M A G M A 213 own plane ;. and iu this way a cow fur instance can be represented drinking, or a donkey cutting amusing capers. A lever slide is represented in fig. 6. In the chromatrope FIG. 6. Lever Slide. slide (fig. 7) two circular disks of glass are placed face to face, each containing a design radiating from the centre, and painted with brilliant transparent colours. By a small pinion gearing in toothed wheels or endless bands the disks are made to move in opposite directions in their own plane. I The effect produced is a singularly beautiful change of design and colour. In astronomical slides the motions of the heavenly bodies, eclipses, the phases of the moon, or the like are similarly represented by mechanical means. Slides can also be made from narrow glass tanks with parallel sides. When these are filled with water contain ing delicate living organisms the forms and movements of the latter are beautifully seen. Such tanks can also be employed to show such phenomena as the gradual growth of crystals, the electrolysis of water between platinum electrodes, <fec. A great variety of physical and chemical experiments can be shown in this way. Dissolving Views. For this purpose two magic lanterns arc necessary, arranged either side by side or the one on the top of the other. The fronts of the lanterns are slightly inclined to each other so as to make the illuminated disks on the screen due to each lantern coincide. By means of a pair of thin metallic shutters terminating in comb-like teeth, and movable by a rack or lever, the light from either lantern can be gradually cut off at the same time that the light from the other is allowed gradually to fall on the screen. In this way one view appears to melt or dissolve into another. This arrangement was first adopted by Childe in 1811. Phantasmagoria. In this arrangement the pictures on the screen Appear gradually to increase or diminish in size and brightness. To < flect this a semi-transparent screen of cotton or other material is used, the lantern being behind and the audience in front. The lantern is mounted on wheels so that it can be rapidly moved up to or withdrawn from the screen ; and an automatic arrangement is provided whereby simultaneously with this the objective is made to approach or recede from the slide so as to focus the picture on the screen in any position of the lantern. In this way a very small picture appears gradually to grow to enormous dimensions. Lantern Polariscope.This, perhaps the most beautiful modifica tion of the magic lantern for scientific purposes, consists of an elbow- shaped tube, containing mirrors, lenses, &c., and attached to the front of the lantern in place of the tube containing the objective. It is represented in section in iig. 8. C is the usual coiidenser belonging to the lantern. G is a set of thin glass plates inclined at the polarizing angle 56 45 to the axis of the tube. Tiie beam of polarized light from L reflected from G passes through the lenses Fio. 8. Lantern Polariscope. F and the analysing Nicol s prism P, and falls on the screen. The objects to be examined by the polarized light are placed in the transverse slit 0. When thin plates of selenite or other doubly refracting crystals are placed in 0, a most beautiful display of com plementary colours is produced on the screen by rotating the Nicol s prism. Almost all the experiments on polarized light can be well shown by this arrangement. The sciopticon (tig. 3) is an excellent and convenient lantern, very suitable for all the requirements of the lecturer, as well as for school use in teaching geography, &c. See Brewster s Optics Ganofs Physics ; and Chadwick s Manual of the Mag-.e Lantern. ( j. BL .) MAGIC SQUARE. A magic square is one divided into any number of equal squares, like a chess-board, in each of which is placed one of a series of consecutive numbers from 1 up to the square of the number of cells in a side, in such a manner that the sum of those in ths same row or column and in each of the two diagonals is constant. From a very early period these squares engaged the attention of mathematicians, especially such as possessed a love of the marvellous, or sought to win for themselves a superstitious regard. They were then supposed to possess magical properties, and were worn, as in India at the present day, engraven in metal or stone, as amulets or talismans. According to the mystic imaginings of the old astrologers relations subsisted between these squares and the planets : a square with only one cell, containing 1, symbolized the unity of the deity; a square of two, containing the four elements, was the symbol of matter; while those of 3, 4, 5, 6, 7, 8 were consecrated respect ively to Saturn, Jupiter, Mars, the Sun, Venus, and Mercury. In later times such squares ranked only as mathematical curiosities ; till at last their mode of con struction was systematically investigated. These squares were at first mere triumphs of the same dogged persever ance as was in later times exhibited by the Dutchman, Ludolph van Ceulen, who, after calculating ?r to 35 places of decimals, directed, like Archimedes, that it should be engraven on his tomb, though his industry was surpassed by M. de Lagry, who continued the decimal to 127 places. The earliest known writer on the subject was Emanuel Moscopulus, a Greek, who lived in the 4th or 5th century, and whose manuscript is preserved in the National Library at Paris. After him Frenicle constructed magic squares, such that if one or more of the encircling bands of numbers be taken away the remaining central squares are still magical. Subsequently M. Poignard constructed squares with numbers in arithmetical progression, having the magical summations. The later researches of M. de la Hire, recorded in the Memoires de i Academic Eoyale in
1705, are interesting as giving general methods of con-