Part 3

By knowing the last figure of the product of any two numbers, to tell the other figures. If the number seventy-three be multiplied by each of the numbers in the following arithmetical progression, 3, 6, 9, 12, 15, 18, 21, 24, 27, the products will terminate with the nine digits, in this order, 9, 8, 7, 6, 5, 4, 3, 2, 1; the numbers themselves being as follows: 219, 438, 657, 876, 1095, 1314, 1533, 1752, and 1971. Let, therefore, a little bag be provided, consisting of two partitions, into one of which put several tickets, marked with the number 73, and into the other put as many tickets, 3, 6, 9, etc., up to 27. Then open that part of the bag containing the number 73, and ask a person to take out one ticket only; after which, dexterously change the opening, and desire another person to take a ticket from the other part. Let them now multiply their two numbers together, and tell you the last figure of the product, by which you will readily determine from the foregoing series what the remaining figures must be. Suppose, for example, the numbers taken out of the bag were 73 and 12, then as the product of these two numbers, which is 876, has 6 for its last figure, you will readily know it is the fourth of the series and the other two figures must be 8 and 7.

―――――◀▶―――――

TO TELL TWO OR MORE NUMBERS WHICH A PERSON HAS THOUGHT OF.

These numbers must not exceed 9. Let him think of two or three numbers, double the first and add 1 to the product, multiply the whole by 5, and add to that product the second number. If there be a third, make him double the first sum and add 1 to it; then desire him to multiple the new sum by 5, and to add to it the third number. If there should be a fourth number, you must proceed in the same manner, desiring him to double the preceding sum, to add 1 to it, to multiply by 5, and then to add the fourth number, and so on. Then ask the number arising from the addition of the last number thought of, and if there were two numbers subtract 5 from it: if three, 55; if four, 555, and so on, for the remainder will be composed of figures, of which the first on the left will be the first number thought of, the next the second, and so of the rest.

Suppose the numbers thought of to be 3, 4, 6; by adding 1 to 6, the double of the first, we have 7, which being multiplied by 5 gives 35; if 4, the second number thought of, be then added, we shall have 39, which doubled gives 78, and if we add 1, and multiply 79 by 5, the result will be 395. Lastly, if we add 6, the third number thought of, the sum will be 401, and if 55 be deducted from it we shall have for the remainder 346, the figures of which 3, 4, and 6, indicate in order the three numbers thought of.

―――――◀▶―――――

AN EASY PROOF FOR SUMS IN MULTIPLICATION.

As boys are always interested in short cuts in arithmetical processes, it may be well to insert for the benefit of those who are studying multiplication, a method of proving their examples which I learned a short time ago from an old banker of New York. This rule is simply to add the digits of both multiplicand and multiplier, divide both answers by 9, and multiply the remainders; divide this product by 9 and the remainder will be, if the example is correct, the same as that obtained by adding the digits of the product and dividing that answer by 9. For instance, suppose after multiplying 4359 by 2786 we have 12144174 for the answer; now instead of performing this operation over a second time to make sure our answer is correct, we simply add the digits in 4359 and divide the sum 21 by 9, we find we have 3 left. As it is the only remainder we have to deal with, we need not keep the other figures. By adding the digits in the multiplier we obtain 23, which divided by 9 gives 2 and 5 remainder. Now, multiplying the first remainder by the second we have 15: this product divided by 9 gives 1 and 6 remainder. If the product 12144174 is correct, the sum of its digits divided by 9 will leave 6 for a remainder. Performing the operation, we find the sum of its digits is 24, divided by 9 equals 2 and 6 remainder. As both the remainders correspond, the answer was correct. After a little practice you will find you can prove your examples very quickly by this method, and where a number of sums are given without the answers it will be of invaluable assistance, besides saving you a great amount of labor.

―――――◀▶―――――

THE SELF-RECTIFYING DART.

The dart, and its larger brother the javelin, were among the earliest weapons used in warfare, and were very skilfully thrown, not only by the Roman soldiers, but by the Goths and other savage tribes who lived in the regions north of them.

These javelins were large affairs, measuring some six or seven feet in length; the handle, a tough piece of wood, was generally four and one-half feet in length, and an inch in diameter, while the rest of the length was taken up by the barbed triangular-shaped head.

Ever since those days children of all nations and climes have made toy implements, resembling those in general appearance, but varying much in size and materials used.

The little dart described below is perhaps the tiniest and least formidable of them all; but even this should not be carelessly tossed about the room in which others are playing; when, however, thrown in the open air, and away from others who might be hurt, there is considerable amusement derived from the airy bit of flying wood, which always comes down with such unerring certainty upon its spear-like head. To make this dart, take half a sheet of note-paper, double it diagonally across, so that its top edge may fall evenly upon that of one side (see Fig. 1), and cut off the surplus piece of paper which remains uncovered at the bottom of the page. Open your square, and fold it again in the other diagonal line _c_, _d_ (the first is represented on Fig. 2, as _a_, _b_). Now, opening again, fold upon the line _e_, _f_, then, after opening, upon _g_, _h_. Crease all the folds as you make them. Now, having prepared your handle, which consists of a piece of wood about 8 inches long and the size of a lead pencil, cut across one end at right angles, with slits nearly or quite an inch in depth; take your paper and open it flat once more. Fold the diagonals so that the four points, _a_, _b_, _c_, _d_, shall all meet together above _x_, and the lines _ax_, _bx_, _cx_, and _dx_ shall meet at the central line of the figure, and the four shorter lines, _ex_, _fx_, etc., form the outside edges of the figure. Insert a tiny wedge or knife-blade at the bottom of the slits, and press the paper down in the opening, bringing the folded edges through each of the four slits; remove the wedge, and the paper will be firmly held in its place. Insert a needle or headless pin in the other end of the wood, and the dart is ready for use.

―――――◀▶―――――

THE BALANCING PIN.

This amusing feat I first saw performed in our little district school-house, many years ago.

One morning, while the teacher was busy with his class at the blackboard, one of the boys drew an old clay pipe-stem from his pocket, and producing a small green gooseberry and a pin from some other part of his clothing, gave us boys to understand that he was about to perform some wonderful trick with them. We were of course all attention, and as the teacher’s back remained turned toward us, he proceeded to astonish us with his remarkable feat. He first stuck the pin through the gooseberry, and then let it fall, point downward, into one end of the pipe-stem; then, placing the other end to his mouth, and holding his head thrown well over backward, he blew into the opening, and the gooseberry and pin arose quite clear of the tube, and began dancing and balancing above it in a very funny way. How long it would have continued its gyrations I cannot tell, probably until his breath gave out, but just then a little boy in the front row made some exclamation, and straightway the teacher’s head came around, the pipe-stem, pin, and gooseberry went on a voyage of discovery out of the school-house window, and the boy got a thrashing for his pains. But the feat was often performed by us all after that, and some years later, when a second generation of boys were having over again the tricks and sports their older brothers had outgrown, I saw the same principle applied under more favorable conditions. Instead of the straight pipe-stem, which necessitated throwing the head over backward, to insure its perpendicular position, a tube bent at a right angle near one end was used, and the balancing of the pin could be much more easily watched by the performer. Instead of the gooseberry, a currant, pea, or any light, round fruit can be substituted, and a small glass tube may take the place of the pipe-stem.

―――――◀▶―――――

A BOX-SLED FOR BABY.

Procure a deep, smooth soap-box, and decide how high you wish the back and front to be; then take a piece of brown paper, the exact size of the sides of the box, and mark on it a curve, which shall unite the high back with the low front. After this has assumed a perfectly satisfactory form, cut it out and tack it on one side of the box. Mark the outline carefully on both side-pieces, and saw the boards as indicated by the line; cut the front straight across, and rasp and sand-paper the edges till they are very smooth and well rounded. Next paint the box inside and out, excepting the bottom, which is to be fastened to the sled, with a thick coat of burnt umber, and give it a good drying. Then with light-blue paint, make a narrow band, one-fourth of an inch wide, entirely around each side, the back, and the front, about half an inch from the edge. Stencil a pretty design on the back, and the name of the little owner on each side; let this thoroughly dry, and finish with two coats of varnish. A little seat can be fitted in the back part if desired, but a pillow answers the purpose much better.

―――――◀▶―――――

A SET OF CARS.

Procure a stick of wood of any length, and an inch and a half square at the ends. Saw it into pieces six inches in length, being careful to cut it evenly, that the blocks may be rectangular in form. Round off the tops slightly at the edges and paint them brown, then give the sides and ends a good coating of yellow.

If you have no oil paints, it would be a good investment to get a few tubes, as they are not expensive, and are of invaluable assistance in adding beauty and naturalness to many things a boy can make. For the cars, a tube of chrome yellow, one of Indian-red, and one of black would be needed, but as those are not over seven or eight cents apiece the whole cost would be small. The windows can perhaps be most conveniently put on by “stencilling.” To do this, cut a piece of stout paper or thin cardboard the exact size of the side of the car, and mark the windows on it in their proper places (see Fig. 2). Then cut out the windows thus drawn with the point of a sharp penknife. Catch the card firmly upon the surface by driving two or three fine pins through it into the wood. Finally, with your brush moderately filled with the black paint, cover all the yellow surface exposed through the openings; then remove the card very carefully and one side of your car will be complete. After painting the whole set, another long time will be needed for drying. During the meantime obtain a few screw-eyes and hooks, and, when perfectly dry, screw a hook into the left and an eye into the right end of each car, join them into a train, and you will find you have a strong set of cars with which your little brother can play to his satisfaction, without a fear of breaking. The locomotive is more difficult to make, but with a little care any boy of ten can be quite certain of success.

―――――◀▶―――――

THE TOY LOCOMOTIVE.

The thin ends of a common soap-box afford very good material for the base of this locomotive, while the end of a curtain-roller makes a capital boiler. The cab can be cut from a cigar-box, and a button-mold will do for the boiler-head. First cut from the thicker wood a base in shape like Fig. 1, and seven inches long by one and a half wide; with a jackknife bevel it on either side of the pointed end to correspond to the shape of the pilot, as shown in the cut. Saw the roller even at either end just four inches in length. Next cut from a solid block of wood a smoke-stack three inches high and an inch in diameter across the top. The cab is cut from the cigar-box wood, and consists of a front like _a_, two side-pieces like _b_, and a top like that seen in Fig. 1; round off the edges of the top to give it a slightly convex surface like the tops of the cars. Now, with brads, fasten these three parts together. Then with a long, slender brass screw fasten the button-mold and smoke-stack on front of the boiler. The screw should have as large a head as it is possible to find, and should be long enough to extend half an inch or more into the round section of wood or boiler. Cover the whole, excepting the cab, with two thick coats of black paint, being careful that the first is perfectly dry before the second is put on. After the blackened surface is thoroughly dry and hard, put the red stripes on the pilot, as seen in the cut: and for the brass bands around the boiler use chrome yellow. The cab is painted Indian-red, and after this is perfectly dry, the windows are painted on with black, as in the cars.

The little ornamental lines on the cab are made with the yellow paint. A large round-headed brass screw driven through a low flat spool (such as is used for button-hole twist), into the top of the boiler in front of the cab, makes a good steam-chest and whistle, and adds the finishing touch to this indestructible little toy. If you anticipate making this train of cars for a Christmas present, begin it in time, as paint dries much more slowly in winter than in summer, and it is absolutely necessary that each coat be perfectly dry before the next is applied. Varnishing greatly improves the durability and appearance of the painted surface. Shellac dissolved in alcohol makes the best varnish for this kind of work. It should be made moderately thick, and if intended for light-colored work, white shellac should be used, as the dark leaves a slight stain upon the surface. I forgot to add in its proper place that a brass button, caught in on top by a stiff wire, is made to represent a bell. The wire should be first bent into the shape seen in the illustration; the button then hung in position, and the wire finally driven into the holes made to receive it.

The tender consists of a piece of wood the same width but only half the length of one of the cars, and one inch high. This is painted black with a narrow band of yellow running around the sides near the top, and is fastened to the locomotive and car by means of the screw-eye and hook.

―――――◀▶―――――

A FREIGHT TRAIN.

The locomotive for this train can be made like the one already described, and the cars are cut from a rectangular stick, in the same manner as the passenger cars. These should receive a thick coat of Indian-red paint, and if this does not cover well, that is, if any of the wood shows through, another coat should be given. After the paint is perfectly dry, put on one edge of the side, near the top, a number in white, and two or three letters in the same color, to represent the sides of the freight cars on different lines. If desired, the cars can be painted different colors, and the side decorations copied from the car you mean to represent. Give the whole a good varnishing with the shellac dissolved in alcohol, and allow plenty of time to elapse before the toy is used, for it to become perfectly dry and hard.

―――――◀▶―――――

A LOT OF PAPER WINDMILLS.

Take a thin stick of wood a foot and a half or two feet long, and nail to it four cross-pieces, graduated in length and six or seven inches apart. The shorter, at the top, should measure about six inches. Cut out of stiff, colored paper (the greater the variety the prettier the effect) fifteen pieces, each three inches square, and slit each piece as indicated by the diagonal lines in the figure. Out of pretty tissue-paper cut three round pieces for each mill, about the size of a silver dollar, and with a dull knife scrape their edges, that they may slightly curl like the petals of a rose; crinkle them at the center if intended for a rose, or from the edge toward the center if for asters or marigolds, and thrust a large, strong pin through the middle of each disk, drawing the flower well down over the head; then, bending the opposite corners of each square of paper so that they shall all rest over the central dot marked on each (Fig. 1), force the pin with the flower on its head, down through the five thicknesses of paper, driving it well into the wood of the frame. In doing this care should be taken to avoid creasing the curved edges of the windmills. They are placed upon the frame-work as indicated in the cut.

Very pretty windmills are often made of only two shades, common note-paper being used for the wheels, and a bright, rosy pink tissue-paper for the flowers. Indeed, those made of common brown wrapping-paper without any flowers at all give more satisfaction in a light wind than the more elaborate ones described above.

―――――◀▶―――――

A WINTER GARDEN.

Most boys love flowers; and many families, especially in the country, would keep more through the winter than they do, if they had the space and time to devote to them, necessary for their preservation. A number of pots, sufficiently large to hold good-sized plants, take up considerable room; and no little time is required each day, to keep the pots clean and the plants well watered. Now, boys, I have a suggestion to make, which I intend for your ears alone. Why can’t you make a winter garden, and, if necessary, take care of it through the season? It will amply repay you for your labor, and do much toward brightening the home life through the long dreary months, when everything without is covered with ice and snow.

First procure a soap-box, the best and tightest you can find: if any cracks are too wide to be easily closed with putty, nail laths over them on the inside, line their edges, and, in fact, stop every seam and crevice with good thick layers of putty. Next paint over the entire inside with any colored pigment you may have, as it does not show when the box is filled with earth, but simply aids in making it water-tight.

Now take four strong pieces of wood, about two and a half feet long; smooth them well and sand-paper; be sure both ends are cut off evenly, and that each leg is the same length as the other three, and, finally, nail them firmly to the four corners of the box, letting the tops come in line with its upper edge, and give the whole thing two good coats of Indian-red. A very pretty stand is made by substituting the straight trunks of young forest trees with their bark left on in place of the smooth, painted legs; bore holes in the bottom of the legs and insert casters, and finish by giving the entire outer surface a thick coating of varnish. Then get a good wheelbarrow-load of fine leaf-mold, about half that quantity of sand, and some common garden soil. Stir these well together, and fill the box half full with the mixture, first covering the bottom with pebbles, to secure drainage. Before this, however, bore a hole with a good-sized gimlet in the bottom of the box, and fit a soft pine peg to close it from the under side. When the plants are watered this peg can be removed, and a dish placed beneath the opening to catch the surplus water.

You are now ready for the plants. I find almost any garden plants thrive well in this box, so any favorites you may have will soon make themselves at home in these new quarters. It is well to put vines around the edge, as they fall over, and their glossy green leaves and stems form an agreeable contrast to the dark-red background of the box itself. In my present winter garden I have German and Cenilworth ivy, partridge-berry, and the common inch-plant for vines. In the center is a large salvia, taken up so carefully that the great ball of dirt was not shaken from its roots. On one side is a calla lily, and on the other a feverfew of the large double variety. At the ends are fuchsias and heliotrope, and scattered over the other available spots are verbenas and petunias, sweet peas and lobelia; one or two fish-geraniums of bright colors also found a place, and a little wood-violet nestled in one corner has bloomed since early spring. A beautiful large purple pansy, too, has been blooming all winter in another corner of the box.

Over this garden are two hanging-pots, one filled with pink oxalis, and the other with a Chinese pink; both have contributed their full share of blossoms during the entire season, and neither seems to tire of well-doing. I must now tell you how to care for these beautiful pets, for they must receive some attention, which, however, is very small when compared with that required by their sisters in pots. First, always water them with warm water (almost as hot as you can bear your hand in), pour this around the roots in sufficient quantities to thoroughly moisten the soil. A good rule to be observed in watering your plants is to pour on the water until it begins to run out of the hole in the bottom of the box. With such thorough wetting down they will not need water oftener than twice a week, except when the sun is very hot, and the moisture evaporates quickly. A little carbonate of ammonia added to the water greatly improves their growth, and half-a-dozen grains of permanganate of potash added once a fortnight to the warm bath turns their foliage a rich dark green. With a whisk broom, sprinkle them once or twice a week with water which is also warm, but not as hot as that used on their roots; this operation takes but little time, scarcely five minutes, and as the stand is on casters it can be easily moved to the middle of the room, and each side can then receive its full share of the washing. It is safe to predict that if any boy would make the stand, and supply it with rich soil, his mother or some one of his sisters would only be too happy to plant and care for the flowers it might hold.

―――――◀▶―――――

THE BOOT PUZZLE.

First take a piece of paper, double it, and cut from it a pair of boots, the fold in the paper coming at the top of the boots, and consequently joining them together. Then take another piece, fold it and cut it in the form of Fig. 2, _a_ being the folded end. Fold still another piece and cut it like Fig. 3, _b_ representing the folding side. Now open the smaller piece, as in Fig. 4, and push the point _a_ through the opening in its center (Fig. 5). Then put one boot through the loop of the long arm, _c_, between _a_ and the smaller piece, which has been pushed forward as far as it will go (Fig. 6). Now pull the smaller piece down over _a_, and open the largest piece, and the boots are fastened on to the larger paper in such a way that it is rather hard for the uninitiated to extricate them.

After they are fastened in place, with your finger-nail smooth out the creases made at _a_, Fig. 5, as their appearance might furnish a clue toward solving the mystery. It is best when cutting Fig. 2 to avoid the creasing if possible.

When you pass them to your friends to take off, explain that they are not to bend the boots. It is an excellent plan to make the last-named articles of cardboard, while the other parts are simply of note-paper.

―――――◀▶―――――

HOW TO TAKE PORTRAITS.