being thus reduced to a common denominator, it is only necessary to divide the numerator of the one by the numerator of the other, as in division of vulgar fractions where a common denominator is found.

Note. There are other rules for special cases in decimal division, one of which would enable us to work the above sum more briefly; but the rule given is the only one that in the end accommodates every case.

SECTION IX.

1. What is the per-centage gained by the newspaper boys who buy the daily papers at 9d. per dozen, and sell them at Id. each? Explain your answer.

2. Describe ratio, and illustrate your definition by an example.

3. If 25 men could set up a mile of telegraph wire in 24 days of 8 hours' work, what length of wire would 20 set up, working 10 hours a day for 20 days?

1. (a.) The question may ask-What is gained by the outlay? Boy pays 9d. per dozen, and receives Is. per dozen. .. on his outlay of 9d. he gains a profit of 3d.

As 9d.: 100 :: 3d. : profit per cent.

or 3d. 100 :: Id. :

= £13° = £33 6 8 on outlay.

(b.) Or the question may take this form: What proportion of the money received by the boy is profit?

Then, of every is. received one fourth is profit, therefore of every £100, one fourth is profit; and one fourth of £100 is £25 £25 per cent. of receipts.

2. Ratio is the relation existing between two numbers, with regard to the number of times the one contains the other.

Illustration. We may consider the numbers 6 and 12. Comparing them, we find that the one is 6 more than the other; but we also find that one is twice the other. By the first comparison, we find their difference; by the second, their ratio. The difference is 6, the ratio 2.

Again, taking the numbers 8 and 24, the ratio is 3; taking 7 and 28, the ratio is 4; and so on.

3. The question may be solved by cancelling, thus :

GEOGRAPHY.

SECTION II.

1. Define the terms estuary, strait, archipelago, valley Illustrate your definition of the first from America, of the second from Asia, of the third from Europe, of the fourth from Great Britain.

2. Give accurately the shape of the earth, its equatorial and polar diameters, the proportion of land and water on its surface, the positions of the polar and tropical circles, the latitudes of London and Edinburgh.

3. State clearly how deltas and glaciers are formed. Draw your illustrations from the continents of Europe and Africa. (1.) Estuary. The mouth of a river so greatly widened as to become an arm of the sea. Such is the St. Lawrence, from Quebec to its mouth. Strait, a narrow portion of water connecting two larger portions. For instance, the Strait of Malacca, joining the Bay of Bengal and the Chinese Sea. Archipelago, a sea more or less studded with islands. For instance, the Grecian Archipelago between Greece and Asiatic Turkey. Valley, the hollow through which a river flows in its course to the sea. For example, the Vale of Clyde, between the Lead and Moffat Hills.

(2.) The earth is spherical, though not a perfect sphere, being a little flattened at the poles. The equatorial diameter is 7,925 miles; the polar, 7,899, or 26 miles less. The proportion of land on its surface is a little over one quarter. The polar circles extend 231° round each pole; the tropical extends 231° on either side (N. and S.) of the equator. The latitude of London is 51° 31'N.; that of Edinburgh 55° 57' N.

(3.) A delta is formed by the deposit of alluvial matter brought down by a river to its mouth. If the river current is sluggish, or if ocean currents in the vicinity check the outflow, the alluvium accumulates, and bars the outlet of the river, which then forces new (and generally more numerous) channels through which to reach the sea. The Danube in Europe and

the Nile in Africa, afford notable examples of the Delta.A glacier is an accumulation of snow-ice, formed in the higher valleys of mountain systems, and gliding, by their own weight, down those valleys with a movement so slow as to be imperceptible. There are several hundred glaciers in the Alps alone, varying from one to fourteen miles in length, and from a quarter of a mile to two or three miles in breadth. The largest is the Great Aletsch glacier, lying around the Finsteraarhorn; one of the best known is the Rhone glacier, the melted ice of which forms the source of the Rhone.

SECTION III.

1. Name the chief rivers which drain the Eastern slope of Great Britain, and the heights in which they rise; distinguish also those that are navigable for some considerable distance above their mouth, and explain why the other rivers are not equally navigable.

2. Give the position of, and some of the historical associations connected with the following towns :-Winchester, Peterborough, Shrewsbury, Boston, Scarborough, Cardiff, Stirling, Aberdeen, Cork, and Drogheda. Point out in each case the natural advantages of situation which suggested their first establishment.

3. Select one of these counties-Hampshire, Staffordshire, Durham, and one of these, Perth, Lanark, Argyll; give an account of the industrial occupations, the chief towns and rivers of the two selected. Explain the terms county and shire.

(1.) The Spey, Dee, and Tay rise among the West Grampians, or their branch ranges; the Forth rises in Ben Lomond. The Tyne is formed of two streams, one rising in the Cheviot, the other in the Pennine, Hills. The Yorkshire Ouse and its tributaries, forming the Humber, rise in the Pennines; the Great Ouse, in the North slopes of Buckinghamshire; the Thames, in the Cotswold Hills. The Tay, Forth, and Tyne, and Thames, are navigable for a considerable distance. Two causes contribute to make the others unnavigable: (1) The débris carried down by the stream; this, owing to the action of tides and cross-currents, settles at or