Nor any drop to drink.
“It’ll just take one more pebble1.”
“Whatever are you doing with those buckets?”
The speakers were Hugh and Lambert. Place, the beach of Little Mendip. Time 1:30 p.m. Hugh was floating a bucket in another a size larger, and trying how many pebbles2 it would carry without sinking. Lambert was lying on his back, doing nothing.
For the next minute or two Hugh was silent, evidently deep in thought. Suddenly he started. “I say, look here, Lambert!” he cried.
“If it’s alive, and slimy, and with legs, I don’t care to,” said Lambert.
“Didn’t Balbus say this morning that, if a body is immersed in liquid it displaces as much liquid as is equal to its own bulk?” said Hugh.
“He said things of that sort,” Lambert vaguely3 replied.
“Well, just look here a minute. Here’s the little bucket almost quite immersed: so the water displaced ought to be just about the same bulk. And now just look at itl” He took out the little bucket as he spoke4, and handed the big one to Lambert. “Why, there’s hardly a teacupful! Do you mean to say that water is the same bulk as the little bucket?”
“Course it is,” said Lambert.
“Well, look here again!” cried Hugh, triumphantly5, as he poured the water from the big bucket into the little one. “Why, it doesn’t half fill it!”
“That’s its business,” said Lambert. “If Balbus says it’s the same bulk, why, it is the same bulk, you know.”
“Well, I don’t believe it,” said Hugh.
“You needn’t,” said Lambert. “Besides, it’s dinner-time. Come along.” They found Balbus waiting dinner for them, and to him Hugh at once propounded6 his difficulty.
“Let’s get you helped first,” said Balbus, briskly cutting away at the joint7. “You know the old proverb, ‘Mutton first, mechanics afterwards’?”
The boys did not know the proverb, but they accepted it in perfect good faith, as they did every piece of information, however startling, that came from so infallible an authority as their tutor. They ate on steadily8 in silence, and, when dinner was over, Hugh set out the usual array of pens, ink, and paper, while Balbus repeated to them the problem he had prepared for their afternoon’s task.
“A friend of mine has a flower-garden — a very pretty one, though no great size ”
“How big is it?” said Hugh.
“That’s what you have to find out!’ Balbus gaily9 replied. “All I tell you is that it is oblong in shape — just half a yard longer than its width — and that a gravel-walk, one yard wide, begins at one corner and runs all round it.”
“Joining into itself?” said Hugh.
“Not joining into itself, young man. Just before doing that, it turns a corner, and runs round the garden again, alongside of the first portion, and then inside that again, winding10 in and in, and each lap touching11 the last one, till it has used up the whole of the area.”
“Like a serpent with corners?” said Lambert.
“Exactly so. And if you walk the whole length of it, to the last inch, keeping in the centre of the path, it’s exactly two miles and half a furlong. Now, while you wind out the length and breadth of the garden, I’ll see if I can think out that sea-water puzzle.”
“You said it was a flower-garden?” Hugh inquired, as Balbus was leaving the room.
“I did,” said Balbus.
“Where do the flowers grow?” said Hugh. But Balbus thought it best not to hear the question. He left the boys to their problem, and, in the silence of his own room, set himself to unravel12 Hugh’s mechanical paradox13.
“To fix our thoughts,” he murmured to himself, as, with hands deep-buried in his pockets, he paced up and down the room, “we will take a cylindrical14 glass jar, with a scale of inches marked up the side, and fill it with water up to the 10-inch mark: and we will assume that every inch depth of jar contains a pint15 of water. We will take a solid cylinder16, such that every inch of it is equal in bulk to half a pint of water, and plunge17 4 inches of it into the water, so that the end of the cylinder comes down to the 6-inch mark. Well, that displaces 2 pints18 of water. What becomes of them? Why, if there were no more cylinder, they would lie comfortably on the top, and fill the jar up to the 12-inch mark. But unfortunately there is more cylinder, occupying half the space between the 10-inch and the 12-inch marks, so that only one pint of water can be accommodated there. What becomes of the other pint? Why, if there were no more cylinder, it would lie on the top, and fill the jar up to the 13-inch mark. But unfortunately — Shade of Newton!” he exclaimed, in sudden accents of terror. “When does the water stop rising?”
A bright idea struck him. “I’ll write a little essay on it,” he said.
Balbus’s Essay
“When a solid is immersed in a liquid, it is well known that it displaces a portion of the liquid equal to itself in bulk, and that the level of the liquid rises just so much as it would rise if a quantity of liquid had been added to it, equal in bulk to the solid. Lardner says precisely19 the same process occurs when a solid is partially20 immersed: the quantity of liquid displaced, in this case, equalling the portion of the solid which is immersed, and the rise of the level being in proportion.
“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 displacement21 of a second portion of the liquid, and a consequent rise of level. Again, this second rise of level causes a yet further immersion22, 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 standing23 at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses: he remains24 steadfast25 and unmoved, and we all know that he must be drowned. The multitudes who daily perish in this manner to attest26 a philosophical27 truth, and whose bodies the unreasoning wave casts sullenly28 upon our thankless shores, have a truer claim to be called the martyrs29 of science than a Galileo or a Kepler. To use Kossuth’s eloquent30 phrase, they are the unnamed demigods of the nineteenth century.”
(Note by the writer — For the above essay I am indebted to a dear friend, now deceased.)
“There’s a fallacy somewhere,” he murmured drowsily31, as he stretched his long legs upon the sofa. “I must think it over again.” He closed his eyes, in order to concentrate his attention more perfectly32, 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.
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1
pebble
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| n.卵石，小圆石 | |
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2
pebbles
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| [复数]鹅卵石； 沙砾； 卵石，小圆石( pebble的名词复数 ) | |
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3
vaguely
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| adv.含糊地，暖昧地 | |
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4
spoke
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| n.（车轮的）辐条；轮辐；破坏某人的计划；阻挠某人的行动 v.讲，谈（speak的过去式）；说；演说；从某种观点来说 | |
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5
triumphantly
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| ad.得意洋洋地；得胜地；成功地 | |
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6
propounded
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| v.提出（问题、计划等）供考虑[讨论]，提议( propound的过去式和过去分词 ) | |
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7
joint
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| adj.联合的，共同的；n.关节，接合处；v.连接，贴合 | |
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8
steadily
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| adv.稳定地；不变地；持续地 | |
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9
gaily
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| adv.欢乐地，高兴地 | |
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10
winding
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| n.绕，缠，绕组，线圈 | |
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11
touching
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| adj.动人的，使人感伤的 | |
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12
unravel
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| v.弄清楚（秘密）；拆开，解开，松开 | |
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13
paradox
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| n.似乎矛盾却正确的说法；自相矛盾的人(物) | |
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14
cylindrical
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| adj.圆筒形的 | |
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15
pint
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| n.品脱 | |
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16
cylinder
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| n.圆筒，柱(面)，汽缸 | |
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17
plunge
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| v.跳入，(使)投入，(使)陷入；猛冲 | |
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18
pints
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| n.品脱( pint的名词复数 )；一品脱啤酒 | |
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19
precisely
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| adv.恰好，正好，精确地，细致地 | |
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20
partially
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| adv.部分地，从某些方面讲 | |
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21
displacement
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| n.移置，取代，位移，排水量 | |
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22
immersion
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| n.沉浸；专心 | |
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23
standing
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| n.持续，地位；adj.永久的，不动的，直立的，不流动的 | |
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24
remains
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| n.剩余物，残留物；遗体，遗迹 | |
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25
steadfast
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| adj.固定的，不变的，不动摇的；忠实的；坚贞不移的 | |
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26
attest
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| vt.证明，证实；表明 | |
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27
philosophical
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| adj.哲学家的，哲学上的，达观的 | |
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28
sullenly
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| 不高兴地，绷着脸，忧郁地 | |
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29
martyrs
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| n.martyr的复数形式；烈士( martyr的名词复数 )；殉道者；殉教者；乞怜者（向人诉苦以博取同情） | |
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30
eloquent
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| adj.雄辩的，口才流利的；明白显示出的 | |
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31
drowsily
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| adv.睡地，懒洋洋地，昏昏欲睡地 | |
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32
perfectly
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| adv.完美地，无可非议地，彻底地 | |
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