Next to that of Euclid, the name of Archimedes is probably that which is the best known of all the mathematicians and mechanics of antiquity, and this is in great part due to the two famous sayings which have been attributed to him, one being "Eureka"--"I have found it," uttered when he discovered the method now universally in use for finding the specific gravity of bodies, and the other being the equally famous dictum which he is said to have addressed to Hiero, King of Sicily,--"Give me a fulcrum and I will raise the earth from its place."

That Archimedes, provided he had been immortal, could have carried out his promise, is mathematically certain, but it occurred to Ozanam to calculate the length of time which it would take him to move the earth only one inch, supposing his machine constructed and mathematically perfect; that is to say, without friction, without gravity, and in complete equilibrium, and the following is the result:

For this purpose we shall suppose that the matter of which the earth is composed weighs 300 pounds per cubic foot, this being about the ascertained average. If the diameter of the earth be 7,930 miles, the whole globe will be found to contain 261,107,411,765 cubic miles, which make 1,423,499,120,882,544,640,000 cubic yards, or 38,434,476,263,828,705,280,000 cubic feet, and allowing 300 pounds to each cubic foot, we shall have 11,530,342,879,148,611,584,000,000 for the weight of the earth in pounds.

Now, we know, by the laws of mechanics, that, whatever be the construction of a machine, the s.p.a.ce pa.s.sed over by the weight, is to that pa.s.sed over by the moving power, in the reciprocal ratio of the latter to the former. It is known also, that a man can act with an effort equal only to about 30 pounds for eight or ten hours, without intermission, and with a velocity of about 10,000 feet per hour. If then we suppose the machine of Archimedes to be put in motion by means of a crank, and that the force continually applied to it is equal to 30 pounds, then with the velocity of 10,000 feet per hour, to raise the earth one inch the moving power must pa.s.s over the s.p.a.ce of 384,344,762,638,287,052,800,000 inches; and if this s.p.a.ce be divided by 10,000 feet or 120,000 inches, we shall have for a quotient 3,202,873,021,985,725,440, which will be the number of hours required for this motion. But as a year contains 8,766 hours, a century will contain 876,600; and if we divide the above number of hours by the latter, the quotient, 3,653,745,176,803, will be the number of centuries during which it would be necessary to make the crank of the machine continually turn in order to move the earth only one inch. We have omitted the fraction of a century as being of little consequence in a calculation of this kind. The machine is also supposed to be constantly in action, but if it should be worked only eight hours each day, the time required would be three times as long.

So that while it is true that Archimedes could move the world, the s.p.a.ce through which he could have moved it, during his whole life, from infancy to old age, is so small that even if multiplied two hundred million times it could not be measured by even the most delicate of our modern measuring instruments.

There is a modern saying which has become almost as famous amongst English-speaking peoples as is that of Archimedes to the world at large.

It is that which Bulwer Lytton puts into the mouth of Richelieu, in his well-known play of that name:

"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 a.s.signed 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

[Ill.u.s.tration: Peace on Earth and Good Will Toward Men.]