PROPHECIES OF 1881-1885. (Vol. XVII, Dec. 1899.) The prophecies of the years referred are probably those of John Trithemius, Abbot of Spanheim, "Concerning the Seven Secondary Gods, or Intelligences Governing the World," published in 1522. His prophecies point to 1879-1880. They relate to the foundation of a new universal kingdom. There have been several claims as to its fulfillment. Some of the Theosophists claim it is the foundation of the Theosophical Society, in 1875, in New York, and the departure of Madame H. B. Blavatsky and Col. H. S. Olcott for India on December 18, 1878. Some others claim that Trethemius referred to the restoration of the Jews to Palestine. Again, that elaborate, well-planned state of of society," Olombia, or Utopia Made Practical," founded on September 29, 1879, by Dr. William H. Von Swartwout, of New York, has been considered as the desideratum. There is considerable literature on this subject explaining this prophet's calculations. Then there are some books that take a different view of the years 1881-1885, of which we name a few: How the World Came to an End in 1881. London, Anno Domini 1884. Anno Dominæ 3. Great Changes of the Near Future, 1881-1882. By H. S. Oswald. San Francisco, 1878. Superstition, and the Dread Prophecies of 1881-1885. By J. S. Daggett. Albany, 1881. Astronomical Etiology; Star Prophecies. Coming Disasters on the Earth, 1881-1885. By Dr. M. L. Knapp. Chicago, 1878. The Voice of the Stars or the Effect of the Coming Perihelia. 1880-1887. By Prof. C. A. Grimmer. San Jose, 1879. The Coming Catastrophe. Startling Predictions. The Malific Conjunctions Now Ruling the Heavens; 1880. By Prof. C. A. Grimmer. Cambridge, Mass., 1881. "Can there be bliss when all that lives must suffer? Shalt thou be saved and hear the whole world cry?" THE PROBLEMS OF THE THREE BODIES, and the Lights and COURIERS. (Vol. XVIII, p. 16, 1900.) The problem of the three round bodies may be stated thus: When a large central body has two smaller bodies revolving around it, the investigations of the purtabations of the system thus formed is called the "problem of three bodies." Its exact solution is beyond the present powers of mathematical analysis. But when the central body is very large in comparison with the others, as in the case of the sun and planets, a sufficiently close approximation can be made. The problem of the couriers involves distance, motion, and time. The problem is taken from Robinson's "New University Algebra," New York, 1868, page 137, where this correspondent will find a three-page discussion : Two couriers, A and B, were travelling along the same road and in the same direction, namely, from C' toward C; the former going at the rate of a miles per hour, and the latter at the rate of miles per hour. At 12 o'clock, A was at a certain point P, and B was d miles in advance of A, in the direction of C. It is required to find when and where the couriers were together. C' Р d C This problem was originally proposed by Clairaut. A full discussion of it will also be found in Lilley's "Higher Algebra," Boston, 1894, pp. 408-412. The The problem of the lights involve similar algebraical operations and results as to conditions as the courier problem. discussion of this will be found in Hackley's "Treatise on Algebra," New York, 1850, pp. 232-234. To find in a line A B, which joins two lights of different intensities, a point which is illuminated equally by each. P3 A P1 B P2 "The thoughts of God are expressed in nature's language." "Often times the best part of a sermon is the original toxt." QUATERNIONS. A correspondent asks "What are quaternions," and what work to obtain to get an idea of them. We will give an idea of them by quoting from the "Introduction to Quaternions" of Kelland and Tait's work on them. He "The notion of separating addition from multiplication, attributing to the one, motion from a point, to the other motion about a point, had been floating in the minds of mathematicians for half of century, without producing many results worth recording, when the subject fell into the hands of a giant, Sir William Rowan Hamilton, who early found that his road was obstructed, he knew not by what obstacle, so that many points which seemed within his reach were really inaccessible. done a considerable amount of good work, obstructed as he was, when, about the year 1843, he perceived clearly the obstruction to his progress in the shape of an old law which, prior to that time had appeared like a law of common sense. The law in question is known as the 'communitative' law of multiplication. Presented in its simplest form, it is nothing more than this: 'five times three is the same as three times five'; more genererally it appears under the form ' ab=ba, whatever a and b may represent.' When it came distinctly into the mind of Hamilton that this law is not a necessity, with the extended signification of multiplication, he saw his way clear, and gave up the law. The barrier being removed, he entered on the new science as a warrior enters a besieged city through a practical breach." We advise our inquirer to obtain "Elements of Quaternions," by A. S. Hardy. Boston, Mass., 1881, a good work of pp. 230. ARITHMETICAL SYSTEMS. (Vol. XVIII, p. 14.) We will add another arithmetical scheme to those mentioned in the January No., 1900. "The Linn-Base Decimal System," designed for adoption of all civilized nations, by W. Wilberforce Mann. Published in New York, 1871. The one hundred millionth part (100,000,000th) of the quadrant of the earth's meridian, or the one hundred millionth part of the distance of the equator to the pole, is assumed as its unit of linear measure. The Metrical System" established for its standard the ten millionth part of the quadrant. ALANSON. 66 " 'Doing good is divine; wishing good, lukewarm charity." "Behind near-sighted eyes there is often a far-sighted mind." BISHOP WILDERFORCE'S Puzzle. The following ingenious puzzle by Bishop Wilberforce on the different parts of the human body is given not so much for its difficulty as for its curious play upon words and names: All pronounce me a wonderful piece of mechanism, and yet few people have numbered the strange medley of which I am composed. I have a large box and two lids, two caps, two musical instruments, a number of weathercocks, three established measures and a great many little things carpenters cannot do without; then I have about me a couple of esteemed fishers, and a great many of smaller kind; two lofty trees and the fruit of an indigenous plant; a handsome stage and a great number of a smaller kind of game; two halls or places of worship, two students or rather scholars, the stairs of a hotel and a half score of Spanish gentleman to attend on me. I have what is the terror of the slave, also two domestic animals and a number of negatives." THE MEMORY OF PAST BIRTHS. By Charles Johnston, M. R. A. S., Bengal Civil Service, Retired. Price, 25 cents. New York. Metaphysical Publishing Company. 1899. 8vo. Pp. 50. "By reading the title, you have already taken the first step towards remembering, for you have sown in your mind the seed of an idea which will germinate and grow till at last it blossoms into full knowledge. Of those who receive this thought of endless life through many births, most accept it at once through a conviction which runs ahead of evidence; many hold it tentatively with gradually growing credence; none altogether reject or forget it. The thought remains, the seed stirs and grows, and as rebirth is a true law of life, every turn and incident in life gives it a new force, until at last belief ripens into certainty. That certainty of the larger life wherein the lives and deaths of this our world are but as days and nights, lightens the burden of death, dull the age of sorrow, takes away the terror of separation. Immortality, the dearest hope in every human heart, becomes once more credible and intelligible; nay, more, demands and compels our belief. We begin to catch the light of our immortal selves, the gleam from beyond the heavens which shall illumine our hidden past, and, still greater boon, bring the clear vision of the path before us, winding through the mists and shadows of the valley, till it rises at last into the everlasting sunshine."-Preface. HOMER. BY WALTER MALONE. What earthly King who envies not my name? As virile and as vigorous is my fame As when mankind first heard my morning hymn. Cæsar has come, has conquered, passed away; Napoleon shared my sceptre for a day, Then saw the snapping of his cobweb scheme. But I, who living begged my daily bread, I see new poets come to take my place; I said the same three thousand years ago. So Babylon and Nineveh have gone, The dear old gods I knew in ancient days, Of Egypt and Assyria, Greece and Rome, The golden-haired Apollo is no more, But songs I sang him still have power to thrill; Lo, by the everlasting throne of God Sits Gabriel with his trumpet in his hand, Not till that trumpet bids the sun grow black, From The Bookman, December, 1899. Dodd, Mead & Co., New York. |