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Intercommunications. 2. (3) Pronouns are used substantively when they stand instead of nouns, and are either Nominative or Objective; as, I saw your boy, he is a good child. When pronouns are used before nouns, as when they denote possession, they really qualify the noun they stand before, and from this are said to be used adjectively, as, His book.

G. HORSFALL. 2. (4)

MOUNTAINS. DEFINITION.- Ask one of the children who has been at the sea-side how the water lies. “Flat or level.” Tell them then that all connected water stands at the same level; thus the sea stands at one level. Elicit from them how the land differs from the water in this respect. Draw from them also what a hill is, and tell them that when land becomes very high, or rises much above the sea-level, it is called a mountain (1).

GROUP AND RANGE (or Chain).-Show them from familiar examples that one mountain scarcely ever exists alone; that we seldom see a large flat country, and one single mountain or hill on it. There are generally many together, and when walking amongst them, as soon as we have got down one we must climb another; or they are joined together sometimes all in a line, at other times in a cluster. Illustrate by a chain rolled up, and stretched out (2).

EFFECT OF MOUNTAINS ON THE CLIMATE OF A COUNTRY.—Draw from them that the higher we ascend a mountain the colder it becomes; tell them how on very high mountains snow stands all the year round. Show them how the clouds, which are vapour, become “condensed" or made into water, aud fall then as rain when made cold. Illustrate by vapour of a kettle coming into contact with the cold air. Show them from this that clouds floating near mountains are thus condensed, and fall as rain. Show from an example that this is true, and that large level tracts of country are generally dry (as Sabara desert). (3) Show them also that they sometimes act as a shield against wind, thus materially affecting the climate, as the Himalayah to India. Compare to taking shelter from a cold wind by getting behind a wall on the shaded side (4).

NAMING OF MOUNTAINS.—Show to the children that when a large collection of buildings exists, we give the collection (or town) one name; as, London. If there are some particular buildings, we also give them names to distinguish them; as, St. Paul's. Apply this to the naming of mountain ranges, and the particular summits in those ranges. Also explain such expressions as, “Himalayahs with Mt. Everest," “ Alps with Mt. Blanc" (5).

HEIGHT OF MOUNTAINS.—Show them that by saying Snowdon is 3571 feet high, we mean that if a person were on the top of this hill, and it were placed in the sea, a stone dropped straight down from the height of its top would drop 3571 feet. Show them thus that mountains are measured from their perpendicular height above the sea (6).

(1) A mountain is land rising far above the level (water) of the sea. (2) A chain of mountains is a lot of mountains joined together like the links of a chain; a group is a lot of mountains in a cluster. (3) Moun. tainous districts are generally rainy. (4) Sometimes mountains act

soft

or

like a wall in sheltering countries from winds. (5) We give names to ranges or chains of mountains, also to the principal summits in the ranges. (6) Mountains are measured from the level of the sea.

G. HORSFALL. 3. (1) Thousands of years ago, upon the tablelands at the north of India, lived our ancestors. At that time they existed as one distinct tribe. But at length they began to migrate to Europe in different companies, and settle in different parts. Thus these “different companies” settling in different parts in course of time became distinct nations speaking different languages, which had the same common roots. Such distinct languages are Teutonic and Latin (with their branches). That the Teutonic race (of which we form part) are descendants of this ancient family (which is named Aryan Family), is proved by the Teutonic languages containing the same roots as is found in this ancient language.

All the Teutonic branches resemble each other more or less, but the English most resembles Frisian.

G. HORSFALL. 3. (3) It is easier for some nations to pronounce some words than it is for others; thus a German, in pronouncing "open," would call it “offen.” Many English words in coming from the classical languages have changed their consonants, but this interchange is regular. Thus (1) an "aspirate consonant" in a classical language, as Latin, becomes

"flat” in English, and “hard” or "sharp" in German; as, Frater (F aspirate), in English becomes Brother (B flat), and Bruder in German (B sharp). (2) A flat consonant in a classical language becomes sbarp in English, and aspirate in German; as, Labi (b flat) in classical, Slip (p sharp) in English, Schleifen (f aspirate) in German. (3) A sharp consonant in a classical becomes aspirate in English, and flat in German; as, Tres in classical (T sharp); Three (Th aspirate) in English; and Drei (D flat) in German. G. HORSFALL.

4. (1) £25 10s. = 51£. By the question, what is sold for £92 cost £100; what would 51 cost ?

51 :: 100£ = 1275£ cost. If sold for £38, 38—1275£ = 178€ would be gained. Or, on an article costing 1275£, 47.3£ is gained, what is gained on an

article costing £100. 1275£ : £100 :: 173£ 1892 £ = £37 ls. 11 d. + 71 Ans.

G. HORSFALL. 5. (1) It is required to shew that 4BE? + 4CF2 = 5BC?.

5BC? = 5BA? +5AC%. Again, 4FC2 = 4AC+4AF, and 4BE* = 4BAP+4AE. But 4AF = BA®, and 4AE= AC?, because the square on the whole

line =

4 times square on half the line.
:: 4FC?+4BE= 4AC? + BA? +4BA+ AC?,
that is, 4FC2+4BE? = 4AC? +BA+4BA' + AC?.

:: 4FC? +4BE= 5AC% + 5BA?.
But 5AC%+5BA% = 5BC” (I. 47). :. 4F02 + 4BE? = 5BC%.

M. V. ARCHER. 5. (1) Another way. If the figure be constructed as the enunciation

92 :

46

51

directs, it will at once be seen that BE? = AB? + AER (Euc. I. 47), and CF = AC2+AF. But square on any line = four times square on half the line (Cor.

I. 47), and AF=of AB. : BE' = 4AF+ AEP. For similar reason, CF2 = 4AE+AF2. Add these squares together. :. BE+CF2 5AF2 +5AE. :: 4BE +4CF = 20ĀF+20AE?.

Bat BC = AB+ AC? = 4AF2 + 4AE? (Euc. I. 47). :. 5BC = 20AF+20AE”. Whence 4BE +40F = 5B0%. Q.E.D.

A. WHITEHOUSE. 5. (2) Amount of £250 for 2 years = £270 = £270.4. :. amount of £1 for 2 years = £

270.4

= £1.0816.

250
:: amount of £1 for 1 year ✓1.0816 = £1.04.
:: interest on £1 for 1 year

= £.04. :. £.04 x 100 = £4 required rate per cent. A. WAITEHOUSE. 5. (3) Amount of £100 for 2 yrs. at 3, per cent., simple int., = £107. :. £107= amount of £100 for 2 yrs. at a certain rate per cent. comp. int. :. 18%£= £1:07 = amount of £1 for 2 yrs. comp. int. at a certain rate. :: „£l.07=£1:034408 = amt. of £1 for 1 yr.

:: interest on £1 for 1 year = £.034408. Wherefore £.034408 x 100 = £3:4408 per cent.

À, WHITEHOUSE. 5. (4) £100 of 1st put out 3 yrs. at 4 per cent. amounts to £112. £100 of 2nd 5

3

£115. £100 of 3rd 2 2.

£105. Bat £115 of 2nd = £224 of 1st. :: 2nd = 11 of 1st. £105 of 3rd = £345 of 2nd. :. 3rd = 0 of 2nd =

:. 3rd = 29 of 1 of 1st = 32 of 1st. .: the three amounts are in proportion, 1 : 115 : 52, or 115 : 224 : 736. :. Ist = jules of £3010 = £322. 2nd = 1245 of £3010 = £627.

3rd 739 of £3010 £2060% A. WHITEHOUSE.

1015 6. (2) A 1st E. obtains a 7s. 6d. prize and certificate; a 1st A. obtains a 12s. 6d. prize and certificate; a 1st Honours obtains a bronze modal.

G. HORSFALL. M. V. Archer, 2, 5, 7. G. Spencer, 2, 5. G. Horsfall, 2, 5, 7. J. H. Harrison, 2. J. T. Price, 2. A. Henry, 2, 4, 5, 7. A. Whitehouse, 2, 3, 4. W. Fairclough, 2, 7. J. L. King, 2, 4, 7. S. H. Sergeant, 2, 4, 7.

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Ta our Readers. We are very happy to congratulate our subscribers on the advent of a new year, and the fifth of our existence. We would like to appeal to onr clients to extend the means of our usefulness in 1880 by bringing the Pupil Teacher before the notice of P. T.'s, Assistants, and Head Teachers. The rate of subscription is so low (2s.6d. annually, post free), that each P. T. in a school should subscribe, and not one for a whole school, as is sometimes the case. For every list of 8 subscribers prepaid for 1880, the sender will receive as bonus 2s. 6d. worth of books, to be selected from H. Major's list of Educational Works at sender's option.

MANUSCRIPT ANSWERS

TO

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EXAMINATION PAPERS.

At the beginning of 1880 the above will be published monthly, SIXPENCE a set, for each month of each year of apprenticeship, and will be after the style of Major's printed Pupil Teachers' Questions and Answers, published at Sixpence each year. The above will contain, as models, fully worked Answers in Manuscript to all the Questions in Arithmetic, Algebra, Mensuration, Grammar, Geography, History, Notes of Lessons, given in each year of apprenticeship for each monthly examination.

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