正如金匠所言，90天后，他奉献给国王一顶漂亮的王冠。所有见到的人都说，这个王冠无与伦比。希尔罗戴在头上感觉很不舒服，但是他并不在乎——他确定其它国王肯定没有这么­精­美的王冠。在对他的王冠反反复复地观赏了一番之后，他把王冠放在自己的天平上。不多不少，重量恰好是他所要求的。

“真该好好嘉奖你，”他对金匠说，“你制作得这么­精­致巧妙，而且一点黄金也没有少。”

国王的宫殿里有一个非常聪明的人，他叫阿基米德。当被召见欣赏国王的王冠时，他拿着王冠翻来覆去地看了很多次，还细心地检查。

“哦，你觉得这个王冠如何？”希尔罗问。

“手工的确很­精­巧，”阿基米德说，“但是，但是，金子——”

“金子全都在这里，”国王喊着，“我在天平上已经称过了。”

“确实如此，”阿基米德说，“但它却并不像原来金块那样富丽的红­色­，而且它一点都不是红­色­的。只是灿烂的黄|­色­，这是显而易见的。”

“绝大多数金子都是黄|­色­的，”希尔罗说，“但你说起这个，我想起当它还是金块的时候，的确颜­色­更深一些。”

“如果金匠从里面拿走一磅或两磅黄金，然后用白银或黄铜补足，会怎样呢？”阿基米德问。

“噢，他不会那么做的。”希尔罗说，“金子只是在制作过程中改变了颜­色­而已。”

但是越想他就越不舒服。最后，他对阿基米德说：“有什么方法检验一下，金匠的确欺骗了我，还是诚实地如数奉还了呢？”

“我毫无办法。”阿基米德说。

但阿基米德不是那种轻言放弃的人。他对难题怀有极大的兴趣。如果有什么难题让他迷惑不解时，他就会一直研究，直到得出答案来。几天来，他思考着黄金的事情，用各种方法检验，破解怎么做到检验但又不将王冠损坏的方法。

一天早晨，他在准备洗澡时还在思考这个问题。大浴盆里的水装得满满的，一直到了盆的边缘。当他跨进浴盆的时候，一些水溢到了石板上。类似的事情以前发生过上百次，但阿基米德第一次注意到了这件事。

“当我跨进到浴盆时，有多少水溢了出来呢？”他自语道，“大家都可以看出溢出水的体积和我身体的体积相等。一个有我一半体积的人，就会溢出一半的水。”

“现在假设，并不是我自己跨进这个浴盆，而是将希尔罗的王冠放进去，有和王冠体积一样的水溢出来。嗯，想想，黄金远比银子重。十磅纯金的体积不可能和七磅的黄金和三磅的白银混合的物体体积一样。如果国王的王冠是纯金的，那么它溢出的水，应该和其它十磅纯金的体积是一样的。但是如果它一部分是黄金，一部分是白银，那么排出水的体积应该比十磅纯金的体积大。我彻底明白了！我发现了！我发现了！”

他忘记了其他事情，从浴盆里蹦了出来，衣服都没有穿好，就穿过大街朝着国王的宫殿一路喊道：“尤里卡！尤里卡！尤里卡！”这是句拉丁语，意即“我发现了！我发现了！”

王冠被拿去检验。结果，王冠溢出的水比十磅纯金溢出的水多出许多。事实证明，金匠有罪。但是，金匠是否受到了惩罚，我不知道，也不关心。

阿基米德在浴盆中的这个小小发现的价值，远远超过国王的王冠。你知道为什么吗？

“我发现了！”（2）

“Eureka!”

THERE was once a king of Syracuse whose name was Hiero. The country over which he ruled was quite small, but for that very reason he wanted to wear the biggest crown in the world. So he called in a famous goldsmith, who was skillful in all kinds of fine work, and gāve him ten pounds of pure gold.

“Take this,” he said, “and fashion it into a crown that shall make every other king want it for his own. Be sure that you put into it every grain of the gold I give you, and do not mix any other metal with it.”

“It shall be as you wish,” said the goldsmith.“Here I receive from you ten pounds of pure gold; within ninety days I will return to you the finished crown which shall be of exactly the same weight.”

Ninety days later, true to his word, the goldsmith brought the crown. It was a beautiful piece of work, and all who saw it said that it had not its equal in the world. When King Hiero put it on his head it felt very uncomfortable, but he did not mind that—he was sure that no other king had so fine a headpiece. After he had admired it from this side and from that, he weighed it on his own scales. It was exactly as heāvy as he had ordered.

“You deserve great praise,” he said to the goldsmith. “You hāve wrought very skillfully and you hāve not lost a grain of my gold.”

There was in the king’s court a very wise man whose name was Archimedes. When he was called in to admire the king’s crown he turned it over many times and examined it very closely.

“Well, what do you think of it?” asked Hiero.

“The workmanship is indeed very beautiful,” answered Archimedes, “but—but the gold—”

“The gold is all there,” cried the king.“I weighed it on my own scales.”

“True,” said Archimedes,“but it does not appear to hāve the same rich red color that it had in the lump. It is not red at all, but a brilliant yellow, as you can plainly see.”

“Most gold is yellow,” said Hiero，“but now that you speak of it I do remember that when this was in the lump it had a much richer color.”

“What if the goldsmith has kept out a pound or two of the gold and made up the weight by adding brass or silver?” asked Archimedes.

“Oh, he could not do that,” said Hiero. “The gold has merely changed its color in the working.”

But the more he thought of the matter the less pleased he was with the crown. At last he said to Archimedes, “Is there any way to find out whether that goldsmith really cheated me, or whether he honestly gāve me back my gold?”

“I know of no way,” was the answer.

But Archimedes was not the man to say that anything was impossible. He took great delight in working out hard problems, and when any question puzzled him he would keep studying until he found some sort of answer to it. And so, day after day, he thought about the gold and tried to find some way by which it could be tested without doing harm to the crown.

“我发现了！”（3）

One morning he was thinking of this question while he was getting ready for a bath. The great bowl or tub was full to the very edge, and as he stepped into it a quantity of water flowed out upon the stone floor. A similar thing had happened a hundred times before, but this was the first time that Archimedes had thought about it.

“How much water did I displace by getting into the tub?” he asked himself. “Anybody can see that I displaced a bulk of water equal to the bulk of my body. A man half my size would displace half as much.

“Now suppose, instead of putting myself into the tub, I had put Hiero’s crown into it, it would hāve displaced a bulk of water equal to its own bulk. All, let me see! Gold is much heāvier than silver. Ten pounds of pure gold will not make so great a bulk as say seven pounds of gold mixed with three pounds of silver. If Hiero’s crown is pure gold it will displace the same bulk of water as any other ten pounds of pure gold. But if it is part gold and part silver it will displace a larger bulk. I hāve it at last! Eureka! Eureka!”

Forgetful of everything else he leaped from the bath. Without stopping to dress himself, he ran through the streets to the king’s palace shouting, “Eureka! Eureka! Eureka!” which in English means, “I hāve found it! I hāve found it! I hāve found it!”

The crown was tested. It was found to displace much more water than ten pounds of pure gold displaced. The guilt of the goldsmith was proved beyond a doubt. But whether he was punished or not, I do not know, neither does it matter.

The simple discovery which Archimedes made in his bath tub was worth far more to the world than Hiero’s crown. Can you tell why?

伽利略和灯

300多年前，意大利有一个名叫伽利略的年轻人。和阿基米德一样，他也在一刻不停地思考问题。还喜欢探究事物的根源。他发明了温度计，还发明了简单的望远镜和显微镜。在科学上，他有许多重要的发明。

18岁那年，快到掌灯的时候，他正在比萨大教堂。那个时代，灯只能靠油来点燃，并用一根木竿挂在天花板上。当灯夫碰到它们，或者风吹过教堂时，它们就会像钟摆似的来回摇摆。伽利略注意到了这个问题。于是他开始仔细地研究它。

他注意到，长度相同的木竿上的灯来回摆动的时间相同。那些较短的木竿的灯比那些较长木竿的灯摇晃速度要快。伽利略观察来回摇摆的灯，非常入迷。数百万人曾看到过灯的摇摆，却没有一个人想到要找出重要、实用的发现与现象之间的关系。

伽利略回到自己的房间，便开始了试验工作。他找出一些不同长度的绳子，挂在天花板上，并在每个绳子的末端挂了一个砝码。接着他晃动所有的绳子，让它们像教堂里的灯一样来回摇摆。每根绳子就就像竹竿一样成了钟摆。

经过长期的观察，他发现：如果是一根长39■英寸的绳子，一分钟正好晃动60次。而绳子是前面绳子的

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