Christian Huygens was born at the Hague on April 14, 1629, and died in the same town on July 8, 1695. He generally wrote his name as Hugens, but I follow the usual custom in spelling it as above: it is also sometimes written as Huyghens. His life was uneventful, and there is little more to record in it than a statement of his various memoirs and researches.
In 1651 he published an essay in which he shewed the fallacy in a system of quadratures proposed by Grégoire de Saint-Vincent, who was well versed in the geometry of the Greeks, but had not grasped the essential points in the more modern methods. This essay was followed by tracts on the quadrature of the conics and the approximate rectification of the circle.
In 1654 his attention was directed to the improvement of the telescope. In conjunction with his brother he devised a new and better way of grinding and polishing lenses. As a result of these improvements he was able during the following two years, 1655 and 1656, to resolve numerous astronomical questions; as, for example, the nature of Saturn's appendage. His astronomical observations required some exact means of measuring time, and he was thus led in 1656 to invent the pendulum clock, as described in his tract Horologium , 1658. The time-pieces previously in use had been balance-clocks.
In the year 1657 Huygens wrote a small work on the calculus of probabilities founded on the correspondence of Pascal and Fermat. He spent a couple of years in England about this time. His reputation was now so great that in 1665 Louis XIV offered him a pension if he would live in Paris, which accordingly then became his place of residence.
In 1668 he sent to the Royal Society of London, in answer to a problem they had proposed, a memoir in which (simultaneously with Wallis and Wren) he proved by experiment that the momentum in a certain direction before the collision of two bodies is equal to the momentum in that direction after the collision. This was one of the points in mechanics on which Descartes had been mistaken.
The most important of Huygens's work was his Horologium Oscillatorium published at Paris in 1673. The first chapter is devoted to pendulum clocks. The second chapter contains a complete account of the descent of heavy bodies under their own weights in a vacuum, either vertically down or on smooth curves. Amongst other propositions he shews that the cycloid is tautochronous. In the third chapter he defines evolutes and involutes, proves some of their more elementary properties, and illustrates his methods by finding the evolutes of the cycloid and the parabola. These are the earliest instances in which the envelope of a moving line was determined. In the fourth chapter he solves the problem of the compound pendulum, and shews that the centres of oscillation and suspension are interchangeable. In the fifth and last chapter he discusses again the theory of clocks, points out that if the bob of the pendulum were, by means of cycloidal clocks, made to oscillate in a cycloid the oscillations would be isochronous; and finishes by shewing that the centrifugal force on a body which moves around a circle of radius r with a uniform velocity v varies directly as v 2 and inversely as r . This work contains the first attempt to apply dynamics to bodies of finite size, and not merely to particles.
In 1675 Huygens proposed to regulate the motion of watches by the use of the balance spring, in the theory of which he had been perhaps anticipated in a somewhat ambiguous and incomplete statement made by Hooke in 1658. Watches or portable clocks had been invented early in the sixteenth century, and by the end of that century were not very uncommon, but they were clumsy and unreliable, being driven by a main spring and regulated by a conical pulley and verge escapement; moreover, until 1687 they had only one hand. The first watch whose motion was regulated by a balance spring was made at Paris under Huygens's directions, and presented by him to Louis XIV.
The increasing intolerance of the Catholics led to his return to Holland in 1681, and after the revocation of the edict of Nantes he refused to hold any further communication with France. He now devoted himself to the construction of lenses of enormous focal length: of these three of focal lengths 123 feet, 180 feet, and 210 feet, were subsequently given by him to the Royal Society of London, in whose possession they still remain. It was about this time that he discovered the achromatic eye-piece (for a telescope) which is known by his name. In 1689 he came from Holland to England in order to make the acquaintance of Newton, whose Principia had been published in 1687. Huygens fully recognized the intellectual merits of the work, but seems to have deemed any theory incomplete which did not explain gravitation by mechanical means.
On his return in 1690 Huygens published his treatise on light in which the undulatory theory was expounded and explained. Most of this had been written as early as 1678. The general idea of the theory had been suggested by Robert Hooke in 1664, but he had not investigated its consequences in any detail. Only three ways have been suggested in which light can be produced mechanically. Either the eye may be supposed to send out something which, so to speak, feels the object (as the Greeks believed); or the object perceived may send out something which hits or affects the eye (as assumed in the emission theory); or there may be some medium between the eye and the object, and the object may cause some change in the form or condition of this intervening medium and thus affect the eye (as Hooke and Huygens supposed in the wave or undulatory theory). According to this last theory space is filled with an extremely rare ether, and light is caused by a series of waves or vibrations in this ether which are set in motion by the pulsations of the luminous body. From this hypothesis Huygens deduced the laws of reflexion and refraction, explained the phenomenon of double refraction, and gave a construction for the extraordinary ray in biaxal crystals; while he found by experiment the chief phenomena of polarization.
The immense reputation and unrivalled powers of Newton led to disbelief in a theory which he rejected, and to the general adoption of Newton's emission theory. Within the present century crucial experiments have been devised which give different results according as one or the other theory is adopted; all these experiments agree with the results of the undulatory theory and differ from the results of the Newtonian theory; the latter is therefore untenable. Until, however, the theory of interference, suggested by Young, was worked out by Fresnel, the hypothesis of Huygens failed to account for all the facts, and even now the properties which, under it, have to be attributed to the intervening medium or ether involve difficulties of which we still seek a solution. Hence the problem as to how the effects of light are really produced cannot be said to be finally solved.
Besides these works Huygens took part in most of the controversies and challenges which then played so large a part in the mathematical world, and wrote several minor tracts. In one of these he investigated the form and properties of the catenary. In another he stated in general terms the rule for finding maxima and minima of which Fermat had made use, and shewed that the subtangent of an algebraical curve f ( x,y ) = 0 was equal to yf y / f x , where f y is the derived function of f ( x,y ) regarded as a function of y . In some posthumous works, issued at Leyden in 1703, he further shewed how from the focal lengths of the component lenses the magnifying power of a telescope could be determined; and explained some of the phenomena connected with haloes and parhelia.
I should add that almost all his demonstrations, like those of Newton, are rigidly geometrical, and he would seem to have made no use of the differential or fluxional calculus, though he admitted the validity of the methods used therein. Thus, even when first written, his works were expressed in an archaic language, and perhaps received less attention than their intrinsic merits deserved.
背景介绍和作者引言
克里斯蒂安·惠更斯是17世纪一位杰出的荷兰科学家和数学家，那个时代的世界正在迅速扩展对科学和宇宙的理解。惠更斯于1629年出生于海牙，生活在科学革命时期，这是一个以开创性发现和发明为标志的时代。他的工作涵盖了许多领域，包括天文学、物理学、数学和计时学（时间测量科学）。尽管惠更斯生活在宗教和政治局势高度紧张的时期，但他一生致力于科学研究和创新。
惠更斯最出名的是发明了摆钟，大大提高了计时精度，以及他的光的波动理论，为现代光学奠定了基础。他对力学的贡献，尤其是他对物体运动和碰撞的研究，挑战了早期的观点，并帮助奠定了经典物理学的基础。
惠更斯工作的详细解释和意义
惠更斯的生活和工作说明了好奇心和细致观察的力量。他对望远镜的改进使天文学家能够更清晰地看到天体，这有助于更好地理解土星等行星。通过发明摆钟，他解决了精确测量时间的关键问题——这是一项对导航和科学实验至关重要的突破。
他最重要的著作之一《振动钟》是科学写作的杰作，它结合了理论和实际应用。在其中，惠更斯解释了摆的运动方式以及这种运动如何用于调节时钟。他还探索了摆线等曲线的性质，摆线具有等时性这一独特的性质——这意味着物体沿其滑动所需的时间与它们的起始点无关。这一发现不仅在数学上很美，而且在时钟设计中也具有实际用途。
惠更斯的光的波动理论是革命性的。在艾萨克·牛顿的微粒说占主导地位的时代，惠更斯提出光以波的形式通过一种叫做以太的介质传播。这个想法比牛顿的理论更好地解释了许多光学现象，如反射、折射和偏振。尽管惠更斯提出的观点花了几个世纪才被完全接受，但今天它们构成了现代物理学和光学的基础。
学生可以从惠更斯的故事中学到什么
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好奇心和毅力的重要性
惠更斯的一生告诉学生，科学进步往往源于提问和仔细检验想法。他对时钟、光和力学的工作表明，好奇心与毅力相结合可以带来突破。 -
跨学科学习的价值
惠更斯并不局限于一个领域；他结合了数学、物理学和工程学。这种方法鼓励学生探索多个学科，并了解它们在现实生活中的联系。 -
批判性思维和挑战既定观念
惠更斯挑战了他那个时代的公认理论，例如笛卡尔关于碰撞的观点和牛顿的光的理论。这向学生表明了批判性思维和接受新证据的重要性。 -
精确性和对细节的关注
他对镜头研磨和制钟的改进突出了小细节在科学工作中的重要性。学生可以了解到，细致的工作和精确性在任何学科中都是必不可少的。
如何在日常生活中应用这些经验
- 在学习中： 在学习时，学生可以通过质疑他们所读的内容、试验想法以及连接不同的学科（如数学和科学）来效仿惠更斯的方法，以加深理解。
- 在解决问题中： 无论是在学校项目还是日常挑战中，学生都不应该害怕以不同的方式思考或尝试新的方法，就像惠更斯在他的发明中所做的那样。
- 在社交互动中： 惠更斯表现出的耐心和毅力可以激励学生对自己和他人保持耐心，理解进步往往需要时间和努力。
- 在个人成长中： 拥抱好奇心和对学习的热爱可以带来终身成长和意想不到的发现，就像惠更斯一样。
从惠更斯的例子中鼓励积极的特质
- 好奇心： 永远问“为什么”，并试图理解你周围的世界。
- 毅力： 即使解决方案不明显，也要继续解决问题。
- 开放的心态： 愿意考虑新想法，即使它们挑战你已经相信的东西。
- 注重细节： 在你的工作中要小心，并力求准确。
- 跨学科思维： 结合不同领域的知识来解决复杂的问题。
通过研究克里斯蒂安·惠更斯的生活和工作，学生不仅获得了关于科学和历史的知识，还获得了关于如何以深思熟虑、坚持不懈和开放的心态来学习和生活的宝贵经验。他的遗产提醒我们，伟大的发现往往源于想象力、辛勤工作和质疑世界的勇气。
