Let us describe the ‘15’ game first. Place the blocks, numbered 1 to 15, on the board irregularly, and then, by sliding them about from square to square, but without removing them from the board, arrange them in the following order:—

This looks simple enough in theory, but to any uninitiated reader who may think it easy of accomplishment in practice, we need merely say, ‘Try it.’

The ‘34’ puzzle consists in arranging the blocks, numbered 1 to 16, so that they will add perpendicularly, horizontally, and from corner to corner; also in arranging the 4 in each corner, the four outside numbers of the two centre lines, and the four groups in each corner; in all, sixteen different ways, and each produce the same total—34.

The ‘15’ puzzle would appear to have been, on its coming to England a few years ago, strictly a new introduction, but the ‘34’ was not only tolerably well-known, but seems to have been familiar to the Arabs in the ninth century. The nature of the game we have already described.

Now a word on the ‘15’ game. A skilful writer has pointed out how, while with two figures only two different arrangements can be obtained, three figures can be placed in six different orders, viz.:—3 1 2—3 2 1; 1 3 2—2 3 1; 1 2 3—2 1 3. Then, while there are thus six different orders that can be produced with three figures, if a fourth figure be placed in every one of the four different positions with regard to these six orders, we shall have four times the different number of orders that can be had with three figures. In the same way by multiplying these twenty-four different orders by five we shall have the number to be obtained with five figures. The rule, therefore, to find the number of different orders that may be obtained with any number of figures is to multiply all the different numbers used by each other. Thus, with six figures there will be 720 different orders; with seven, 5,040; with eight, 40,320, and so forth until we come to fifteen, when it will be found that the enormous number of 1,307,674,368,000 represents the different orders in which the fifteen numbers can be placed. This, of course, is the number of arrangements in which the cubes in the game of ‘15’ can be placed in the box. Let us consider how long it would take to test the solution of the different arrangements possible. Let us suppose that the cubes were worked to their consecutive or 15—14 order at the rate of one in every five minutes, which would, working day and night, be at the rate of about 105,000 arrangements a year. In this case it would take not less than twelve million years to test all the different arrangements!

The question now arises, whether out of this enormous number of different arrangements there are certain of them that cannot be shifted into the required consecutive order. The answer is, that exactly half of these arrangements are soluble, and the other half insoluble. The whole question turns upon the fact that in the arrangement of a certain number of figures in a row, otherwise than in consecutive order, the arrangement is made up either by an odd or an even number of transpositions. In the total number of different rows in which any given number of figures can be arranged, half of them will consist of rows containing an odd number, and the other half an even number of transpositions, just in the same way that in the numbers one to one hundred there are fifty odd and fifty even numbers. Take the case of six figures, 1, 2, 3, 4, 5, 6. If the first pair of figures is transposed the row will read 2, 1, 3, 4, 5, 6. In this row there is an odd number, namely, 1, of transpositions. If from this order the second pair is transposed the result will read 2, 1, 4, 3, 5, 6, and in this row there is an even number (2) of transpositions made from the original consecutive order. Suppose the last pair is transposed, the order will be 2, 1, 4, 3, 6, 5, and an odd number (3) of transpositions has been made. This may be continued until all the different rows possible have been worked, when it is evident that the first, third, fifth, etc., rows will each consist of an odd number of transpositions, while the intermediate rows will each contain an even number of transpositions.

Suppose we take the third row given above, 2, 1, 4, 3, 6, 5, this contains an odd number of transpositions. It is therefore impossible, by making an even number of transpositions each time, to bring 2, 1, 4, 3, 6, 5 to the original position of 1, 2, 3, 4, 5, 6, because it contains an odd number of transpositions, one of which will always remain, and cannot be eliminated by any even number of transpositions. Just in the same way we cannot, by the addition of even numbers, to any quantity or amount, to an odd number, produce an even number as the result. Every arrangement of a certain number of figures in a row contains therefore an odd or even number of transpositions which must be made before the figures can be brought into consecutive order, but it is immaterial whether these transpositions are made in such order as will the soonest produce the consecutive order, so long as they are made, and the number, whether odd or even, is noted.

By writing down a row of fifteen figures, and transposing two numbers each time, and noting whether an odd or even number of transpositions are required to produce the consecutive order, it can be ascertained whether the cubes, in this order, can or cannot be moved into the consecutive order. If the required number of transpositions is an odd number it will be impossible.

CHAPTER XIX.—SOME MINOR GAMES.

I.—A NEW INDOOR GAME.

This is a good indoor game for boys, which I believe has not yet appeared in any form in England. It is a modification of one played by the students in Germany, but adapted to English words, and with a special arrangement of the figures, which the original game does not admit of, the words not being so suitable.

The above diagram is chalked on the floor, the figures being about one foot across and one foot apart. Then one player takes his place on the middle figure, facing Fig. 6. The other players then sing the old rhyme of the ‘Crooked Man’ to the ‘King Pippin Polka,’ known also as ‘My mother said,’ etc.

Then the player, with his feet together, jumps to No. 1, No. 2, etc., as the words ‘man,’ ‘mile,’ etc., are mentioned. He must not turn round, or put his feet outside the figures. The others keep time by clapping with their hands. If the player jumps to a wrong figure, or to one before it is sung, he pays a forfeit, especially for the last line.

The verse is then repeated to the second part of the tune, the player jumping to each figure before it is mentioned, and giving a second jump on it, before going to the next. The last line finishes off with a wild repetition of the figure, the player stepping from one figure to the next as fast as he can, finishing on No. 7 to the last word. The player must place both feet on Fig. 7 to the words ‘and they,’ then the right on Fig. 1, and so on, to the last one. The great difficulty in the last line is to get the left foot from Fig. 4 to Fig. 6 in time. This is done by passing the right foot behind the left, when moving it from Fig. 3 to Fig. 5, which will enable the player to finish without tying his legs in a knot. The words and the numbers of the figures for the player to jump to are here given (commencing on No. 7 and facing Fig. 6)—

1. There was a crooked (jump to Fig. 1 to the word) man,
   He went a crooked (jump to Fig. 2 to word) mile,
   He found a crooked (Fig. 3) sixpence
   Against a crooked (Fig. 4) stile;
   He bought a crooked (Fig. 5) cat
   That caught a crooked (Fig. 6, and pause) mouse.
   And they all lived together in a little crooked (Fig. 7) house.
2. There (jump to Fig. 1) was a crooked (2nd jump on Fig. 1) man,
   He (to Fig. 2) went a crooked (2nd Fig. 2) mile,
   He (Fig. 3) found a crooked (2nd time Fig. 3) sixpence
   A- (to Fig. 4) -gainst a crooked (2nd Fig. 4) stile;
   He (Fig. 5) bought a crooked (Fig. 5) cat
   That (Fig. 6) caught a crooked (Fig. 6) mouse,
   (Step to Fig. 7, left foot) And they (right to Fig. 1 to word) all (left to Fig. 2) lived (right to Fig. 3 to) together (left to Fig. 4 to) in a (right behind left to Fig. 5) little (left to Fig. 6) crooked (both feet to Fig. 7) house.

II.—KNUCKLE BONES.
By Captain A. S. Harrison.

The game is played with five bones, and the stages are as follows:—

1. Beginnings.—The five bones are gathered in the palm of the hand and thrown up, any number being caught on the back of the hand; they are then tossed up again, and caught in the palm. One is selected, thrown into the air, and one at a time the remainder picked up, while the one thrown is in the air. This must be caught and again thrown for the next bone. The bone thrown up is called the ‘dab,’ and must be caught clear, without touching any part of the person but the right hand under all circumstances of the game.

2. Ones.—The five bones are thrown on to the table, and the dab selected is thrown up, and the remainder are taken up, one by one, without touching any other bone.

3. Twos.—The same again, but two taken up for each throw of the dab.

4. Threes.—Three picked up, and then one.

5. Fours.—Four picked up.

In twos, threes, and fours, it is permitted by consent of the adversary to push the selected bones together while the dab is in the air. The touching of any other than the selected bones, or the failure to pick up the proper number, forfeits the turn.

6. Short Spans.—Two bones are placed on the table, each side of the left hand, one pair close to the thumb, the other pair at the tip of the little finger. Each pair must be taken up separately, without any pushing together.

7. Long Spans.—A bone is placed at the extremities of the thumb and little finger, stretched out to the widest. Another pair is put in the same way about six inches farther on the table. These pairs must be taken up without any touching together: any bone displaced may be put back again three times; failure on the third trial forfeits the turn.

8. Creek Mouse.—The five bones are tossed from the palm, and any number caught on the back of the hand; all but one are shaken off; the remainder are then gathered into the palm, without disturbing the one on the back, which is then tossed and caught in the palm, with the others.

9. Second Creek Mouse.—The five bones are tossed from the palm as before, and one is retained on the back. The remainder are taken one between each finger and thumb, the one on the back is then tossed and caught in the extended palm.

10. Bridges.—The hand is laid on the back on the table, the bones held between the fingers are then dropped in a row on the table. An arch is formed with the first finger and thumb of the left hand at about six inches from the left-hand bone of the four. They are then one by one pushed through this bridge; when all are through the left hand is removed, and the four are taken up at one sweep. No touching together is allowed.

11. Cracks.—The bones are thrown on the table, and the four picked up one by one; the dab in falling and being caught to make a distinct crack on the one picked up.

12. No Cracks.—Same as before, but the dab must be caught without touching the other bone. The slightest sound forfeits the turn.

13. Exchanges.—The four bones are laid at the corners of a square, a full span on each side. The first bone is picked up from the lower right-hand corner, and at the next throw is exchanged for the one above. This is exchanged for the one at the top left-hand corner, this for the lower left, and that is placed at the point of starting. The bones are then taken up in diagonal pairs.

14. Everlastings.—The whole of the bones are tossed from the palms, and any number caught on the back. These are tossed from the back and caught in the palm; and any that have fallen in the first toss have to be picked up while the whole of the others are in the air, so that at one moment there may be four dabs and one to pick up. This task, as the name implies, approaches the everlasting.

The game is an excellent one for exercising and developing that perfect sympathy between the eye and the hand which is certain to be of great service in after life.

SECTION IV.
THE MAGIC-LANTERN, AND ALL ABOUT IT.

CHAPTER XX.—THE MAGIC-LANTERN, AND ALL ABOUT IT.

I.—Pleasant Hours with the Magic-Lantern.—By A. A. Wood, F.C.S.

1.—ALL ABOUT LANTERNS.

The magic-lantern is of very respectable antiquity. As early as the seventeenth century a Jesuit, named Kircher, had constructed one. He was not unwilling to excite the fears of the persons who witnessed the effects of his apparatus, and not only did he apply the word magic to his lantern, but when exhibiting it he had the darkened room divided into two compartments, in one of which was the lantern, and in the other the spectators. These gazed on the shadowy forms before them in amazement, and were unable to perceive how they were produced.

Kircher’s lantern consisted of a large wooden box, with a door on one side and an opening in front for the reception of a tube containing a magnifying lens. The light was obtained by means of an oil lamp with a polished brass reflector, the smoke of the lamp being conveyed away by a chimney in the top. The pictures exhibited were painted on long strips of glass, and were passed through a groove in the front tube, and although the effects thus obtained must have been of the most imperfect character, yet from their novelty they produced a most profound impression.

There are reasons to believe that the lantern was in use even earlier than the seventeenth century, and that the mysterious figures which the old astrologers produced in the smoke of their mystic fires were produced in the same way as Kircher’s, the smoke forming the screen. With this brief description of the history of the magic-lantern, we must be content. Our main business is to describe the construction and use of the lantern as manufactured now.

2.—VARIOUS KINDS OF LANTERNS.

The magic-lantern, as now constructed, consists of a box or chamber of japanned tin-plate, with a lamp for the source of light, a large lens to converge the light, and a smaller lens to magnify the object to be exhibited. The large lens is called the condenser, and the smaller lens is designated the objective. Between the condenser and the objective, immediately in front of the former, an aperture is provided for the reception of the painted slide. This aperture is called the slide-holder. We may separate magic-lanterns into three great divisions, the distinguishing difference between them being the kind of light employed. In the first division the lamps are constructed to burn colza or sperm oil; in the second division a mineral oil (purified paraffin) takes the place of the sperm or colza oil; and in the third division some form of lime-light is employed. We will describe these varieties in order.

First, then, let us deal with the lanterns illuminated by a lamp burning colza or sperm oil. Of these lanterns there are two subdivisions, those whose condensing lenses are of a size suitable for exhibiting the standard slides (slides three and a quarter inches in diameter), called phantasmagoria lanterns, and lanterns of a smaller size, which may be described as toys, and for which but a very limited variety of slides can be obtained. We give an illustration (Fig. 1) of one of these small lanterns, from which it will be seen that the lamp is of very simple construction, and provided with a silvered reflector behind it. Magic-lanterns, the condensing lenses of which are from one and a half inch to two and a half inches in diameter, are calculated to produce discs of light from four feet to six feet in diameter. Such discs are usually obtained when the distance of the lantern from the screen is about one-third more than the desired diameter of the disc. Lanterns such as these are described, according to their size, by number, and include all from Nos. 1 to 6.

In preparing this lantern for use the lenses should be carefully cleaned with a soft cloth, and the lamp freshly trimmed. The cotton must be long enough to reach to the bottom of the lamp, and be freshly and evenly cut; the oil should be supplied to the lamp an hour before it is lighted, that the wick may become thoroughly saturated. The best oil to use is sperm oil in which camphor has been dissolved in the proportion of one ounce to one pint of oil. The object of the addition of the camphor is to increase the brilliancy of the light. If, however, sperm oil cannot be obtained, colza oil may be substituted, and this should be treated with camphor in the same way.

The room in which the exhibition is to take place should be entirely darkened, and a clean white screen or sheet hung up for the reception of the magnified pictures. The lantern is to be placed in front of the screen, upon a table or other suitable support, and at such a distance as will produce the required disc or circle of light.

The painted slide must be placed in the slide-holder upside down, and if the representation on the screen be not clear and sharp, the objective (the front lens) must be moved towards or away from the slide-holder, until the picture is well defined, or, as it is called, properly focused.

3.—THE PHANTASMAGORIA LANTERN.

We have given a description of the simpler forms of the magic-lantern burning sperm or colza oil with a solid wick, and now we will explain the construction of that known as the phantasmagoria lantern. The term ‘phantasmagoria’ was originally applied to a lantern exhibition, in which the figures on the screen varied suddenly in their dimensions, seeming at one time as though they were rushing on to the spectators, and at another vanishing away in the distance. At present this name is used as the distinctive title of a particular form of magic-lantern, otherwise known as the ‘No. 8.’

In the phantasmagoria lantern the condenser consists of two lenses (usually a meniscus convex and a double convex) fitted into a brass cell and placed in the lantern with the concave side towards the lamp. The objective is also formed of two lenses fitted into a brass tube with a diaphragm in front. This tube slides into a brass jacket fixed in front of the lantern, and the lenses are placed in the tube with their convex sides towards the condenser.

The lamp employed for illuminating the phantasmagoria lantern is the Argand fountain lamp, with hollow cylindrical wick (Fig. 2). In preparing this lamp for use, a new cotton should be fitted to it. To do this with facility the cotton should be put on to a taper-stick (Fig. 3), on to the base of which the brass wick-holder fits, the cotton can then be pushed on to the wick-holder without any difficulty. The wick-holder and wick are to be replaced in the lamp and screwed down to the bottom, and if there be any superfluous wick standing above the top of the lamp it is to be ignited and allowed to burn itself out. (This must be done before any oil is supplied to the lamp.) The wick being ready, the cistern at the back of the lamp is to be lifted out and inverted, and then filled with oil. The plug or valve which serves to close the orifice in the cistern through which the oil has been poured is to be pulled up and so held while the cistern is replaced in the lamp. The oil should be supplied to the lamp about half an hour before it is required for use, in order that the wick may be thoroughly saturated, and camphorated sperm oil is decidedly the best oil to be used in this lamp. When the lamp is first lighted the wick should be raised but a short distance above the tube that supports it, and after it is ignited all round, the lamp should be replaced in the lantern, the glass chimney (which is screwed on to a metal oxydator and gallery) placed on it, and the wick turned up as high as it will admit of without smoking. The lantern is then to be placed on the stand or table in front of the screen, at a distance of from nine to twelve feet off, a disc of six feet in diameter being obtained at the former distance, and eight feet diameter at the latter. After the lamp has been placed in the sliding tray provided for it at the bottom of the lantern, its position has to be adjusted. If the lamp be too near to the condenser, the centre of the disc will be darkened; if too far off, the margin of the disc will be obscured; the proper distance will be easily ascertained when the lamp is lighted and placed in the lantern.

4.—THE EUPHANERON LANTERN.

The phantasmagoria lantern continued for some years to maintain its character as the best lamp-lit lantern ever made. And this might have still continued, but for the discovery that the art of photography could produce transparent slides suitable for the magic-lantern.

The necessity for a superior illuminating arrangement was at once experienced, and attention was given to the lamps that were fed with the mineral oils, instead of animal or vegetable oils. Although various forms of mineral oil lamps were tried, they were not successful, until Mr. L. Marcy, of Philadelphia, conceived the idea of constructing a lantern sufficiently small to make one chamber serve as the lantern and the lamp. He used for his wick two flat cottons parallel to one another, with the tops almost in contact, and the edges of the wicks turned towards the condenser. This lamp he charged with mineral oil, and thus obtained an instrument surpassing anything of the kind previously constructed.

Since then many improvements have been made, each modification receiving a distinctive title. We have thus ‘The Silber Light,’ ‘The Triplexicon,’ ‘The Duplexicon,’ ‘The Refulgent,’ ‘The Euphaneron.’ It will not be necessary to explain each of them in detail, as they have many things in common, and it will suffice to describe ‘The Euphaneron,’ which is perhaps the best of the series.

The Euphaneron (that which shows well) differs in several important particulars from the phantasmagoria lantern. The body of the lantern (which serves to support the condenser and objective) is made of Russian plate iron, which neither rusts nor blisters. The condenser consists of two 4-in. lenses of the form we have already described, and the objective is a double achromatic combination. The outer lens of the objective, designated the ‘front lens,’ is in form a plano-convex lens. The inner lens, called the ‘back lens,’ consists of two separate lenses, one an unequi-convex lens, the other a meniscus-concave lens. This combination gives a beautifully-defined picture on the screen, with flatness of field and abundance of light.

The lamp is entirely distinct from the body, and will burn equally well either outside or inside the body of the lantern, the chimney being attached to the lamp and not to the body. The cistern of the lamp forms its base, and is filled with mineral oil. From the top of the cistern rise two rectangular tubes, sloping together as they rise; these contain the two wicks. The wicks do not stand parallel to each other, but form an acute angle with the base of the triangle towards the condenser, and this is the peculiarity that brings about the equal illumination of the disc. The wicks are raised and depressed by the action of two milled heads at the back of the lamp. Now, instead of surrounding the flames with a glass chimney, as is ordinarily the case, a metal combustion chamber is provided, and to this chamber the chimney is attached. The ends of the chamber are open, the front being closed by a glass plate, the back by a silvered reflector. Attempts have recently been made to add a third wick to this lamp, but they have not been very successful, the lantern being rendered very much hotter without affording a corresponding gain in brilliancy. The Euphaneron exhibits photographic slides in a most satisfactory manner on a disc 10 ft. in diameter. The disc is uniformly illuminated, and the picture well in focus all over the screen.

Directions for trimming the Euphaneron Lamp.—Remove the lamp from the lantern, carefully clean the front glass and the mirror. Turn back the combustion-chamber on its hinge, so as to expose the tops of the wicks. These should be cut quite smooth and straight, without any projecting filaments. The cistern should be nearly filled with the best mineral oil, and the wicks turned up a little way and lit. The combustion chamber should be now restored to its place, the lamp put into the lantern, and the chimney fixed on. The wicks should then be gradually raised as high as they will bear without smoking. In putting the oil into the lamp care should be taken not to spill any on the outside. The general directions already given for showing the pictures are then to be followed in using the Euphaneron.

5.—DISSOLVING VIEWS.

The lanterns that we have hitherto been describing have been those capable of exhibiting single pictures only; we have now to explain the production of dissolving views.

Dissolving views, as the name implies, is an exhibition of pictures in which there is a fading away of one and the appearance of another, as though the one picture grew out of the wreck of the other. To produce these results, two lanterns of similar size are required (see Fig. 4), together with some contrivance for diminishing the light forming the first picture, until that has quite faded away, simultaneously allowing that forming the second picture to fall upon the screen until this one has arrived at its complete intensity, and the first picture is no longer seen. This latter contrivance is known as the mechanical dissolver, and it consists of two serrated plates attached to a movable bar fixed to the front edge of the base upon which the lanterns are supported. These plates come immediately in front of the lanterns, and require to be so arranged that when the whole of the light from one lantern is seen on the screen, the light from the other is entirely stopped. By means of a rack and pinion motion, the plates can be moved simultaneously, and each lantern alternately closed and opened.

In order to make the discs of light produced by the two lanterns coincident, the lanterns must be slightly inclined towards each other.

There is another class of results obtained by the dissolving-views apparatus, which may be designated as the production of ‘composite’ pictures or ‘effects,’ as, for instance, a soldier is seen asleep by the watch-fire, he dreams, and the subjects of his dream appear, one after the other, on the screen, and then fade away. A ship is seen at sea; day turns into night; the moon rises; a violent storm comes on; the lightning flashes, and the ship is set on fire. A water-mill is shown with the stream running and the wheel revolving; a swan appears on the water and moves across the stream; night comes on, the wheel ceases to revolve, and the windows of the house are lit up; clouds flit across the sky; the moon rises—day returns, but the scene has changed to winter; the water is frozen, and its surface occupied by skaters, and a fall of snow takes place.

To produce such effects as these, both lanterns are required to be open at the same time, and the serrated plates forming the dissolver must be so contrived that the one which would otherwise obscure the fixed picture is turned aside, or removed altogether, and therefore only one lantern is alternately opened and closed. The foundation picture (the sleeping soldier, for example) is placed in the lantern that remains constantly open, and to this the addition (the dream) are made with the second lantern.

For dissolving views proper, only two lanterns are required, and for the simpler form of effects two lanterns suffice; but for very complex pictures, three, four, or even five lanterns are required. Any two lanterns of equal size and power may be employed to produce dissolving views; but the phantasmagoria lantern is the smallest that can be advantageously used.

6.—THE LIME-LIGHT.

We have described the typical oil-lit lanterns, and now we shall explain the production of the lime-light in its two principal modifications of the ‘oxycalcium’ and the ‘oxyhydrogen’ light. The lime-light is obtained by intensely heating a piece of lime, in which condition it emits a most brilliant light. The lime is generally used in the form of a cylinder seven-eighths of an inch diameter and one and a quarter inch long, having a hole along its centre from end to end; these cylinders are sold in tin boxes, each containing twelve.

When a box containing lime cylinders has been opened, it is best to transfer the cylinders to a wide-mouth stoppered bottle, and keep the same in a dry place, as moisture causes the lime to crumble to dust. As the lime is only required to furnish some solid material capable of being rendered incandescent, many other substances can be used for this purpose—the best substitute, if lime cannot be obtained, being chalk.

The oxycalcium light requires for its production a large loose flame, a jet of oxygen gas, and a cylinder of lime. The two instruments now to be described—one known as the oxycalcium jet and the other as the oxycalcium lamp—fully realise these conditions, and although accomplishing the purpose in somewhat different ways, each form of instrument possesses some special advantage.

The oxycalcium lamp is represented at Fig. 5, and it consists of a vessel with an aperture in its base, is provided with a valve to close the same when needed, and is capable of holding about a half-pint of spirits of wine. This is called the cistern, and it is placed valve downwards into a second or outer cylinder rather deeper than itself. This operation opens the valve of the cistern, and allows a sufficiency of spirit to flow out so as to fill the space between the bottom of the cistern and the bottom of the outer cylinder. From this outer cylinder proceeds a long horizontal tube, terminating in a small chamber that holds the wick, and it is here that the lamp is lighted.

Behind the wick is a steel pin for holding the cylinder of lime, and in front of the wick is the small end of a bent tube (marked o o), carrying the oxygen gas. This oxygen gas tube passes along the under side of the tube connecting the outer cylinder with the wick chamber, and extending some little distance behind the outer cylinder, there terminates in a tap. This tap is to be connected with the bag containing the oxygen gas by means of a flexible pipe.

In arranging the oxycalcium lamp for use the cistern should be filled with spirits of wine, and the wick cut off smooth. The lime cylinder is to be placed on the support, and the tap o connected with the bag containing the oxygen gas.

A weight equal to about 40 lb. or 50 lb. is to be placed on the bag, and the apparatus is ready for use. The lamp is to be lighted at the wick and the gas admitted by gradually turning the tap at the end of the tube o; the tap attached to the bag having been previously turned fully on. The oxygen gas now issues from the point of the tube in front of the flame and forces the flame against the lime, producing thus the oxycalcium light.

The quantity of gas admitted requires to be regulated to the size of the lamp flame, for if the gas be in excess, the lime will be cooled down and the light diminished. A similar loss of light will result from having too little gas; so that some attention will be required to enable the operator to adjust the apparatus satisfactorily.

The wick should be carefully put into the wick-holder in straight lengths, not twisted together, and not too tightly packed. A slight separation should be made in the top of the wick to allow the stream of gas to pass freely. The point of the jet should be about one-tenth of an inch below the top of the wick, and should not project into the wick. The wick should be kept up close to the point of the jet, and not be allowed to bend towards the lime cylinder.

The spirit to be used with the oxycalcium lamp is to be alcohol or the best methylated spirit; paraffin spirit will not do. It is best to renew the wick each time the lamp is used.

It is now necessary to describe the other form of oxycalcium light—the oxycalcium jet.

The oxycalcium jet is shown at Fig. 6, and it will be seen that the cistern and wick-holder required by the oxycalcium lamp are both dispensed with. There are, instead, two horizontal tubes lying side by side, each having a stopcock at one end, the other end of each tube being turned up, one—the hydrogen tube—at right angles and inserted into the stem of a sort of oblique T-shaped tube. The end of the other horizontal tube—the oxygen tube—is bent into a bow form, so that it may pass through the crosspiece of the oblique T-shaped tube before mentioned. The stopcock of the oxygen tube is to be connected with the bag containing the oxygen gas, and the stopcock of the hydrogen tube is to be attached by a flexible tube to any of the gas-fittings in the room where the apparatus is to be used. By this arrangement a stream of ordinary hydrogen or street gas will pass through the hydrogen tube into the oblique T-shaped tube, and will issue out at its open end, where it is to be lighted. This flame, by the action of the stream of oxygen issuing from the end of the oxygen tube, will be forced against the lime cylinder, and produce, as in the former case, the oxycalcium light. The same attention to the adjustment of the quantity of oxygen gas to the size of the hydrogen flame that was necessary for the oxycalcium lamp is equally needed with the oxycalcium jet, and by means of the two taps this can be managed with the greatest facility. It is usual to drill a hole through the flat part of the key of the oxygen stopcock, so that it may be readily distinguished. It sometimes occurs that the gas-fittings from whence the supply of hydrogen is to be obtained have immovable nipples. In this case it will be found advantageous to connect, by means of a T-piece, two or even more of the nipples with the tube that is to convey the hydrogen to the jet; closing, of course, those that are not thus used.

It is obvious that in using the oxycalcium jet the operator is dependent for his flame upon a supply of the ordinary hydrogen or street gas, and therefore this modification of the oxycalcium apparatus cannot be employed in any place unprovided with the means of obtaining the same. The oxycalcium lamp, on the other hand, as it carries with it the means of producing the required flame, can be used anywhere. The light obtained by the oxycalcium arrangement, although not equal to the oxyhydrogen light, is admirably adapted for exhibitions on a moderate scale, and it requires only one gas-bag.

In both of the oxycalcium arrangements the lime cylinder does not need any alteration of position while in use. The proper distance between the oxygen jet and the surface of the lime varies from one-eighth of an inch to one-quarter of an inch.

7.—OXYHYDROGEN JET.

Having explained the oxycalcium lamp and jet, we have now to describe the oxyhydrogen jet, by which the brightest form of lime-light is produced. The oxyhydrogen jet differs from those previously described in one important particular, viz. that the two gases are mingled together as gases before being ignited. Like the oxycalcium jet, it consists of two tubes lying side by side (see Fig. 7), having a tap at one end of each. The ends of these tubes are inserted into the base of a small chamber, from which proceeds a single curved tube, which rises up in front of the holder upon which the lime cylinder is placed. The end of this tube is contracted by a platinum point screwed into it, and this forms the jet. Two bags are required for this light, one containing hydrogen gas (common house gas will do), and the other bag filled with oxygen gas, and these bags are to be connected with the taps at the end of the jet by means of flexible tubes in the usual manner. The two gases are thus kept separate until they enter the chamber at the base of the curved pipe. This chamber is provided with layers of wire gauze, so as to facilitate the admixture of the gases, which eventually issue thoroughly mingled from the point of the jet. In this condition they are capable of being ignited, and as soon as the flame impinges on the lime cylinder a most intense light results.

The lime-holder of the oxyhydrogen jet is made to slide, so as to be capable of being moved towards or away from the point of the jet. This adjustment is necessary to rectify any slight difference in the diameter of the lime cylinders, for, in order to obtain the full amount of light, the face of the lime cylinder requires to be brought as close to the point of the jet as it can be without being in contact with it. In addition to this movement, the stem on which the lime cylinder is supported is also made to revolve, in order to provide a fresh surface of lime to be presented to the action of the flame. The heating power of the flame of the oxyhydrogen gases is so intense that a cavity is soon burnt in the face of the lime cylinder, and if this part of the cylinder were to be allowed to continue opposite to the jet, the light would be greatly diminished and the general effect marred. To provide against this, the stem of the lime-holder is made with a screw at its lower end, this screw working in a corresponding socket, so that by turning the stem of the lime-holder round on its axis a second motion in a perpendicular direction is also given to it. By this means the face of the lime passes before the point of the jet in a spiral direction, and consequently the same part of the lime cylinder is not brought a second time under the action of the flame. In order to facilitate the rotation of the lime cylinder, the screw is sometimes set in motion by clockwork; but the better plan is to turn the lime by means of a horizontal rod with bevel wheels.

Having described the various forms of apparatus constructed for producing the lime-light by means of oxygen and hydrogen gases, a few general observations will not be out of place. It should be borne in mind that oxygen gas is a supporter of combustion, and is neither explosive nor inflammable. The hydrogen gas will ignite, but will only do so in the presence of oxygen. With the oxycalcium lamp and oxycalcium jet, there is complete safety from explosion. In the oxyhydrogen jet there is also complete safety if care is taken not to fill up the hydrogen-bag with oxygen, and vice versâ. Such an admixture is explosive, and nothing can prevent an explosion when a light is applied. The contents of one bag will not pass into the other during an exhibition, and even if the weights were to fall off the bags, the only effect would be to put the light out.

8.—THE GAS AND GAS-BAGS.

Several times in describing the production of the lime-light reference has been made to gas-bags; and now we will explain more fully what they are. Gas-bags are usually made of stout india-rubber cloth, wedge-shaped, their length being half as much again as their width, and the base usually equal to their width. A tap is provided and attached to the apex of the bag, so as to allow of the admission and expulsion of the gas. In order to press out the gas from a filled bag, two boards are used. These boards are of similar dimensions to the bag, and being hinged together along one edge, can be separated to allow of the introduction of the inflated gas-bag. A projecting ledge is fixed on the outside of the upper board, about eight inches from its end, against which the weight required to press out the gas can rest. The weights should be square-shaped, and the most convenient size is a half-hundredweight. When two bags are required (as in the case of the oxyhydrogen light), the double pressure-board (Fig. 8) should be employed; the two bags are then placed one above the other, and one set of weights only is required instead of two sets. The weight required to be used with a bag of eight feet capacity when employed for the oxycalcium lamp or jet should be about 56 lbs., but at least three times that amount should be placed on the bags for the production of the oxyhydrogen light.