nearer and nearer he came, up went his cap

full at the “Swallow-tail.” It was so well aimed, that the insulted TABLE OF THE PRINCIPAL PLANETS OF THE SOLAR SYSTEM. butterfly indignantly swept into a neighbouring field, leaving the

young hunter in a rage at the useless expenditure of so much Approximate

toil. To make his defeat more ignominious, the cap had stuck Mean

Times of
Names
Distances

Rotation

in a thorn bush, from which the little biped did not recover it from the Sun Planets.

upon without sundry pricks and provoking scratches. We rejoiced in Miles.

in the escape of the insect, knowing well that its hunter did not

wish to examine the wonders of that tiny “thing of life," but to Vulcan (?) 13,082,000(?)

12'10'(?) 20(?)

gratify his bump of destructiveness. Mercury 35,392,600 2,900 630 0

0' 88 24h. 5m. Now we are not going to write the history and adventures of Venus.

66,131,500 7,510 73° 32 3° 23 225 23h. 21m. that particular butterfly ; we are not certain that we ever saw The Earth 91,430,220 7,913 66° 32 000

365 23h. 56m. this particular insect again, but wish to make a few remarks Mars

139,312,200 4,920 61° 18 1° 51' 687 2th. 37m. on his relations and friends. In summer they are glancing hither Planetoids

and thither over meads and gardens, and we cannot let such Jupiter 475,693,100 88,390 86° 55' 1° 18 4,333

9h. 56m. beauties pass unnoticed. 872,134,600 71,900 58° 41' 2° 29' 10,759 10h. 29m. Uranus H 1,753,851,000 | 33,000

0° 46' 30,687

It seems almost an insult to call such a brightly-robed creature

9h. 30m. Neptune * 2,746,271,200 36,600

an insect, but we must not flatter the proudest butterfly, merely 1° 46' 60,127

because he wears a fine coat. How vast seems the difference In the preceding table it will be observed that the new planets Ay! yet the latter cannot deny his distant relationship to that

between the abhorred cockroach and the splendid peacock butterare found in the space intermediate between Mars and Jupiter. creeping thing, hated by all housemaids : both are insects. A These planets were discovered in this space because they were sought for; and the origin of their search is curious. Kepler the less honoured orders. Lepidoptera (a term meaning scale

long Greek name separates the princes of the insect world from had discovered that the distance between Mars and Jupiter was winged) is the title of nobility applied by the great Swedish anomalous as compared with the distances between the other historian of the animal kingdom, Linnæus, to the butterflies planets, that it was greater in proportion to their distances from the sun, and he strove by some analogies of Nature to find and moths. We must pass over the latter for the present, and out the reason, but failed. Titius, a professor of Wittenberg, confine our attention to their less numerous but more admired

relations. in Saxony, endeavoured to discover the law of progression in the distances of the planets, and to a great extent succeeded. This

The term “butterfly" seems to be unsuitable for an insect discovery was published by Bode, in 1772, in the Connaissance du which has a taste far too refined for butter. The name was, it Ciel Etoilé; and hence it is usually called Bode's

law. It is the is thought, given to the insect by our Saxon ancestors, because it following :-Calling the earth's distance from the sun 10, it was

appeared in the butter-making season. Be it so; many a finer

name has had a lower origin. Has the butterfly a memory? If found that the distances of the other planets with that of the earth were very near to one another in the proportion of the fol. so, does the insect recollect the two previous states through lowing numbers :

which it has passed ? Perhaps not; but we must not forget the

former condition of our brilliant white admiral, or swallow-tail. Planets-Mercury, Venus, Earth, Mars, Jupiter, Saturn. Numbers, 4,

First a caterpillar; then cramped in bands and folds, which we 7, 10, 16, 52, 100.

call a chrysalis; and, lastly, a winged fairy of the air. Catch On further inquiry it was discovered that these numbers were that large “White Cabbage,” lady butterfly (Pontia Brassica), related as follow :

and ask her a few questions about “auld lang syne," just to 4 =4.

illustrate what are called metamorphoses. 7 = 4 + 3.

Om the 1st of May last year-we like to be particular in 10 = 4 + 3 X 2.

dates—her grandmother was a bandaged chrysalis, and about 16 = 4 + 3 x 2 x 2.

the end of the month became a butterfly. Her elegantly-shaped 52 = 4 + 3 X 2 X 2 X 2 X 2.

eggs were carefully laid on the under side of nicely-selected 100 = 4 + 3 X 2 X 2 X 2 X 2 X 2.

cabbage leaves, without permission of the gardener. Mighty An inspection of the foregoing series will show that between was his rage when, in a few days, his choicest cabbages were 16 and 52 there should be another number, 4 + 3 X 2 X 2 X 2,

sawn into the most intricate patterns by a thriving family or 28, to make its progression regular and complete, and this of ravenous caterpillars. To kill them all was out of the quesencouraged the belief, originated by Kepler, that there was a tion. Napoleon's artillery might have failed to accomplish that. planet revolving in an orbit between those of Mars and Jupiter Many did perish; the sparrows especially delighted in such that had not yet been discovered.

delicious morsels. One, however, escaped, in consequence of her That there were good grounds for entertaining this idea was exceeding cleverness in feeding on leaves concealed from the further shown by the discovery of Uranus, when it was found birds' eyos. Having formed a chrysalis, she socured the cradle that its distance from the sun represented by 191:93, supposing like bit of work to a sunny wall by a strong but elegant silken the earth's distance be 10, agreed closely with the distance at band. which it should be according to Bode's law, namely, 4 + 3 X 2 From this came a butterfly about August, the mother of the one X 2 X 2 X 2 X 2 X 2, or 4 + 3 x 64 = 196. Astronomers which is supposed to have been just caught by the reader. From in all parts of Europe anxiously searched the field of the heavens her eggs sprang another succession of caterpillars, which changed for the planet that was supposed to be whirling through to chrysalidos in September last. Now mark what followed. illimitable space between the orbits of Mars and Jupiter, and the supposition was shown at last to be true by the discovery of Ceres, the first of the long list of minor planets, by the for the name of a famous physician present at the siege of Troy, and desig.

* The term Papilio is applied to a large butterfly family; Machoon is tunate Italian Piazzi.

nates this particular species.

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