It will be seen that the difficulty arises from each ring passing round the wire of its right-hand neighbor. The extreme ring at the right hand, of course, being unconnected with any other wire than its own, may at any time be drawn off the end of the bow at A, raised up, dropped through the bow, and finally released. After you have done this, try to pass the second ring in the same way, and you will not succeed, as it is obstructed by the wire of the first ring; but if you bring the first ring on again, by reversing the process by which you took it off, viz., by putting it up through the bow, and on to the end of it, you will then find that by taking the first and second rings together, they will both draw off, lift up, and drop through the bow. Having done this, try to pass the third ring off, and you will not be able; because it is fastened on one side to its own wire, which is within the bow, and on the other side to the second ring, which is without the bow. Therefore, leaving the third ring for the present, try the fourth ring, which is now at the end all but one, and both of the wires which affect it being within the bow, you will draw it off without obstruction; and, in doing this, you will have to slip the third ring off, which will not drop through for the reasons before given; so, having dropped the fourth ring through, you can only slip the third ring on again. You will now comprehend that (with the exception of the first ring) the only ring which can at any time be released is that which happens to be second on the bow, at the right-hand end; because both the wires which affect it being within the bow, there will be no impediment to its dropping through. You have now the first and second rings released, and the fourth also—the third still fixed; to release which we must make it last but one on the bow, and to effect which pass the first and second rings together through the bow, and on to it; then release the first ring again by slipping it off and dropping it through, and the third ring will stand as second on the bow, in its proper position for releasing, by drawing the second and third off together, dropping the third through, and slipping the second on again. Now to release the second, put the first up, through and on the bow; then slip the two together off, raise them up, and drop them through. The sixth will now stand second, consequently in its proper place for releasing; therefore draw it toward the end, A, slip the fifth off, then the sixth, and drop it through; after which replace the fifth, as you cannot release it until it stands in the position of a second ring; in order to effect this you must bring the first and second rings together, through and on to the bow; then in order to get the third on, slip the first off and down through the bow; then bring the third up, through and on to the bow; then bring the first ring up and on again, and, releasing the first and second together, bring the fourth through and on to the bow, replacing the third; then bring the first and second together on, drop the first off and through, then the third the same, replace the first on the bow, take off the first and second together, and the fifth will then stand second, as you desired; draw it toward the end, slip it off and through, replace the fourth, bring the first and second together up and on again, release the first, bring on the third, passing the second ring on to the bow again, replace the first, in order to release the first and second together; then bring the fourth toward the end, slipping it off and through, replace the third, bring the first and second together up and on again, release the first, then the third, replacing the second, bring the first up and on, in order to release the first and second together, which having done, your eighth ring will then stand second, consequently you can release it, slipping the seventh on again. Then to release the seventh, you must begin by putting the first and second up and on together, and going through the movements in the same succession as before, until you find you have only the tenth and ninth on the bow; then slip the tenth off and through the bow, and replace the ninth. This dropping of the tenth ring is the first effectual movement toward getting the rings off, as all the changes you have gone through were only to enable you to get at the tenth ring. You will then find that you have only the ninth left on the bow, and you must not be discouraged on learning, that in order to get that ring off, all the others to the right hand must be put on again, beginning by putting the first and second together, and working as before, until you find that the ninth stands as second on the bow, at which time you can release it. You will then have only the eighth left on the bow; you must again put on all the rings to the right hand, beginning by putting up the first and second together, till you find the eighth standing as second on the bow, or in its proper position for releasing; and so you proceed until you find all the rings finally released. As you commence your operations with all the rings ready fixed on the bow, you will release the tenth ring in one hundred and seventy moves; but as you then have only the ninth on, and as it is necessary to bring on again all the rings up to the ninth, in order to release the ninth, and which requires fifteen moves more, you will, consequently, release the ninth ring in two hundred and fifty-six moves; and, for your encouragement, your labor will diminish, by one half, with each following ring which is finally released. The eighth comes off in one hundred and twenty-eight moves, the seventh in sixty-four moves, and so on, until you arrive at the second and first rings, which come off together, making six hundred and eighty-one moves, which are necessary to take off all the rings. With the experience you will by this time have acquired, it is only necessary to say, that to replace the rings, you begin by putting up the first and second together, and follow precisely the same system as before.
46. MOVING THE KNIGHT OVER ALL THE SQUARES ALTERNATELY.
EULER'S METHOD.
The problem respecting the placing the knight on any given square, and moving him from that square to any house on the board, has not been thought unworthy the attention of the first mathematicians. Euler, Ozanam, De Montmart, De Moivre, De Majron, and others, have all given methods by which this feat might be accomplished. It was reserved, however, for the present century to lay this down on a general plan; and the only English writer who has noticed this is Mr. George Walker, in his Treatise on Chess. The plan is this: Let the knight be placed on any square, and move him from square to square, on the principle of always playing him to that point, from which, in actual play, he would command the fewest other squares; observing, that in reckoning the squares commanded by him you must omit such as he has already covered. If, too, there are two squares, on both of which his powers would be equal, you may move him to either. Try this on the board, with some counters or wafers, placing one on every square; and, when you clearly understand it, you may astonish your friends by inviting them to station the knight on any square they like, and engaging to play him, from that square, over the remaining sixty-three in sixty-three moves. When the automaton Chessplayer was last exhibited in England, this was made part of the wonders he accomplished, though as the above plan was not then known here, he could not adopt it, but used something like the method laid down by Euler, and which we subjoin.
Our young Chess-players must remember that it does not matter on which square the knight is placed at starting; as, by acquiring the plan by heart, which is soon done, he can play him over all the squares from any given point, his last square being at the distance of a knight's move from his first. It is obvious that this route may be varied many ways, and we have often amused ourselves by trying to work it on a slate.
ANOTHER METHOD.
The problem of the knight's covering successively each square of the board, has, in all ages, attracted the attention of the first mathematicians; it is only lately, however, that this very ingenious system for performing the feat without seeing the board, has been invented by an Edinburgh gentleman. We well recollect the surprise occasioned among chess-amateurs when it was first performed; indeed it was generally considered a greater mental effort than that of playing three games of chess at the same time, without seeing the board.
The general rule for moving the Knight upon all the squares of the board, is to commence by moving him to that square which commands the fewest points of attack, and by continuing this principle he will occupy all the squares in rotation, observing, that if on any two or more squares his power would be equal, he may be placed indifferently on either of such squares. Thus we see, that there are different routes which the Knight-errant may take in his progress over all the board; still, whichever of these routes for covering the sixty-four squares may be adapted, each move forms, if we may so express ourselves, a link in an endless chain, so that whatever square we start from, by taking one known route, we are sure to arrive at a square, the last link of the chain, a Knight's move distant from the square of our departure. Consequently, if any person could commit to memory the consecutive moves of any one route over the board, he would be able to start from any one square in that route, in the same manner that any of us, if required to mention the numerals up to sixty-four, could as easily start at thirty and end at twenty-nine, as if we started at one and ended at sixty-four.
These considerations greatly reduce the apparent impossibility of performing the feat; but the reader will exclaim, "What an immense undertaking it would be, to commit to memory the moves forming a Knight's route over the sixty-four squares!" and we reply, "Certainly it would be, if we used the language of Chess to designate the squares;" and herein lies the beauty of the invention. A set of names, whose application can be understood at a glance, are invented for the squares, and the performer of the feat, having learned a route of the Knight, expressed by these invented names, thinks in the new language which he directs the moves in the terms of chess—just as many of us think in English, when we are writing or speaking French.
The diagram given above represents the chess-board; the distinction of white and black squares is not necessary for our purpose. The files, commencing from the right hand are distinguished by the consonants in alphabetical succession (C and J are, for obvious reasons, omitted.) Thus, the King's rook's file is known as B, the King's Knight's as D, the King's Bishops as F, the King's as G, the Queen's as H, the Queen's Bishop's as K, the Queen's Knight's as L, and the Queen's Rook's as M. This is all that has to be learned, in this system of Chess notation; for the lines of squares tell their own numbers—one being un, two oo, three ee, four or, six ix, seven en, eight et—being, in fact, the terminal sounds of the first eight numerals. Bun being B one, or King's Rook's square; Gix, G six, or King's sixth square. We consider it quite unnecessary to say another word in explanation of this system; its ingenious simplicity causes it to be understood and learned at a glance. All that is required now is, to select a Knight's route over all the squares of the board, and commit it to memory, not in the complicated terms of Chess, but in these simple equivalents. Suppose we start from the Queen's Knights seventh square, len, the route will be as follows:
Len het fen bet. Dix bor doo gun
Koo mun lee kun. Moo kee goo dun.
Bee div ben fet. Hen let mix lor.
Hee kiv gor hix. Liv men ket gen.
Kix giv fee hor. Gix for hiv gee.
Fiv den biv dee. Bun foo hun loo.
Mor lix met ken. Get fix det bix.
Dor boo fun hoo. Lun mee kor miv
The only trouble is to commit this cabalistical-looking table to memory, which may be all accomplished in half an hour; the process will be greatly facilitated by the learner frequently playing the route over on the chess-board. He will be amply rewarded by the astonishment he will cause to the natives of his locality, who may have the great misfortune of being unacquainted with our book's enlightening pages; and, if not quite a first-rate player, he will acquire an intimate knowledge of the peculiar powers and perplexing peregrinations of the eccentric Caballeros, who
ANOTHER METHOD.
Let Black Queen's Rook's Square count 1, (as in the diagram,) Black King's Rook 8, and count all the other Squares in the same way from 9 to 64. Place the Knight upon Black King's Rook's Square, 8, and move as follows: 23, 40, 55, 61, 51, 57, 42, 25, 10, 4, 14, 24, 39, 56, 62, 52, 58, 41, 26, 9, 3, 13, 7, 22, 32, 47, 64, 54, 60, 50, 33, 18, 1, 11, 5, 15, 21, 6, 16, 31, 48, 63, 53, 59, 49, 34, 17, 2, 12, 27, 44, 38, 28, 43, 37, 20, 35, 45, 30, 36, 18, 29, and 46. It may be well to chalk the figures on the board, as a guide, until the feat is well understood.
47. ROSAMOND'S BOWER.
The subjoined cut represents, it is said, the Maze at Woodstock, in which King Henry placed Fair Rosamond to protect her from the Queen. It certainly is a most ingenious contrivance, and may be made productive of much amusement. The puzzle consists in getting, from one of the numerous outlets, to the bower in the center, without crossing any of the lines.
ROSAMOND'S BOWER.
48. A MAZE OR LABYRINTH.
This maze is a correct ground-plan of one in the gardens of the Palace of Hampton Court. No legendary tale is attached to it, of which we are aware, but its labyrinthine walks occasion much amusement to the numerous holiday parties who frequent the palace grounds. The puzzle is to get into the center, where seats are placed under two lofty trees; and many are the disappointments experienced before the end is attained; and even then, the trouble is not over, it being quite as difficult to get out as to get in.
49. THE CHINESE PUZZLE.
This puzzle, being one for the purpose of constructing different figures by arranging variously-shaped pieces of card or wood in certain ways, requires no separate explanation. Cut out of very stiff cardboard, or thin mahogany, which is decidedly preferable, seven pieces, in shape like the annexed figures and bearing the same proportion to each other; one piece must be made in the shape of figure 1, one of figure 2, and one of figure 3, and two of each of the other figures. The combinations of which these figures are susceptible, are almost infinite; and we subjoin a representation of a few of the most curious. It is to be borne in mind, that all the pieces of which the puzzle consists, must be employed to form each figure.
50. TROUBLE-WIT.
Take a sheet of stiff paper, fold it down the middle of the sheet, longways; then turn down the edge of each fold outward, the breadth of a penny; measure it as it is folded, into three equal parts, with compasses, which make six divisions in the sheet; let each third part be turned outward, and the other, of course, will fall right; then pinch it a quarter of an inch deep, in plaits, like a ruff, so that, when the paper lies pinched in its form, it is in the fashion represented by A; when closed together, it will be like B; unclose it again, shuffle it with each hand, and it will resemble the shuffling of a pack of cards; close it and turn each corner inward with your fore finger and thumb, it will appear as a rosette for a lady's shoe, as C; stretch it forth, and it will resemble a cover for an Italian couch, as D; let go your fore finger at the lower end, and it will resemble a wicket, as E; close it again, and pinch it at the bottom, spreading the top, and it will represent a fan, as F; pinch it half way, and open the top, and it will appear in the form shown by G; hold it in that form, and with the thumb of your left hand turn out the next fold, and it will be as H.
In fact, by a little ingenuity and practice, Trouble-wit may be made to assume an infinite variety of forms, and be productive of very considerable amusement.
1. THE CHINESE CROSS ANSWER.
Place Nos. 1 and 2 close together, as in Fig. 1; then hold them together with the finger and thumb of the left hand horizontally and with the square hole to the right. Push No. 3—placed in the same position facing you (a) in No. 4—through the opening at K, and slide it to the left at A, so that the profile of the pieces should be as in Fig. 2. Now push No. 4 partially through the space from below upwards, as seen in f, Fig. 2. Place No. 5 cross-ways upon the part Y, so that the point R is directed upwards to the right hand side; then push No. 4 quite through, and it will be in the position shown by the dotted lines in Fig. 2. All that now remains is to push No. 6—which is the key—through the opening M and the cross is completed as in Fig. 3.
2. ANSWER TO THE "PARALLELOGRAM."
Divide the piece of card into five steps, and by shifting the position of the pieces, the desired figures may be obtained.
3. THE DIVIDED GARDEN ANSWER.
4. ANSWER TO THE ENDLESS STRING.
The string must be put through the armhole, and over the head, then through the opposite armhole; then the hand must be put up underneath the waistcoat, and the string drawn down around the body until the former drops down about the waist, when the experimenter may jump out of it and claim his coat.
5. ANSWER TO THE CHINESE MAZE.
KOONG-SEE'S WHISPERS.
6. ANSWER TO VERTICAL LINE PUZZLE.
7. THE THREE RABBITS, ANSWER.
8. THE ACCOMMODATING SQUARE.
9. ANSWER TO THE CIRCLE PUZZLE.
Thrust it upwards from the other side.
10. ANSWER TO THE CUT CARD PUZZLE.
Double the cardboard or leather lengthways down the middle, and then cut first to the right, nearly to the end, (the narrow way,) and then to the left, and so on to the end of the card; then open it and cut down the middle, except the two ends. The diagram shows the proper cuttings. By opening the card or leather, a person may pass through it. A laurel leaf may be treated in the same manner.
11. ANSWER TO THE BUTTON PUZZLE.
Draw the narrow slip of the leather through the hole, and the string and buttons may be easily released.
12. ANSWER TO THE QUARTO PUZZLE.
Divide the figure in the direction shown by the lines, and you will have four pieces of the same size and shape.
13. ANSWER TO THE PUZZLE OF FOURTEEN.
14. ANSWER TO THE SQUARE AND CIRCLE PUZZLE.
15. THE SCALE AND RING PUZZLE.
The puzzle consists in releasing the ring; to effect which, you have only to reverse the former process, by passing the loop through the holes D, C, B, and A, in the manner before described.
16. ANSWER TO THE HEART PUZZLE.
Loosen the string, and draw the loop through the hole No. 2; pass it behind, and bring it through No. 1, and slip it over the smaller heart; then the string may be easily drawn out.
17. ANSWER TO THE CROSS PUZZLE.
18. ANSWER 10 THE YANKEE SQUARE.
Arrange the pieces as shown in the figure above.
19. ANSWER TO THE CARD PUZZLE.
In order to take the pipe off, the card must be doubled (as in Fig. 2), the slip passed through it, until there is sufficient of the loop below the pipe to allow one of the square ends of the slip (Fig. 3) being passed through it. Fig. 3 is then to be taken away, and the pipe slipped off. The card for this puzzle must be cut very neatly, the puzzle handled gently, and great care taken that, in doubling the card to put on the pipe no creases are made in it, as they would in all probability spoil your puzzle, by betraying to an acute spectator the mode of operation.
20. ANSWER TO THE THREE SQUARE PUZZLE.
Takeaway the pieces numbered 8, 10, 1, 3, 13, and three squares only will remain.
21. ANSWER TO THE CYLINDER PUZZLE.
Take a round cylinder of the diameter of the circular hole, and of the height of the square hole. Having drawn a straight line across the end, dividing it into two equal parts, cut an equal section from either side to the edge of the circular base, a figure like that represented by the woodcut in the margin would then be produced, which would fulfill the required conditions.
22. ANSWER TO THE FOUR TENANTS.
23. THE PUZZLE WALL.
24. ANSWER TO THE NUN'S PUZZLE.
25. HORSE SHOE PUZZLE.
By cutting off the upper circular part containing two of the pins, and by changing the position of the pieces, another cut will divide the horse shoe into six portions, each containing one pin.
26. ANSWER TO CARD SQUARE PUZZLE.
27. THE DOGS PUZZLE ANSWERED SEE DOTTED LINES.
28. PUZZLE OF THE TWO FATHERS.
The first father divided the land in this way:
The second father divided the land in the following manner:
The different colors represent the several sons' portions.
29. THE TRIANGLE PUZZLE.
The solution of this puzzle may be easily acquired by observing the dotted lines in the engraving; by which it will be seen that four triangles are to be placed at the corners, and a small square made in the center. When this is done, the rest of the square may be quickly formed.
30. ANSWER TO CUTTING OUT A CROSS PUZZLE.
Take a piece of writing paper about three times as long as it is broad, say six inches long and two wide. Fold the upper corner down, as shown in Fig. 1; then fold the other upper corner over the first, and it will appear as in Fig. 2; you next fold the paper in half lengthwise, and it will appear as in Fig. 3. Then the last fold is made lengthwise also, in the middle of the paper, and it will exhibit the form of Fig. 4, which, when cut through with the scissors in the direction of the dotted line, will give all the forms mentioned.
31. ANSWER TO ANOTHER CROSS PUZZLE.
32. ANSWER TO THE FOUNTAIN PUZZLE.
33. ANSWER TO THE STAR PUZZLE.
34. THE COUNTER PUZZLE ANSWER.
Place 4 on 7, 6 on 2, 1 on 3, and 8 on 5; or, 5 on 2, 3 on 7, 8 on 6, 4 on 1, &c.
35. ANSWER TO THE JAPAN SQUARE.
36. ANSWER TO THE CABINET MAKERS' PUZZLE.
The cabinet-maker must find the center of the circle, and strike another circle, half the diameter of the first, and having the same center. Then cut the whole into four parts, by means of two lines drawn at right angles to each other, then cut along the inner circle, and put the pieces together as in the above diagram.
37. ANSWER TO THE STRING AND BALLS PUZZLE.
Draw the loop well down, slipping either ball through it. Push it through the hole at the extremities, pass it over the knot, and draw it through again. The same process must be repeated with the other ball; the loop can then be drawn through the hole in the center, and the ball will slide along the cord until it reaches the other side. The string is then replaced, having both balls on the same side.
There is another and perhaps a neater way of performing this trick. Draw the loop through the central hole, and bring it through far enough to pass one of the balls through. Having done this, draw the string back, and both balls will be found on the same side.
38. ANSWER TO THE DOUBLE-HEADED PUZZLE.
Arrange them side by side in the short arms of the cross, draw out the center piece, and the rest will follow easily. The reversal of the same process will put them back again.
39. ARITHMETICAL PUZZLE.
The four figures are 8888, which being divided by a line drawn through the middle, become 0000/0000, the sum of which is eight 0s, or nothing.
40. GRAMMATICAL PUZZLE.
Take away L in the subjunctive "Let" at the beginning of the first line, and substitute S, and so turn it into the imperative "Set," when the changes which necessarily follow will be immediately apparent.
41. ANSWER TO THE TREE PUZZLE.
42. ANSWER TO AN EPITAPH ON ELLINOR BACHELLOR, AN OLD PIE WOMAN.
43. ANSWER TO A CURIOUS LETTER.
"Sir, between friends, I understand your overbearing disposition; a man even with the world is above contempt, whilst the ambitious are beneath ridicule."
44. ANSWER TO THE PUZZLE INSCRIPTION.
By the use of the single vowel E, the following couplet was formed,
An almost endless source of amusement, combining at the same time a considerable amount of instruction, may be obtained in the following manner. Take a card or piece of pasteboard, or even stiff paper, and draw upon it the form of an egg—an oval in outline. The dimensions of the oval are immaterial, and the experimenter may suit his own fancy in this respect. With a stout needle, or tracing point, prick quite through the outline, for the purposes of tracing. Some of our readers may be unacquainted with the mode of tracing an outline, and it may be advisable to particularize one method among many. Having pricked out the oval upon the card, get a little red or black lead, powdered, and placing the card upon apiece of drawing paper—any white paper will however do—rub it over the pricked-out oval, which will be found to be transferred to the white paper beneath, thus:
The powder may be applied either with a piece of wool or wadding, or by means of a dry camel's-hair pencil; care should be taken not to let the tracing-powder get beyond the edge of the pricked card, as in that case a soiled, dirty appearance is given to the tracing. The pierced card will serve, if carefully done, for hundreds of tracings, and it is obviously the best plan to take a little extra pains with that in the first instance.
With this traced oval for a basis, (a little further on we shall speak of other figures, to be used singly or in combination with each other) any one with a very little skill will be able to form an infinite number of objects.
The best drawing tool will be found to be an ordinary black lead pencil.
Figs. 1, 2, 3, 4, 5, 6 are very easy results, suggestive also of others. The rules of procedure are the same in all. Leaving the traced-out oval at first in its dotted form, with the pencil you draw a horizontal line as the basis of your figure. Let this and the other lines, which serve merely as the scaffolding of your figure, be done faintly or in dots. Next, draw a line through the center of the oval and perpendicular to the first. These will ensure your making the object square and properly balanced. After this you may draw lines parallel to the others: but these are not so material, although they serve as guides.
Now the imagination and fancy may step in to produce forms having the oval for a foundation; and not only is a very rational source of amusement opened out, but the opportunity is given to a cultivation of the noble art of design, whether as applied to utility or ornament.
It is obvious to remark that the hand of many an amateur artist will readily be able to form the oval without having recourse to the pierced card; but as this portion of our work is intended for all, we have suggested the above mode as sure to succeed under every circumstance.
Following the same plan in every particular, we subjoin some examples of what may be done with the square.
The dotted lines (figs. 7, 8) represent the traced or sketched square and plan lines; the firmer lines suggest objects formed upon that figure. In the same way the thin square outline (fig. 9) suggests the inner sketch of a church.
I stated before that the size of the fundamental oval or square made little difference; but I would recommend my younger readers to get these as large as possible, or convenient. If a large black board, such as is used in most schools, could be obtained, and the tracings prepared proportionably large (pounded chalk being used instead of the black or red powder in transferring the forms thereto), and the designs made upon these with a piece of chalk, so much the better. However, this matters little; and each one will suit his or her own taste in that respect. I now proceed to submit some examples of what may be done with other rudimentary forms.
Following the instructions previously given, in place of the square suggested in Figs. 7, 8, 9, describe a circle. This may be done with a pair of compasses, or simply sketched or traced by means of any round object, such as a coin laid flat upon the paper. Figs. 10, 11, 12, 13, 14, 15, are given merely as suggestions, the circle forming an important part of their figure. The mind of the experimenter will immediately revert to other objects—thousands such are to be met with around us—having the circle or the sphere for their basis. And it will be no mean result of my labors, if any number of my younger readers are led thereby to a habit of observation, whereby they will not fail to notice that nearly all natural objects have the curved line for a basis, if they are not actually distinguishable thereby from those that are artificial.
Fig. 16 is drawn upon two circles in combination with each other. The dotted lines of the plan will be readily perceived; but lest there should be any difficulty, they have been drawn separately in Fig. 17. With this duplex figure little skill will be required to present the lord of the farm yard. The three outlines, Figs. 18, 19, 20, are based upon the square turned diamond-wise, and will need no further remark: examples upon this plan may be multiplied easily. Those given will serve as hints in the several directions of flowers, foliage, and landscapes generally.
Before proceeding to show what may easily be done by a simple combination of the figures we have constructed, i. e., the oval, square, and circle, let me introduce another, which enters, by a kind of natural law, into almost all forms or groups of forms, namely, the triangle. Observe in the annexed cut, Fig. 21, how naturally, although unconsciously, the girl seats herself within one.
A moment's reflection will show, that from the little nymph in the cut to the great pyramid, everything that rests solidly upon the earth must take the form, more or less, of this broad-based tapering figure. Roofs of houses, churches, and towers, are all triangular in their form, as are all great trees, differing from each other only in the width of their angles.
Construct a triangle,[14] and trace it according to former directions, and from the examples, Figs. 22, 23, 24, look around you for others, and make various exercises upon this foundation.
Now, to proceed to something more complicated. Suppose you had either in your mind, or sketched out upon paper, the plan of a garden; that is to say, suppose you had the dimensions of a piece of ground, and intended to lay it out as a garden, allotting so much space to this and that bed, so much to gravel walks, and wanted to see how such an arrangement would look in perspective,—in other words, in reality, for perspective, however alarming it may look in books, with its net-work of lines, cross and across, like an insoluble riddle or a monster cobweb, is nothing more than the actual representation of things as they meet the eye.