`Suppose a solid held above the surface of a liquid and partially immersed: a portion of the liquid is displaced, and the level of the liquid rises. But, by this rise of level, a little bit more of the solid is of course immersed, and so there is a new displacement of a second portion of the liquid, and a consequent rise of level. Again, this second rise of level causes a yet further immersion, and by consequence another displacement of liquid and another rise. It is self-evident that this process must continue till the entire solid is immersed, and that the liquid will then begin to immerse whatever holds the solid, which, being connected with it, must for the time be considered a part of it. If you hold a stick, six feet long, with its ends in a tumbler of water, and wait long enough, you must eventually be immersed. The question as to the source from which the water is supplied--which belongs to a high branch of mathematics, and is therefore beyond our present scope--does not apply to the sea. Let us therefore take the familiar instance of a man standing at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses: he remains steadfast and unmoved, and we all know that he must be drowned. The multitudes who daily perish in this manner to attest a philosophical truth, and whose bodies the unreasoning wave casts sullenly upon our thankless shores, have a truer claim to be called the martyrs of science than a Galileo or a Kepler. To use Kossuth's eloquent phrase, they are the unnamed demigods of the nineteenth century.'1
`There's a fallacy somewhere,' he murmured drowsily, as he stretched his longs legs upon the sofa. `I must think it over again.' He closed his eyes, in order to concentrate his attention more perfectly, and for the next hour or so his slow and regular breathing bore witness to the careful deliberation with which he was investigating this new and perplexing view of the subject.
Old Song
`HOW very, very sad!' exclaimed Clara; and the eyes of the gentle girl filled with tears as she spoke.
`Sad--but very curious when you come to look at it arithmetically,' was her aunt's less romantic reply. `Some of them have lost an arm in their country's service, some a leg, some an ear, some an eye--'
`And some, perhaps, all!' Clara murmured dreamily, as they passed the long rows of weather-beaten heroes basking in the sun. `Did you notice that very old one, with a red face, who was drawing a map in the dust with his wooden leg, and all the others watching? I think it was a plan of a battle--'
`The Battle of Trafalgar, no doubt,' her aunt interrupted briskly.
`Hardly that, I think,' Clara ventured to say. `You see, in that case, he couldn't well be alive--'
`Couldn't well be alive!' the old lady contemptuously repeated. `He's as lively as you and me put together! Why, if drawing a map in the dust--with one's wooden leg--doesn't prove one to be alive, perhaps you'll kindly mention what does prove it!'
Clara did not see her way out of it. Logic had never been her forte.
`To return to the arithmetic,' Mad Mathesis resumed--the eccentric old lady never let slip an opportunity of driving her niece into a calculation--`what percentage do you suppose must have lost all four--a leg, an arm, an eye, and an ear?'
`How can I tell?' gasped the terrified girl. She knew well what was coming.
`You ca'n't, of course, without data,' her aunt replied: `but I'm just going to give you--'
`Give her a Chelsea bun, miss! That's what most young ladies like best!' The voice was rich and musical, and the speaker dexterously whipped back the snowy cloth that covered his basket, and disclosed a