In the following pages I have endeavored to give a simple account of problems which have occupied the attention of the human mind ever since the dawn of civilization, and which can never lose their interest until time shall be no more. While to most persons these subjects will have but an historical interest, yet even from this point of view they are of more value than the history of empires, for they are the intellectual battlefields upon which much of our progress in science has been won. To a few, however, some of them may be of actual practical importance, for although the schoolmaster has been abroad for these many years, it is an unfortunate fact that the circle-squarer and the perpetual-motion-seeker have not ceased out of the land.

In these days of almost miraculous progress it is difficult to realize that there may be such a thing as a scientific impossibility. I have therefore endeavored to point out where the line must be drawn, and by way of illustration I have added a few curious paradoxes and marvels, some of which show apparent contradictions to known laws of nature, but which are all simply and easily explained when we understand the fundamental principles which govern each case.

In presenting the various subjects which are here discussed, I have endeavored to use the simplest language and to avoid entirely the use of mathematical formulae, for I know by large experience that these are the bugbear of the ordinary reader, for whom this volume is specially intended. Therefore I have endeavored to state everything in such a simple manner that any one with a mere common school education can understand it. This, I trust, will explain the absence of everything which requires the use of anything higher than the simple rules of arithmetic and the most elementary propositions of geometry. And even this I have found to be enough for many lawyers, physicians, and clergymen who, in the ardent pursuit of their professions, have forgotten much that they learned at college. And as I hope to find many readers amongst intelligent mechanics, I have in some cases suggested mechanical proofs which any expert handler of tools can easily carry out.

As a matter of course, very little originality is claimed for anything in the book,—the only points that are new being a few illustrations of well-known principles, some of which had already appeared in "The Young Scientist" and "Self-education for Mechanics." Whenever the exact words of an author have been used, credit has always been given; but in regard to general statements and ideas, I must rest content with naming the books from which I have derived the greatest assistance. Ozanam's "Recreations in Science and Natural Philosophy," in the editions of Hutton (1803) and Riddle (1854), has been a storehouse of matter. Much has been gleaned from the "Budget of Paradoxes" by Professor De Morgan and also from Professor W. W. R. Ball's "Mathematical Recreations and Problems." Those who wish to inform themselves in regard to what has been done by the perpetual-motion-mongers must consult Mr. Dirck's two volumes entitled "Perpetuum Mobile" and I have made free use of his labors. To these and one or two others I acknowledge unlimited credit.

Some of the marvels which are here described, although very old, are not generally known, and as they are easily put in practice they may afford a pleasant hour's amusement to the reader and his friends.

John Phin

Paterson, N. J., July, 1905.