Page:The New International Encyclopædia 1st ed. v. 12.djvu/760

MAGIC LANTERN. 678 MAGIC SQUARE. ing film, on whitli liave been photographed a series of piutiires taken iu quick sueeession. As the successive images follow each other on the screen more rapidly than the eye is able to re- ceive the sejiarate and distinct impressions, they accordingly blend into each other and the effect of moving pictures is produced. MAGIC MIRROR OF JAPAN. A few of the small, round mirrors used by the Japanese have the property of retlecting light to a screen or other surface so as to form images correspond- ing to the ornamental designs on their backs. As these mirnns do not differ in appearance from those that do not furnish such images, thoy have been termed magic mirrors, and their pecu- liar property furnished an interesting problem to scientists for a number of years. The Japan- ese hand mirrors in general are made of bronze, more or less convex ou their reflecting side, with a polished surface of mercurial amalgam, and have on their back ornamented figures, such as flowers, dragons, and similar patterns. Professors Ayrton and Terry ascertained that there were certain portions of the retlecting surfaces corre- sponding to the designs on the back, which were more worn away in the covirse of polishing and thus became concave, or at least less convex than the rest of the surface. This circumstance, which results from a mere accident in the process of manufacture, served to explain the formation of the briglit images on a dark ground when the mirror was used to reflect light to a surface. The magic mirrors, which are extremely valu- able, have been produced in England by following this prineijile. See Thompson. Lirjht Msihlc and Iiiiisihic (Xew York, 1897) : and Proceed iiMix of the Roiial Society of London, vol. xxviii. (Lon- don, 1879). MAGICO PRODIGIOSO, ma'Hl-ko pro'di-ni- o'su. El. One of the most striking plaj's of Calderon. The theme is the contest between good and evil. Cypriano is tempted by Satan, the re- ward being the possession of a woman. But when the prize is finally delivered to him it turns into a skeleton in Cypriano's arms. MAGIC SQUARE. A term applied to square arrays of numbers possessing the property that the sums of the various columns and rows, and of the two diagonals, are equal. In Fig. 1 this sum is 34. This square (the earliest known in Europe! was represented in Diirer's copperplate entitled Mrlancholia. The origin of magic squares is generally ascribed to India, although with- out an_y strict proof. A magic square is found on one of the gates of the fortifications, in the Sanskrit characters, in the East Indian city of (Jwaloir, but its " an- tiquity is not sneh as to justify the assump- tion of Hindu oriirin. Magic squares were, however, certainlv known to the Arab astrologers, who claimed itor them a peculiar supernatural power and recommend- ed them as talismans and amulets. A similar power is attributed to them to-dav among the Hindus and to some extent in Europe. There are various methods for construetin" magic squares of an odd number of cells. One o~f 1 14 15 4 12 7 6 9 8 11 10 5 13 2 3 16 Fig. 1. the oldest of which we have any knowledge is described by De la Loub&rc in his work Du royaume dc Siam (1691), and by him ascribed to the Hin- dus of Surat. The rule is as follows: Write 1 in the middle cell of the top row, 2 in the first cell to the right of the mid- dle of the bottom row, then following the diagonal to the right until the right hand margin is reached; then go to the row above and take the left-hand cell, and again fol- low the diagonal upward to the right, and when the upper margin is reached, go to the lowest row and one cell to the right. If progress is barre<l by a filled cell, go one cell down from the last number written and proceed as before. (See Fig. 2.) Another well-known method for an odd 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 Fig. 2. 5 4 10 3 9 15 2 8 14 20 1 7 13 19 25 6 12 18 24 . ' 11 17 23 16 22 21 number of cells, due to Bachet de Meziriac (see Baciiet), is as follows: Take, for example, 25 cells. Arrange and number them as in Fig. 3. Then slide the outside cells to the sides opposite those on which they rest, thus filling all cell':, as Fig. 4. It is not so simple to construct magic squares with even numbers of cells. The following method is, however, not particularly difficult. Suppose 3 16 9 22 15 20 8 21 14 2 7 25 13 1 19 24 12 5 18 6 11 4 17 10 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Fig. 5. Fig. 4. the cells are filled, in the first place, with the numbers arranged in the natural order, as in Fig. 5. I