air is filled with vapour it is lighter than usual, and the column of mercury stands low; but when air is dry and free from vapour it is heavier than usual, and the mercury stands high. Thus the barometer, by showing the variations in the weight of the air, indicates when it is moist, and likely to rain or not.

A barometer also helps us to ascertain the heights of mountains, for as the weight of air decreases the higher we ascend, the mercury of a barometer will gradually fall and indicate the height of our ascent for the density of air decreases upwards in regular geometrical series; thus at the height of three and a half miles the density of the air is only half what it is on the earth's surface; at seven miles only one-fourth; at fourteen miles onesixteenth. Though the atmosphere probably extends forty or fifty miles above the level of the sea, yet at an elevation of twenty miles it has but little weight. It is useful to remember that there are certain special rules to guide us in knowing the probable changes of the weather by marking the mercury of a barometer.

1. The barometer is highest of all during a long frost, because the air is then exceedingly dry, which causes the mercury to rise. It generally rises also with a north-east wind, because it makes the air both cold and dry, and being much condensed, and without vapour, it is much heavier.

2. The barometer is lowest of all during a thaw which follows a long frost, because the air which had been much dried by the frost, absorbs the moisture of the fresh warm current of wind from the south or south-west, and becomes laden with vapour. These winds also cause the barometer to fall at any period of the year, because they generally come heavily laden with vapour, aud vaporized air is lighter than dry air. From these rules it appears that the barometer is high when the wind blows between the EAST and the NORTH, but it is low when the wind blows between the SOUTH and WEST.

3. When the barometer stands above 30°, the air must be very dry or very cold, or perhaps both; and no rain may be expected, because in the former case dry air will absorb moisture, and not part with it in rain; and in the latter case the air is so much condensed, that it has already parted with as much moisture as it can spare.

4. When the barometer stands very low indeed, there will not be much rain, though a fine day will seldom occur at such times : there will be more likely short heavy showers, with sudden squalls of wind from the west.

5. In summer-time, after a long continuance of fine weather,

the barometer will fall gradually for two or three days before rain comes; but if the fall of the mercury is very sudden, a thunderstorm may be expected.

6. When the sky is cloudless, and seems to promise fair weather, if the barometer is low, the face of the sky will soon be suddenly overcast.

7. When the barometer is high, dark, dense clouds will pass over without rain; but if the barometer be low, it will often rain without any appearance of clouds.

8. The higher the barometer, the greater will be the probability of fair weather, because the air in fine weather contains very little vapour, and the drier the air the higher does the mercury of the barometer rise.

9. When the mercury begins to rise, because the air is becoming more dry, fine weather is at hand; but when the mercury is in a sinking state, indicating that the air is either laden with vapour or disturbed by wind, then foul weather may be expected.

10. If in frosty weather it begins to snow, the barometer generally rises to 30°-where it remains so long as the snow continues to fall. If after this the weather clears up, very severe cold may be expected.

It is easy to tell whether the mercury is rising or falling by noticing whether it is convex or concave. When the top of the column is convex (i. e., higher in the middle than at the sides) the mercury is rising, but when the top of the column is concave (or hollow in the middle) the mercury is falling.

The mercury is convex when rising, because the parts of the mercury in contact with the tube are delayed by the capillary attraction of the glass, in consequence of which the middle part rises faster than the sides, and the surface is convex ; but when the mercury is falling, the parts of the mercury in contact with the tube are delayed by capillary attraction, in consequence of which the middle part sinks faster than the sides, and the surface is concave.

Heat and cold of themselves have no effect upon the barometer; but as cold weather is generally dry, or accompanied with northeast winds, the mercury rises in cold weather. And as warm

weather is generally moist, and accompanied by south-west winds, the mercury sinks in warm weather. If the barometer rises or falls very suddenly, the corresponding fine or foul weather will not continue long; and if the mercury fluctuates much, the weather will be very changeable and unsettled.

ARITHMETIC.

STANDARD VI.-PROPORTION AND VULGAR AND DECIMAL FRACTIONS.

PROPORTION, OR RULE OF THREE.

A. This may be simple or compound (single or double), as the case may be.

In Simple Proportion, or Single Rule of Three, as it is sometimes called, only three quantities are given, from which by analogy we find a fourth. Thus,

If three books cost 15s., what will 6 books cost?

In Compound Proportion, or Double Rule of Three, the same analogy exists, but the quantities proportional to each other are more than three in number. Thus,

If 3 men mow 20 acres in 8 days, how long ought 6 men to be mowing 30 acres?

In SIMPLE PROPORTION, or Single Rule of Three, results may be obtained by the following methods:

(1) By Multiplication—

"If 3 books cost 15s., what will 6 books cost?"

"If 3 books cost 15s., what will 1 book cost ?"

The cost of 3 books 15s.

(3) By Division and Multiplication

"If 3 books cost 15s., what will 7 books cost ?"

The cost of 3 books 15s.

of 15s. = 5s.

7 books 7 times 5s. = 35s. = £1 15s. Ans.

(4) By Division and Addition, or by Multiplication, Division,

and Addition. Thus :

"If 8 books cost 15s., what will 10 books cost?"

The cost of 8 books = 15s.

Or

"If 12 books cost 28s., what will be the cost of 18 books?" In this case we find that 18 equals 12 + 6, and 6 is of 12, so that The cost of 12 = 28s.

of 28s. 148.

12+6=28s. + 14s. 42s. = £2 2s. Ans.

(5) By Division and Subtraction, or by Multiplication, Division, and Subtraction. Thus :

"If 12 books cost 28s., what will 9 cost?"

The cost of 12 = 28s.

"If 12 books cost 28s., what will 23 books cost?" The cost of 24 = 2 × 28s. = 56s. Od.

“If 12 books cost 28s., what will be the cost of 15 ?”

5

Cost of 15 of 28s. = 7s. × 5s. = 35s. = £1 15s. Ans.

"If 12 books cost 28s., how many may be bought for 70s. ?" Every 28s. will give us 12 books, and therefore as often as we take 288. out of 70s., so many times 12 books can we have, and therefore the number of books required

"If 12 books cost 28s., how many may be bought for 70s.?

Here the number will increase with the books; the answer required being greater than the number of books given, and so we make a proportion thus:

As 28 70: 12 the number required.

By this we mean that the third term bears the same relation to the term required as the first term bears to the second; or in other words, 70 is as many times 28 as the number required is that of 12; and hence in a proportion the required term equals the product of the two middle terms divided by the first.

In COMPOUND PROPORTION, or Double Rule of Three, the processes are similar to the above; only we have more than two quantities given proportional to each other. See examples on following pages.

EXAMPLES IN RULE OF THREE.

(Where knowledge of Fractions is not required.)

B.-1. If the rent of 80 acres is £168 11s. 6d., what will be the rent of 30 acres?

2. If 48 articles cost £24 8s. 7 d., what will be the price of 4 such articles ?

3. If 35 lbs. of sugar cost £4 13s. 9d., what is that for 5 lbs.? 4. If 40 horses cost £375, what will be the cost of 8 at the same rate?

5. If a man walks 80 miles in 24 hours, how far will he walk in 9 hours?

6. If 12 plates cost 10s., how many may be bought for £2 6s. 8d.?

7. A workman receives 50s. for 6 days: how many days must he work to earn £9 3s. 4d.?

8. If 6 lbs. 4 oz. of tea cost £2 10s. 10d., what should be paid for 1 lb. 14 oz. at the same rate?

9. What will be the cost of 30 sheep, if 25 sheep cost £30? 10. If 7 lbs. of rice cost 9d., what must be paid for 168 lbs. 11. What will be the cost of 45 gals. of wine, if 40 gals. cost £90 ? 12. If 3 shawls cost £52, what must be given for 5 of the same kind?