INDEX

Absurdities in perpetual motion, 42

Accuracy of modern methods of squaring the circle, 17

Adams, perpetual motion, 71

Ahaz, dial of, 133

Air, liquid, 65

Alkahest, or universal solvent, 104

Altar of Apollo, 30

Angelo, Michael, finely engraved seal, 136

Angle, Trisection of, 33

Apollo, Altar of, 30

Approximations to ratio of diameter to circumference of circle, 17 De Morgan's Illustration of, 18 New Illustration of, 19

Archimedean screw, 49

Archimedes, area of circle, 13 Ratio of circumference to diameter, 14

Archimedes and his fulcrum, 171

Arithmetic of the ancients, 15

Arithmetical problems, 163 Chess-board problem, 163 Nail problem, 164 A question of population, 165 How to become a millionaire, 166 Cost of first folio Shakespeare, 168 Arithmetical puzzles, 170 Archimedes and his fulcrum, 171

Army Medical Museum, 142

Ball, Prof. W. W. R., 39, 129, 133, 134

Balloons for conveying letters, 147

Balls—proportion of weight to diameter, 32

Bean, jumping, 128

Bells kept ringing for eight years, 41

Bible in walnut shell, 136

Bible, written at rate of 22 to square inch, 141

Boat-race without oars, 129

Bolognian phosphorus, 102

Boots—lifting oneself by straps of, 128

Boyle and palingenesy, 107

Bramwell, Sir Frederick, 38

Brick, to look through, 151

Buckle and geometrical lines, 119

"Budget of Paradoxes," De Morgan, 6, 18, 118

Carbon bisulphide for perpetual motion, 67

Capillary attraction, 53

Carpenter, Edward—fourth dimension, 122

Catherine II, 118

"Century of Inventions," 74

Chess-board problem, 163

Child lifting two horses, 131 Perpetual motion by a, 64

Circle, squaring the, 9 Supposed reward for squaring the, 9 Resolution of Royal Academy of Sciences on, 10 What the problem is, 12 Approximation to, by Archimedes, 14 Jews, ratio accepted by, 13 Egyptians, ratio accepted by, 14 Symbol for ratio introduced by Euler, 14 Graphical approximations, 22

Circumference of circle, to find, when diameter is given, 22

Clock that requires no winding, 38

Columbia College seal, 140

Column of De Luc, 40

Compass, watch used as a, 134

Congreve, Sir William, 53

Cube, duplication of, 38

Crystallization seen by microscope, 108 Mistaken for palingenesy, 100

Dancer—microphotographs, 144

Dangerous, fascination of the, 1

Declaration of Independence, 145

De Luc's column, 40

De Morgan—Legend of Michael Scott, 6 Ignorance v. learning, 8 Illustration of accuracy of modern attempts to square the circle, 18 "Budget of Paradoxes," 6, 18 Trisection of angle, 34, 118 On powder of sympathy, 112 Anecdote of Diderot, 118

Dial of Ahaz, 133

Diderot, anecdote of, 118

Digby, Sir Kenelm, and palingenesy, 109 Sir Kenelm and powder of sympathy, 111

Dircks, 56, 71, 75

Discoveries, valuable, not due to perpetual-motion-mongers, 36

Duplication of the cube, 30

Elixir of life, 95

Engineering, insect, 130

Euler, 14, 118

Fallacies in perpetual motion, 65

Falstaff and the philosopher's stone, 97

Faraday's discovery, 93

Farrants, Prest. Royal Mic. Soc, 140

Figure, a, enlarged by cutting, 126

First folio Shakespeare, cost of, 168

Fixation of mercury, 92

Follies of Science, The Seven, 2 D'Israeli's list, 2 An inappropriate term, 3

Fourth dimension—conception of, 117 Flatland, 120 Kant and Gauss, 121 Spiritualists, 121 Edward Carpenter on, 122 Possibility of a new sense, 123

Frauds in perpetual motion, 69

Freezing of mercury, 93

Froment, micrographs, 139

Gases, liquefaction of, 93

Geiser's clock, 71

Geometrical quadrature impossible, 21

Gibberish, origin of word, 96

God, demonstration of existence of, 118

Hammer made of solid mercury, 93

Hand, to look through, 156

Heat and cold, illusions, 150

Hesse, Landgrave of, 77

Hindoos, ratio accepted by, 16

Holmes, O. W., and powder of sympathy, 111

Homer's Iliad in nutshell, 136

Honecourt, Wilars de, 42

Horses lifted by child, 131

Hydrofluoric acid, 104

Hydrostatic paradox, 46

Iliad of Homer in nutshell, 136

Impossible, fascination of the, 1

Insect engineering, 130

Irradiation, 152

Jews, ratio accepted by the, 13

Keeley gold cure, 97

Keeley motor, 69

Kircher and palingenesy, 106

Lacomme, on squaring circle, 27

Lamps, ever-burning, 100

Library, Congressional, in hand-bag, 145

Light from electric earth-currents, 103

Lines, geometrical, 119

Lines, direction of, deceptive, 154 Length of, deceptive, 153

Liquid air, 65

Lodge, Sir Oliver, on conservation of energy, 5

Longitude, relation of squaring the circle to, 10

McArthur, on arithmetic of ancients, 15

Machin, 16

Magnetism for perpetual motion, 61

Man lifting himself, 128

Mathematicians—how they go to heaven, 8

Mercury, fixation of, 92 Freezing of, 93

Metals. See Transmutation.

Metius, Peter, 16

Micrography, or minute writing, 136 Homer in a nutshell, 136 Michael Angelo's seal, 136 Ten Commandments, 136 Bible in a nutshell, 136 Earliest micrographic engraving, 139 Micrographic copy of seal of Columbia College, 139 Peters' machine, 141 Lord's Prayer written at rate of 22 Bibles to square inch, 141 Webb's fine writing, 142 Calculation in regard to, 143 Microphotographs by Dancer, 144 Pigeon-post in Franco-Prussian War, 146

Millionaire, to become a, 166

Miracle—dial of Ahaz, 133

Morgan. See De Morgan.

Morton, President Henry, 66

Motion, perpetual. See Perpetual motion.

Muir, Prof. On Archimedes, 14

Musitanus, Carolus, 96

Nail problem, 164

Nicomedean line, 29

Orffyreus—his real name, 77 His fraudulent machine, 77

Overbalancing wheels, 43

Paint, luminous, 102

Palingenesy, 106

Patent office U. S. and perpetual motion, 42

Pen mightier than the sword, 173

Perpetual lamps, 100

Perpetual motion, 36 What the problem is, 37 Clock that requires no winding, 38 Watch wound by walking, 39 Clock wound by tides, 41 By electricity, 41 Absurdities, 42 Overbalancing wheels, 43 Dr. Young, on, 44 Bellows action, 45 Hydrostatic paradox, 46 Bishop Wilkins, 48 Archimedean screw, 49 Archimedean screw, by mercury, 51 Congreve's, by capillary attraction, 53 Tube and balls, 56 Tube and rope, 59 Magnetism, 61 Self-moving railway carriage, 63 A child's perpetual motion, 64 Fallacies, 65 Liquid air, 65 Bisulphide of carbon, 66 Frauds, 69 Keeley motor, 69 Geiser's clock, 71 Adams, 71 Redhoeffer, 72 Lukens, 72 How to stop the machine, 73 Marquis of Worcester, 74 Dircks' model, 75 Orffyreus, 77 Possibility of, 78

Peters' micrographs, 141

Philosopher's stone, 97

Phosphorus, discovery of, 101

Pigeon-post, 146

Population, a question of, 165

Power, the, of the future, 40

Ptolemy, on the circle, 15

Puzzles, arithmetical, 170

Railway carriage, self-moving, 63

Ramsay, Sir William, 80, 98

Ratio of diameter to circumference carried to 127 places, 17

Redhoeffer's perpetual motion, 72

Rosicrucius, 100

Rutherford, 16

Schott, Father, and palingenesy, 107

Schweirs, Dr., 52

Scott, Michael, and his slave demons, 6

Scott, Sir Walter, legend of the great Wizard, 6 Powder of sympathy, 112

Self-moving railway carriage, 63

Senses—illusions of, 148 Taste and smell, 149 Heat and cold, 150 Hearing, 150 Touch, 150 Sight—size of spot, 152 Length of lines, 153 Direction of lines, 154 Objects seen through hand, 156 Looking through a brick, 158

Sense, possibility of a new, 123

Shadow going backward on dial, 133

Shakespeare, cost of first folio, 168 Philosopher's stone, 97 Witchcraft, 114

Shanks—value of ratio carried to 707 places, 16

Sharp, Abraham, 16

Sight, sense of, deceived, 152

Smith, James, on squaring circle, 28

Snake lifted by spider, 130

Solvent, universal, 104

Space enlarged by cutting, 126

Spider lifting a snake, 130

Sun-dial—shadow going backward, 133

Taste and smell—illusions, 149

Tides, clock moved by, 40 Will be the great source of power of the future, 40

Time it would take Archimedes to move the world, 171

Touch, sense of, deceived, 150

Transmutation of the metals, 79 Ancient fables, 79 Hermes Trismegistus, 80 Treatises not allegorical, 81 Seven metals, 82 Metals named after planets, 82 Methods of cheating, 83 "Brief of the Golden Calf," 84 Story of unknown Italian, 87 Possibility of effecting, 88 Sir William Ramsay, 89 Effect of such discovery on our currency system, 90

"Tribune," New York, 29

Trisection of angle, 33

Tube and balls, 56

Tube and rope, 59

Universal medicine. See Elixir of Life.

Van Ceulen, Rudolph, 16

Wallich, Dr., 35

Watch that is wound by walking, 39 Used as a compass, 134

Webb micrographs, 142

Whewell's refutation of 31⁄8 ratio, 28

Wilkins, Bishop, 48

Witchcraft or magic, 113

Worcester, Marquis of, 74

Writing, fine, 139

Young, Dr. Thomas, 44

Transcriber's Note: Minor spelling and typographical errors have been corrected without note.