"Beneath the rule of men entirely great THE PEN IS MIGHTIER THAN THE SWORD." About thirty years ago it occurred to the writer that these two epigrammatic sayings--that of Archimedes and that of Bulwer Lytton, might be symbolized in an allegorical drawing which would forcibly express the ideas which they contain, and the question immediately arose--Where will Archimedes get his fulcrum and what can he use as a lever? And the mental answer was: Let the pen be the lever and the printing press the fulcrum, while the sword, used for the same purpose but resting on glory, or in other words, having no substantial fulcrum, breaks in the attempt. The little engraving which, with a new motto, forms a fitting tail-piece to this volume, was the outcome. It is true that the pen is mighty, and in the hands of philosophers and diplomats it accomplishes much, but it is only when resting on the printing press that it is provided with that fulcrum which enables it to raise the world by diffusing knowledge, inculcating morality, and providing pleasure and culture for humanity at large. When assigned to such a task the sword breaks, and well it may. But we have a well-grounded hope that through the influence of the pen and the printing press there will soon come an era of universal [Illustration: Peace on Earth and Good Will Toward Men.] 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