37 multiplied by 3 gives 111, and 3 times 1 = 3 37 " 6 " 222, " 3 " 2 = 6 37 " 9 " 333, " 3 " 3 = 9 37 " 12 " 444, " 3 " 4 = 12 37 " 15 " 555, " 3 " 5 = 15 37 " 18 " 666, " 3 " 6 = 18 37 " 21 " 777, " 3 " 7 = 21 37 " 24 " 888, " 3 " 8 = 24 37 " 27 " 999, " 3 " 9 = 27 The singular property of numbers the most different, when added, to produce the same sum, originated the use of magical squares for talismans. Although the reason may be accounted for mathematically, yet numerous authors have written concerning them, as though there were something "uncanny" about them. But the most remarkable and exhaustive treatise on the subject is that by a mathematician of Dijon, which is entitled "Traité complet des Carrés magiques, pairs et impairs, simple et composés, à Bordures, Compartiments, Croix, Chassis, Équerres, Bandes détachées, &c.; suivi d'un Traité des Cubes magiques et d'un Essai sur les Cercles magiques; par M. Violle, Géomètre, Chevalier de St. Louis, avec Atlas de 54 grandes Feuilles, comprenant 400 figures." Paris, 1837. 2 vols. 8vo., the first of 593 pages, the second of 616. Price 36 fr. I give three examples of magical squares:-- 2 7 6 9 5 1 4 3 8 These nine ciphers are disposed in three horizontal lines; add the three ciphers of each line, and the sum is 15; add the three ciphers in each column, the sum is 15; add the three ciphers forming diagonals, and the sum is 15. 1 2 3 4 1 7 13 19 25 2 3 2 3 18 24 5 6 12 4 1 4 1 10 11 17 23 4 3 4 1 2 22 3 9 15 16 14 20 21 2 8 The sum is 10. The sum is 65. But the connection of certain numbers with the dogmas of religion was sufficient, besides their marvellous properties, to make superstition attach itself to them. Because there were thirteen at the table when the Last Supper was celebrated, and one of the number betrayed his Master, and then hung himself, it is looked upon through Christendom as unlucky to sit down thirteen at table, the consequence being that one of the number will die before the year is out. "When I see," said Vouvenargues, "men of genius not daring to sit down thirteen at table, there is no error, ancient or modern, which astonishes me." Nine, having been consecrated by Buddhism, is regarded with great veneration by the Moguls and Chinese: the latter bow nine times on entering the presence of their Emperor. Three is sacred among Brahminical and Christian people, because of the Trinity of the Godhead. Pythagoras taught that each number had its own peculiar character, virtue, and properties.