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noughts have been omitted we need only compare one with the other—e.g., if for Portugal I find in “oranges" 428, I only have to observe that Portugal is much smaller than Spain. If Spain has 15, Portugal cannot have 42 ; consequently it is 4 only.

When we can find easy points of comparison in the numbers themselves, and especially when it is not a matter of very great importance to get the numbers exact to one or two figures, as, e.g., in the heights of mountains and lengths of rivers, it will be better, when possible, to drop the figure-alphabet and rely simply on the points of similarity and contrast in the numbers. This idea has been suggested under the heading of General Rules, p. 34.

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The highest mountains in South America are Aconcagua, 23,910 feet, and Chimborazo, 21,424 feet.

In North America the highest is Mt. St. Elias, 19,500 feet.

In Central America, Popocatepetl, 17,800 feet; in Europe, Mt. Blanc, 15,760 feet. Thus it will be seen that there is always a difference of 2000 feet. Of course the odd feet are not of great importance. The highest mountain in the world is Mt. Everest, 29,000 feet ; in North America, Mt. St. Elias, 19,000 feet high, or 10,000 less. In Africa, Kilmanjaro, 19,000, or nearly the same as Mt. St. Elias. Next to Mt. Everest, 29,000 feet, comes Mt. Kinchinjunga, 28,000 ; next to Mt. Kilimanjaro, 19,000, comes Mt. Kenia, 18,000, a similar

case to the above. The most important mountains in Europe descend in thousands of feet.

Mt. Blanc and Monte Rosa.. 15,000 feet.
Matterhorn..

14,000 Jungfrau.

13,000 Wetterhorn..

12,000 Mt. Maladetta...

11,000 Atna...

10,000 Olympus. .

9,000

Now and then we may make use of our letter-alphabet in some very striking case ; e.g., the exact height of Olympus is 9150 feet, which we have in gods, and as Olympus was the fabled seat of the gods of Grecian mythology, the height of Olympus can never be forgotten. Of course 915 is impossible ; therefore it is 9150. Mt. Ararat is 17,000, which gives us Dove, and as Noah sent the dove out of the ark after the flood, from Mount Ararat, its height will be easily remembered.

RIVERS.

As in the case of the mountains, the lengths of the rivers also present strong points of resemblance. The longest rivers in North America, South America, and Africa are each 4000 odd miles long, viz., the MissouriMississippi, 4650 ; the Amazon, 4000; and the Nile, 4100, respectively. In Asia the longest is 3000 odd miles ; in Europe, 2000, odd. The exact numbers are

not of so much consequence. The Missouri-Mississippi is 4600 ; the St. Lawrence, the next in size, is 2200, or almost exactly half as long. In Asia the longest—the Yang-tse-Kiang, 3300; then the Obi, 3000; the Indus, 2000–present easy points of comparison. The Ganges, 1600, or about half the length of the longest, a similar case to the North American rivers. The Euphrates is 1750; the Danube, the second longest and by far the most important in Europe, 1725; the Elbe is 780, and the lengths of the Danube and the Elbe added equal approximately the Volga, 2400 miles long, the longest in Europe. The Rhine and the Loire are each 600, and the Rhone 580, and the three added give you the length approximately of the Danube.

It will be noticed that the lengths of the European rivers descend in hundreds of miles, as the mountains descend in thousands of feet.

Elbe, 780.
Loire, 600 and Rhine, 600.
Rhone, 580 and Tagus, 550.
Seine, 497.

Ebro, 342. M..r..n, marron or chestnut. The finest chestnuts in the world grow on its banks.

Thames, 220.

Strange to say that, with the exception of the Ebro, these rivers come almost in alphabetical order, as we can take the Loire and Rhine together, being of the same length, and the Rhone and Tagus, nearly so.

THIRD LESSON.

THE REMEMBERING OF DATES.

if we

The alphabet which I gave in the preceding lesson enables us to find a large number of dates in the facts themselves, if we try to find as many figures only as are necessary in order to remember the date ; for in many cases, two figures only, or even a single figure, will be found sufficient to remind us of a date: e.g., know the year of birth or death of an individual, or one prominent date of a shorter period than a person's life,

-say a war or revolution—in all other dates of the same individual, war, etc., two figures, and often a single figure only, is sufficient to give us the date required ; e.g., if I know that Napoleon I. was born in 1769 and died in 1821, the date of the battle of Austerlitz, which is 1805, must be remembered if I know that I can find it in the word Austerlitz itself: s-t = 51, which is impossible, as it can be neither 17 nor 1851; consequently it is 5, and of course 1805. If I know that Richard III. died in 1485, and all I know of his successor, Henry VII., is that he died in the year 9, I have no difficulty in finding out that it is 1509, as he follows immediately after Richard III.

In recent dates we cannot easily make a mistake with the century, as will be shown further on. We will therefore always omit the century in these cases, e.g.:

Queen Victoria was born in 1819.

=

9;

We find 19 in the Queen, viz., th=1, q= 9. 19 is of course 1819.

1789 we find the date of the first French revolution ; Jacobins, J 8, c= 89 cannot be 1889, it is consequently 1789. We cannot take 3 letters, as they would give J-c-b, 896, which is impossible.

If we know 1789, it helps us to remember the other dates—16, 15, 1489, as given before.

Before going on with dates, I wish to show another application of the principles given in the First Lesson.

Order assists the memory, for the simple reason that it is based on the principle of making the known the starting point of comparison. As we know how to count, as we know the alphabet, any numerical or alphabetical order helps the memory. We have sometimes a number of things to remember where each thing by itself is easy, but the difficulty is to remember the order in which they occur, e.g., the names of the kings of England. The names present no difficulty in themselves, but it is not so easy to remember their order.

In such a case the best thing to do is to see if there is any order, any points of comparison, which may help

us.

Kings of England.

The names are as follows :
William I. Edward I. Edward IV. Mary.
William II. Edward II. Edward V. Elizabeth.
Henry I. Edward III. Richard III. James I.
Stephen. Richard II. Henry VII. Charles I.

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