The King and His Wonderful Castle. VIII.

A TEMPERANCE STORY FOR THE LITTLE FOLKS.

I think you are beginning to learn that there are very many wonderful things in this castle of our king. The way in which the food of the servants was carried to them where they were at work is not less. wonderful than was the way in which it was prepared. You must

know that the castle was filled with a great number of pipes; so many that the king was never able to count them; and some of them were so small that he could not see them without a magnifying glass. These pipes were arranged very much like the sewer pipes or gas pipes of a large city. There was one large pipe connected with the pump-room in the middle of the castle, which separated into smaller pipes, and these separated into smaller ones, and these divided up into smaller ones still until they were smaller than a hair. These smallest pipes the king called capillaries, which in his language meant hairs. I think if this king had been an Englishman he

would not have sought out so long a name for these little pipes, but he lived a long time ago, before any Englishman was born.

These pipes were separated into so many of these capillaries, and ran out in so many directions in the castle, that wherever there was a servant at work, no matter how small he was, there was a little pipe close beside him. Then if you had followed one of these little pipes still further you would have found it opening into another and the two making a larger pipe, and this larger pipe unit

one, these pipes began to unite and finally all joined in a large pipe which connected with the same pumping machine in the center of the castle.*

I will now show you a picture of the reservoir and pumps that are found in the center of the castle and are used for pumping the food for the servants into these pipes, and forcing it into every part of the castle. In this picture you will see two reservoirs and two pumps all connected together and looking very much like your heart, if you could see it. One of these reservoirs is marked 3 in

ing with another making a still larger pipe; and if you continued to follow it you would see it growing larger and larger at every step as the others joined it until it became one large pipe again, and then it entered a reservoir near the room from which the first large pipe proceeded.

So you see that our big pipe with which we started, separated into a great number of smaller ones as it extended through the castle, and then after every servant in the castle was supplied with

the picture; into this the food comes after it has been prepared by the butler and his assistants.

This reservoir the king calls one of his auricles. This is a queer name for a reservoir, but auricle was the king's

*NOTE TO THE TEACHER.-The teacher should use either a chart of the circulatory system, or some pictures, or should make a drawing upon the blackboard which will give the child a correct notion of the way in which the aorta divides into arteries and capillaries, and these again unite into veins which return to the heart.

name for his ear, and I suppose that when the king first saw this reservoir he thought it looked like his ear and so he called it auricle. All the fluid that runs through the pipes of the castle finally comes into this reservoir through the big pipes marked 1 and 2 in the picture. I shall tell you more about this fluid by and by, and how it not only helps to feed all the servants, but helps to keep the castle clean also. But I wish to tell now about these reservoirs and pumps. All the fluid in the pipes that run through the castle flows into the reservoir marked

3 in the picture. The reservoir opens into the pump-room just below it by means of a valve. This pump-room is

Diagram illustrating the flow of blood through the heart: (1) and (2) veins; (3) right auricle; (4) right ventricle; (5) pulmonary artery; (6) pulmonary veins; (7) left auricle; (8) left ventricle; (9) aorta.

marked 4 in the picture. When the pump-room is full of this fluid, which the king calls his blood, it begins to contract and grow very small, and this squeezes the blood out through the pipe marked 5 through another valve that opens into the pipe from the pump-room. After it has pressed all the blood out of the room the walls expand again, and the blood from the reservoir flows into the pumpas before. The king calls this pump-room his right ventricle. This ventricle contracts and expands about

room

seventy times in a minute, and in less than a minute all the blood that flows through the castle comes into this pumproom and is pressed out of it again into the pipe marked 5. There is a valve between the reservoir and the pump-room that admits the blood from the reservoir, but this valve closes when the ventricle begins to squeeze the blood into the pipe, so that none of it goes back into the reservoir. The walls of the pump-room press so hard upon the blood that it is forced through the pipe 5 and a great number of little pipes that pass into some large air chambers that fill a large space in the center of the castle. These small pipes then all unite into two large pipes, marked 6 in the picture, and the blood flows through them into another reservoir, marked 7, which the king calls his left auricle. From this reservoir the blood flows into another pumproom, marked 8 in the picture. pump-room the king calls his left ventricle. This ventricle contracts and presses the blood through the pipe marked 9 in the picture. Then it goes out through all the pipes that run through the castle, then comes back to the right reservoir. So you see there are two pumps and two reservoirs. The right pump, marked 4, pumps the blood through the air chamber, and the left pump, marked 8, pumps the blood through the castle. The left pump-room is larger and the walls are thicker than the right, because it requires more strength to pump the blood through the castle than through the air chamber.

This

In my next I will tell you how the servants receive their food, and some other curious things. PLINY.

The White House, or Executive Mansion.

The corner-stone was laid October 13, 1792. John Adams. in 1800, was the first president who resided there. It was a plain two-story house, devoid of ornament, and called the White House after Martha Washington's home in Virginia. Mrs. Adams writes "there is not a single apartment finished, and the East room I make a drying-room to hang up the clothes." It was burned by the British in 1814, and the next year Congress authorized its restoration, and it was

occupied in 1818, when President Madison gave a New Year reception. Later, the south portico was added, and in 1829 the north portico. The money expended on the Executive Mansion from 1800 to

1885 was $2,500,000. The average amount annually expended in maintaining the mansion, including the care of grounds, parks, and gardens, is $43,000. The furniture of the East room, after the restoration of the White House, was brought from France, and the American eagle replaced the crown of Louis XVIII upon it. It is not known what has become of it, the present furniture having been bought within the past twelve years.

Go About Your Business.

Upon the old Temple clock in London is a singular inscription the origin of which is said to have been a lucky accident.

About two hundred years ago a master workman was employed to repair and put a new face upon the clock. When his work was nearly done he asked the Benchers for an appropriate motto to carve upon the base. They promised to think of one. Week after week he came for their decision, but was put off. day he found them at dinner in commons. "What motto shall I put on the clock, your lordship?" he asked of a learned. judge.

One

"Oh, go about your business!" his

honor cried angrily.

"And very suitable for a lazy, dawdling gang!" the clock-maker is said to have muttered as he retreated. It is certain that he carved "Go about your business" on the base.

The lawyers laughed and decided that no better warning could be given them at any hour of the day, and there the inscription still remains. -Youth's Companion.

More About Factors.

It is important that the pupil should be able to resolve numbers into their prime factors accurately and rapidly. In order to do this, he should know all prime numbers less than 100, he should be familiar with the factors of those that are not prime, and he should be ready to apply

quickly the tests that have already been prime. (See October JOURNAL). There is one method of resolving a number into its prime factors which is better than any other. It may be stated in the following words: Write the number to be resolved with the sign of equality to the right; test the presence of every prime factor in order, taking out such as are successively found, writing them as factors at the right of the sign of equality; in each case, write the remaining factor under the number, and when the last factor so written is found to be a prime number, then place it with the other prime factors, -the work is complete, and the equation is justified.

648945

72105

24035

4807 437 23

ILLUSTRATION.

32X3×5×11×19×23=33×5X11X23. Explanation: We see by the test that the number does not contain 2. The sum of the shapevalues of the figures is 36; this shows that two 3's may be taken out. We take them out, writing them at the right of the sign, and writing the other factor, 72105, below. It is not certain that this number may not contain one 3 or more; applying the test, we find that it contains one, but not two. Taking out this 3, and writing it in the proper place, we write the other factor, 24035, below. The tests show that this number contains one 5, but not two. Taking out the 5, as before, the remaining factor is 4807. Actual trial shows that no 7 is in this number; but the test shows that it contains 11. Taking this out, 437 remains; by actual trial, we find in this number no other 11, no 13, and no 17. But we find its factors are 19 and 23; these we write with the other factors, and the work is complete.

By such a process, which we have explained fully, we may readily factor any number of moderate size; and it is astonishing how rapidly a little practice will enable pupils to do it.

Note that we must be careful to pass no factor till we are sure that we have taken out all of its kind. If more than one factor of any kind is found, the number of such factors may be indicated by a small figure at the right-thus 3o means that the factor 3 is found three times. The small figure is called an exponent.

Many numbers will present more diffi.

culty than the one just factored, even when they are smaller. Let us try 58828.

58828=2X7X11X191

14707 2101 191

Explanation: The tests show the of two 2's but not presence three. We take them out. The other factor, 14707, contains no 3 and no 5; by trial we find a 7, which we take out. The factor 2101 contains no other 7, but the test shows that it contains 11, which we take out, leaving 191. This contains no other 11 and we find by trial that it does not contain 13. We now know that it is prime, and write it with the other prime factors. It is important to see how we know that 191 is prime as soon as we have found that it contains no prime factor below 17. The square of 17 is 289, a larger number than 191; hence, if 191 could be divided by 17 or any number greater, the other factor must be less than 17; but we know from trial that it can have no factor less than 17. Hence this important principle: When we have tried unsuccessfully to factor a number, by all the prime numbers in order until the square of the next prime exceeds the one we are trying to factor, we may be sure that the number is prime.

3. The product of these factors is a common multiple of 28 and 21 because it contains the prime factors of each; and as it contains no factors which are not necessary, it is their least common multiple. The pupil should be held strictly to an explanation of every step, somewhat like the one here given, in order that he may see clearly what he is doing, and why he is doing it as he does.

Take one other example: Find the least common multiple of 50, 40, 36, and

5, 3, 2.

7

2

14

5

70

It

210

Least Common Multiple. A common multiple of several numbers is a number which is a multiple of any of them. is therefore necessary that it should contain the prime factors of every one of them. If it contains no other factor than these, it must be their least common multiple. Hence, an obvious way to find the least common multiple of several numbers is this: Factor the several numbers; then, to find their least common multiple, take the product of such prime factors as each contains, and no others.

Example: Find the least common mul28=29X7 tiple of 14, 21, and 28. 21=3X7 We disregard the 14, 1.c.m.=22X3X7=84 because any number that contains 28, must contain its factor 14. We resolve 21 and 28 into their prime factors by inspection. We now write 1.c.m. with the sign of equality at the right; after this sign, we put the factors of 28, 22×7.

These will make a number that will contain 28; but we are to find a number which will also contain 21; it must contain the prime factors of 21, which are 3 and 7. We have the factor 7, but we must put with the factors we now have, the factor

How not to do it. Suppose we are to 7) 70, 42, 28 find the least common mul2) 10, 6, 4 tiple of 70, 42, and 28. The way not to follow is shown in the margin, no matter how many respectable textbooks give it. Any bright pupil, with a little practice, would solve this without figures. He knows that the least common multiple must contain the largest number, or 70. He sees that 42 has the factor 3 which 70 has not; and he sees that he must have two 2's to contain 28 and 70 contains only one 2. Hence, he must put 2 and 3, or 6, with 70, giving 420 at once for the least common multiple.

420

Let us glance at an example where the numbers are somewhat larger, say 7257 and 6895. It is a little troublesome to factor these numbers. Is it necessary? It will be of no use if they have no common factor, for in that case their product is their least common multiple.