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Image from page 253 of “Mathematical recreations and essays” (1920)

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Identifier: mathematicalrecr1920ball
Title: Mathematical recreations and essays
Year: 1920 (1920s)
Authors: Ball, W. W. Rouse (Walter William Rouse), 1850-1925
Subjects: Mathematical recreations Geometry Astrology Space and time Matter Magic squares
Publisher: London, Macmillan
Contributing Library: Harold B. Lee Library
Digitizing Sponsor: Brigham Young University

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more elaborate toy, knownas Chinese Rings, which is on sale in most English toy-shops, * La Nature, Paris, 1884, part i, pp. 285—286. t It was described by Cardan in 1550 in his De Subtilitate, bk. xv,paragraph 2, ed. Sponius, vol. in, p. 587; by Wallis in his Algebra, Latin edition,1693, Opera, vol. ii, chap, cxi, pp. 472—478; and allusion is made to it alsoin Ozanams Recreations, 1723 edition, vol. iv, p, 439. 230 MISCELLANEOUS PROBLEMS [CH. XI is represented in the accompanying figure. It consists of anumber of rings hung upon a bar in such a manner that thering at one end (say A) can be taken off or put on the barat pleasure; but any other ring can be taken off or put ononly when the one next to it towards A is on, and all therest towards A are off the bar. The order of the rings cannotbe changed. Only one ring can be taken off or put on at a time. [Inthe toy, as usually sold, the first two rings form an exceptionto the rule. Both these can be taken off or put on together. Cxg

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To simplify the discussion I shall assume at first that only onering is taken off or put on at a time.] I proceed to show that,if there are n rings, then in order to disconnect them from thebar, it will be necessary to take a ring off or to put a ring oneither J (2**+^— 1) times or J (2^+^ — 2) times according as n isodd or even. Let the taking a ring off the bar or putting a ring on thebar be called a step. It is usual to number the rings from thefree end A. Let us suppose that we commence with the firstm rings off the bar and all the rest on the bar; and supposethat then it requires x—1 steps to take off the next ring,that is, it requires x—1 additional steps to arrange the ringsso that the first m +1 of them are off the bar and all therest are on it. Before taking these steps we can take off CH. Xl] MISCELLANEOUS PROBLEMS 231 the (m 4- 2)th ring and thus it will require x steps from ourinitial position to remove the (m + l)th and {m + 2)th rings. Suppose that these x steps

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Image from page 375 of “Mathematical recreations and essays” (1920)

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Identifier: mathematicalrecr1920ball
Title: Mathematical recreations and essays
Year: 1920 (1920s)
Authors: Ball, W. W. Rouse (Walter William Rouse), 1850-1925
Subjects: Mathematical recreations Geometry Astrology Space and time Matter Magic squares
Publisher: London, Macmillan
Contributing Library: Harold B. Lee Library
Digitizing Sponsor: Brigham Young University

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About This Book: Catalog Entry
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theloop. There are now two dorsal strings and one palmar string on the righthand. Third. P puts a similar loop on the left hand by bending it overoutside the radial string and up into the space between the hands. Lastly.P with the back of the right middle-finger takes up from the proximal side {i.e.from below) the left palmar string. And then similarly with the back of theleft middle-finger takes up from the proximal side that part of the right palmar 352 STRING FIGURES [CH. XVIII string which lies across the base of the right middle-finger. The hands arenow drawn apart so as to make the strings taut. The figure known as Snuffer-Trays—^eo. figure ii—ie formedby six loops, three on each hand. Four of the strings crossdiamond-wise in the middle so as to form two side crosses andtwo end crosses, the other two strings are straight, one beingnear and the other far. All the strings lie in a horizontalplane. This figure is also known as Soldiers Bed, the GhurchWindow, and the Fish-Pond.

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Figure ii. Snuffer-Trays. Snuffer-Trays can be got from the Cradle thus. I suppose that the Cradleis held by one operator, P, and that the other operator, Q, faces P. First.Q inserts the thumb and index-finger of his left hand from his far side in thoseangles of the cross of the Cradle farthest from him which lie towards Ps hands.Similarly Q inserts the thumb and index-finger of his right hand from his nearside in those angles of the cross nearest to him which lie towards Ps hands,both thumbs being towards Ps right hand, and his index-fingers towards Psleft hand. Second. Q takes hold of each cross by the tips of the thumb andfinger, then pulls each cross outwards {i.e. away from the centre of the figure)over and beyond the corresponding horizontal string, then down, and thenround the corresponding horizontal strings. Third. Q turns the thumbs andfingers upwards through a right angle, thus passing the cross up between thetwo horizontal strings. By this motion the thumb and index-finger

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Image from page 32 of “The sage’s key to character at sight; special student’s course” (1919)

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Identifier: sageskeytocharac00orms
Title: The sage’s key to character at sight; special student’s course
Year: 1919 (1910s)
Authors: Ormsby, Frank Earl. [from old catalog]
Subjects: Astrology Characters and characteristics
Publisher: Chicago, Pyramid-cube university
Contributing Library: The Library of Congress
Digitizing Sponsor: The Library of Congress

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position of book-keeper, librarian, literary and stenographicwork; teaching, nursing, demonstrating special products;soliciting and introducing various utilities in homes, shoosand offices. Activity on the feet makes for a restless life,and for this reason the employment should be changeable. HEALTH—Your feet are the sensitive region of yourbeing, and these require careful attention to keep them freefrom some one or other aggravation. Soap, water and oiland a good barefoot romp in the wet mud, dewy grass andin the hot sands, is the best in the way of simple treatment.The tissues should be kept soft. CO-ORDINATIONS—In business, marriage and sociallife, you blend more favorably with those born in the signsTaurus, Cancer, Virgo, Scorpio, and Capricornus. Your Astral gem or birth-stone is the pearl, the gem ofthe deeps. Your aura of being is reflective of the deeps offeeling and emotion, hence, your appearance is enhanced bydecorations in harmony with the pearl. CHARACTER AT SIGHT Zf)

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Rising Sign After considering the INDIVIDUALITY, as shown bythe sign of birth, take the hour or the time of day and locatethe sign of the East, the Rising Sign and incorporate itsmeaning in the continuation of the delineation. For ex-ample: take the figure and date January first. Cancer isthe sign of birth, of Individuality, and the rising sign beingLibra> it shows the form, height, weight, complexion, colorof hair and eyes, general appearance, and tendencies of themind toward vocational en.deavor. The following delinea-tions of the Rising signs relate to PERSONALITY, thesurface appearance and expression of Individuality. To illustrate the composition and connection of the twofeatures of the reading, suppose one is born in the sign Aries,between September 22 and October 23, and the sign rising isfound to be Leo. First read the Individuality from Ariesand add the Personality reading Leo- This would show acharacter with the head and heart, the mental and emotionalqualities blended to

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