数学家传记
乔凡尼·多美尼科·卡西尼(乔凡尼·多美尼科·卡西尼一世)是一位意大利数学家和天文学家,研究了到两个固定焦点的距离之积为常数的点的轨迹曲线。
在这本传记中,我们首先应该澄清的是乔凡尼·多美尼科·卡西尼的名字。他在意大利出生后,父母Jacopo Cassini和茹利亚 Crovesi给他取名为卡西尼 卡西尼。然而他也使用Gian 卡西尼这个名字,搬到法国后,他将名字改为Jean-Dominique Cassini的法语版本。再补充一点关于他名字的评论,他是著名的卡西尼天文学家家族的第一人,因此常被称为卡西尼 I。
我们对他的父母知之甚少,但可以肯定他的父亲是托斯卡纳人。事实上,卡西尼不是由父母抚养,而是由他的舅舅、母亲的兄弟茹利亚 Crovesi抚养长大。在Vallebone接受两年教育后,卡西尼进入热那亚的耶稣会学院,师从Casselli。此后,他在San Fructuoso修道院学习。Taton写道[1]:-
他展现出极大的求知欲,尤其对诗歌、数学和天文学感兴趣。
然而,他最初的兴趣是占星术而非天文学。他广泛阅读这方面的书籍,很快便学识渊博,却坚信占星术的预言毫无真实性。颇为奇怪的是,正是他对占星术的广博知识促成了他的首次任职。1644年,博洛尼亚的元老、对占星术极感兴趣的科内利奥·马尔瓦西亚侯爵邀请卡西尼前往博洛尼亚。他提供给卡西尼一个职位,在他当时正在建造的潘扎诺天文台工作。
从1648年起,卡西尼在Panzano天文台用他从Malvasia侯爵的财政资源中购买的仪器进行观测。这对卡西尼来说是一个重要时期,他从杰出的耶稣会科学家乔万尼·巴特斯达·里奇奥利和弗朗西斯科·马里亚·格里马尔迪(后者后来发现了衍射)那里学到了很多。1650年,卡西尼成为博洛尼亚大学的数学和天文学教授,填补了自1647年11月底博纳文图拉·卡瓦列里去世以来一直空缺的讲席。这一任命是通过Malvasia侯爵的支持实现的,他在博洛尼亚的重要地位使他在提名博纳文图拉·卡瓦列里的继任者方面具有相当大的影响力。
卡西尼在1652-3年观测了一颗彗星,并发表了他观测的记述,献给摩德纳公爵。从这项工作中我们可以看出,此时卡西尼相信以地球为中心的太阳系,彗星在土星之外但起源于地球。观测将使他接受第谷·布拉赫提出的太阳系模型,并且在1659年,他提出了一个以地球为中心的系统,月球和太阳绕地球运行,其他行星绕太阳运行。后来他逐渐接受了哥白尼模型的一个版本。
卡西尼在博洛尼亚担任数学和天文学教授的前任之一,是1576年获得任命的埃尼亚齐奥·当蒂。埃尼亚齐奥·当蒂曾在博洛尼亚的圣彼得罗尼奥教堂建造了一座日晷,那是已建成的最大基督教教堂之一。一个小孔让太阳光线射入教堂。光线在地面的刻度上形成一个小像,从而可以精确确定太阳的位置。圣彼得罗尼奥教堂的大部分建于1445年至1525年间,但扩建工作仍在继续,就在卡西尼抵达博洛尼亚前不久,进一步的建筑施工使埃尼亚齐奥·当蒂的日晷无法使用[1]:-
1653年,卡西尼希望使用这样一台仪器,便草拟了一份新的、更大的[日晷]的建造方案,但这座日晷建造起来会很困难。他的计算精确;建造完美成功;这一成功为卡西尼赢得了辉煌的声誉。
他用新日晷进行了许多重要观测,并发表在Specimen observationum Bononiensium ……Ⓣ(《在博洛尼亚所做的一些观测……》)(1656年)中,他将这部著作献给了当时流亡意大利的瑞典女王克里斯蒂娜。
然而,他的专业知识涵盖天文学以外的许多领域。他是水力学和工程学专家,因此就1657年博洛尼亚与费拉拉之间关于雷诺河河道的争端被咨询。争端由教皇亚历山大七世根据卡西尼的建议解决,此后数年他经常作为河流管理专家被教廷咨询。他就这方面的工作撰写了论文,特别是关于波河洪水。1663年他还被教皇聘为防御工事总监,然后他于1665年再次前往罗马,当时他被任命为教会国家水域总监。
教皇要求卡西尼接受圣职,因为他希望看到他永久为自己工作。然而,卡西尼更愿意保留他在博洛尼亚的数学与天文学教授职位,在不履行教皇职责时在那里任教。他继续天文学研究,提出了一个大气折射模型,但后来证明是错误的,对太阳进行了深入研究,于1662年发表了表格,并继续寻找彗星。1664年他观测到一颗彗星,这使他提出一个新理论,即彗星以圆形轨道绕太阳运行,轨道中心指向天狼星方向。
从1664年起,卡西尼得以使用由罗马杰出的镜片制造者朱塞佩·坎帕尼制作的新的强力望远镜进行观测。借助这些仪器,卡西尼做出了一系列新发现。1664年7月,他测量了木星绕其轴的自转周期,发现了该行星上的条纹和斑点,并看到该行星在两极处是扁平的。1666年,他测量了火星绕其轴的自转周期,所得数值与正确值相差不到三分钟,并观测到了表面特征。1668年,他发表了关于木星卫星的详细系列观测。卡西尼发现了其数据中的差异,起初他将此归因于光具有有限速度:-
……光从卫星传到我们这里需要一些时间;而穿过等于地球轨道半径的距离大约需要十到十一分钟。
卡西尼 的观点过于传统,无法接受自己的想法,很快便将其摒弃,转而寻找对这一差异的其他解释。颇具讽刺意味的是,七年后勒默正是利用 卡西尼 的数据来计算光速的。
卡西尼的辉煌发现为他赢得了国际声誉,并导致他于1668年被路易十四邀请到巴黎。巴黎天文台的建设刚刚开始,卡西尼被提供了丰厚的薪水、免费住宿和良好的旅行津贴来监督该项目。博洛尼亚元老院和教皇克莱门特九世同意此行,他们认为这最多是两年的短途旅行。然而,卡西尼立即参与了Académie des Sciences的工作,尽管在这个阶段他几乎没有尝试安顿下来并提高他的法语,因为他仍然完全打算迅速回到意大利的职责。1671年成为巴黎天文台台长后,他很快改变了对返回意大利的看法,并于两年后成为法国公民,改名为Jean-Dominique Cassini。1674年,他与热纳维耶芙·德·莱斯特结婚,她是克莱蒙伯爵领地的中将的女儿。在他们的婚姻中,热纳维耶芙带来了一份嫁妆,其中包括瓦兹省的塞萨尔-弗朗索瓦·卡西尼·图里城堡,该城堡成为家族后代在卡西尼的夏季住所。这段婚姻有两个儿子,较小的雅克·卡西尼生于1677年,最终继承了他父亲作为巴黎天文台台长的职位。
在巴黎天文台,卡西尼继续做出革命性的发现,就像他在意大利时一样,使用他随身携带的望远镜。他是第一个观察到土星的四颗卫星的人:土卫八(1671年)、土卫五(1672年)、土卫三(1684年)和土卫四(1684年)。他在1675年发现了土星环系统中的缝隙,现在被称为卡西尼缝。令人印象深刻的是,他正确地提出环是由大量微小的卫星组成的,每颗卫星都围绕行星运行。他绘制了一幅大型的月球图,并于1679年将其呈献给Académie des Sciences。在天文摄影发明之前,这仍然是可用的最好的月球图。
卡西尼的木星卫星表被用来通过提供通用时间来确定经度,以便与地球上各个位置的本地时间进行比较。当法国探险队测量了许多地方的经度时,卡西尼留在巴黎协调他们的数据并进行自己的测量。1672年,让·里歇尔在法属圭亚那的卡宴对火星进行了测量,而让-费利克斯·皮卡德和卡西尼在巴黎进行了测量。根据他们的数据,首次找到了太阳视差的第一精确值,从而给出了地球到太阳的距离。让·里歇尔进行的另一项测量,即周期为一秒的摆钟在卡宴比在巴黎短,使他通过提出地球在两极扁平来解释这一点。这支持了艾萨克·牛顿和克里斯蒂安·惠更斯的理论提议,但卡西尼不接受让·里歇尔的解释。他寻求另一个实验来确定地球是否是一个完美的球体。
为了确定地球的形状,卡西尼提议测量从法国北部到南部的子午线弧。该项目于1683年开始,卡西尼从巴黎向南测量,而菲利普·德拉伊尔从巴黎向北测量。由于资金原因,该项目于1684年取消,当时卡西尼已到达布尔日,该地几乎正好位于法国中部。
1695年,卡西尼在意大利旅行。他带着他十八岁的儿子雅克·卡西尼,他们进行了大量的测地观测,并返回博洛尼亚,在那里他们修复了博洛尼亚圣彼得罗尼奥教堂的日晷,该日晷是卡西尼近三十年前设计的。1700年,子午线项目重新启动,现在除了许多其他科学家外,卡西尼还有他的儿子雅克·卡西尼协助他。他们测量了从巴黎到佩皮尼昂的子午线,佩皮尼昂位于地中海海岸以西13公里处。他获得的结果错误地表明地球在两极拉长。作为一个拒绝艾萨克·牛顿引力理论的人,这个结果相当令人满意,因为艾萨克·牛顿的理论使他得出了地球在两极扁平的理論证明。然而,在观察到木星在其两极扁平后,他竟如此强烈地主张地球拉长,这令人惊讶。
1680年,他研究了卡西尼曲线,即到两个固定焦点的距离乘积为常数的点的轨迹。他将其作为研究地球和太阳相对运动的一部分,并提议将其作为行星轨道的曲线,而不是约翰内斯·开普勒提出的椭圆。雅各布·伯努利的 lemniscate 是卡西尼曲线的一个成员,但这一点在100年后才被意识到。
大约从1709年起,雅克·卡西尼逐渐接替了他父亲作为巴黎天文台负责人的职责。卡西尼的健康开始恶化,特别是他的视力变得很差,以至于到1711年他几乎完全失明。贝尔纳·勒布耶·德·丰特奈尔 [4]说,卡西尼平静温和的性格,源于深厚的宗教信仰,使他能够愉快地承受几乎完全的失明。
塔东在 [1] 中对 卡西尼 作了如下评价:——
对 卡西尼 工作的评价差异极大。许多历史学家追随 [让·巴蒂斯特·约瑟夫·德朗布尔],指责他最好的想法都是从前辈著作中得来的,并将法国天文学引向专制和倒退的方向;另一些人则坚持认为他作为观测者和天文台研究组织者的工作十分重要。尽管 卡西尼 的控制确实限制了天文台的研究,尽管他确实反对大多数新理论,但他的行为并不像 [让·巴蒂斯特·约瑟夫·德朗布尔] 所描述的那样一味专横和有害。他不是理论家;然而,他是一位有天赋的观测者,他无可争辩的发现足以使他在前牛顿时代的天文学家中占据很高的地位。
The first thing we should clarify in this biography is Giovanni Cassini's name. He was given the name Giovanni Domenico by his parents, Jacopo Cassini and Julia Crovesi, after his birth in Italy. However he also used the name Gian Domenico Cassini, and after he moved to France, he changed his name to the French version of Jean-Dominique Cassini. To add just one more comment to the question of his name, he was the first of the famous Cassini family of astronomers and as such is often known as Cassini I.
We know little of his parents but certainly his father was a Tuscan. In fact Giovanni was brought up, not by his parents but by an uncle, a brother of his mother Julia Crovesi. After spending two years being educated at Vallebone, Cassini entered the Jesuit College at Genoa where he studied under Casselli. After this he studied at the abbey of San Fructuoso. Taton writes [1]:-
He showed great intellectual curiosity and was especially interested in poetry, mathematics and astronomy.
His first interest, however, was in astrology rather than astronomy. He read widely on this topic and soon was very knowledgeable, yet was convinced that there was no truth in astrological predictions. It was, rather strangely, his extensive knowledge of astrology that led to his first appointment. In 1644 the Marquis Cornelio Malvasia, who was a senator from Bologna with a great interest in astrology, invited Cassini to Bologna. He offered him a position in the Panzano Observatory which he was constructing at that time.
From 1648 Cassini observed at the Panzano Observatory with instruments which he had purchased with financial resources from the Marquis Malvasia. This was an important time for Cassini who learnt much from the outstanding Jesuit scientists Giovanni Battista Riccioli and Francesco Maria Grimaldi (who later discovered diffraction). In 1650, Cassini became professor of mathematics and astronomy at the University of Bologna, filling the chair which had been vacant since the death of Cavalieri at the end of November 1647. This appointment came about through the support of the Marquis Malvasia whose important position in Bologna gave him considerable influence in naming Cavalieri's successor.
Cassini observed a comet in 1652-3 and he published an account of his observations which he dedicated to the Duke of Modena. From the work we can see that at this time Cassini believed in an Earth centred solar system, with comets beyond Saturn but originating from the Earth. Observations would lead him to accept the model of the solar system proposed by Tycho Brahe and, in 1659, he presented an Earth centred system with the moon and sun orbiting the Earth and the other planets orbiting the sun. Later he came to accept a version of the Copernican model.
One of Cassini's predecessor's as professor of mathematics and astronomy at Bologna had been Egnatio Danti who had been appointed in 1576. Danti had built a gnomon at the Church of San Petronio in Bologna, one of the largest Christian churches ever built. A small hole allowed the rays of the sun to enter the church. They formed a small image on a scale on the floor which allowed the position of the sun to be accurately determined. The church of San Petronio had mostly been built between 1445 and 1525, but work continued on extending it and not long before Cassini arrived in Bologna further building work had made Danti's gnomon unusable [1]:-
In 1653, Cassini, wishing to employ such an instrument, sketched a plan for a new and larger [gnomon] but one which would be difficult to build. His calculations were precise; the construction succeeded perfectly; and its success made Cassini a brilliant reputation.
He made many important observations with his new gnomon which he published in Specimen observationum Bononiensium ... Ⓣ (1656), a work he dedicated to Queen Christina of Sweden who was in exile in Italy at this time.
His expertise, however, covered many areas other than astronomy. He was an expert in hydraulics and engineering and as such was consulted regarding the dispute of 1657 between Bologna and Ferrara on the course of the River Reno. The dispute was settled by Pope Alexander VII with advice from Cassini and for several years after this he was regularly consulted by the Papal Court as an expert on river management. He wrote treatises on this aspect of his work, in particular on the flooding of the river Po. He was also employed by the Pope in 1663 as superintendent of fortifications, then he travelled to Rome again in 1665 when he was named Superintendent of the waters of the ecclesiastical states.
The Pope asked Cassini to take Holy Orders for he wished to see him permanently working for him. However, Cassini preferred to keep his post as professor of mathematics and astronomy at Bologna where he taught when not undertaking Papal duties. He continued with his research in astronomy, proposing a model for atmospheric refraction which turned out to be incorrect, making an intensive study of the sun, publishing tables in 1662, and continuing to search for comets. In 1664 he observed a comet which led him to propose a new theory that comets travelled in circular orbits around the sun with the centre of the orbit in the direction of the star Sirius.
Beginning in 1664 Cassini was able to observe with new powerful telescopes made by the excellent lens maker Giuseppe Campani of Rome. With these instruments Cassini made a series of new discoveries. In July 1664 he measured the period of rotation of Jupiter on its axis, discovered the bands and spots on the planet, and saw that the planet was flattened at its poles. In 1666 he measured the period of rotation of Mars on its axis, getting a value within three minutes of the correct one, and observed surface features. He published detailed series of observations of the moons of Jupiter in 1668. Cassini discovered discrepancies in his data which at first he attributed to light having a finite speed:-
... light takes some time to come from the satellite to us; and it takes approximately ten or eleven minutes to traverse a distance equal to the semi-diameter of the Earth's orbit.
However, Cassini was too traditional in his views to accept his own idea, and he soon rejected it and looked for other explanation for the discrepancy. It is rather ironical that it was Cassini's data that was used by Rømer in calculating the speed of light seven years later.
Cassini's brilliant discoveries gave him an international reputation and led to him being invited to Paris by Louis XIV in 1668. The construction of the Paris Observatory had just begun and Cassini was offered a generous salary, free accommodation, and a good travel allowance to oversee the project. The senate of Bologna and Pope Clement IX agreed to the trip which they believed would be a short one of at most two years. However Cassini was immediately involved in the work of the Académie des Sciences although at this stage he made little attempt to settle down and improve his French as he still fully intended a quick return to his duties in Italy. After he became head of the Paris Observatory in 1671, he soon changed his views on returning to Italy and became a French citizen two years later, changing his name to Jean-Dominique Cassini. In 1674 he married Geneviève de Laistre who was the daughter of the lieutenant general of the compté of Clermont. On their marriage Geneviève brought with her a dowry which included the Château de Thury in the Oise which became the Cassini summer residence for succeeding generations of the family. There were two sons from this marriage, the younger one Jacques Cassini being born in 1677 and eventually succeeding to his father's position as head of the Paris Observatory.
At the Paris Observatory Cassini continued to make revolutionary discoveries, as he had done in Italy, using a telescope he had brought with him. He was the first to observe four of Saturn's moons: Iapetus (1671), Rhea (1672), Tethys (1684), and Dione (1684). He discovered the gap in the ring system of Saturn now known as the Cassini division in 1675. Impressively he correctly proposed that the rings were composed of large numbers of tiny satellites each orbiting the planet. He drew a large Chart of the Moon, which he presented to the Académie des Sciences in 1679. This remained the best that was available prior to the invention of photography for astronomical purposes.
Cassini's tables of Jupiter's moons were used to determine longitudes by providing a universal time with which to compare the local time at various positions on the Earth. While French expeditions measured the longitudes of numerous places, Cassini remained in Paris coordinating their data and making his own measurements. In 1672 Jean Richer made measurements of Mars from Cayenne, French Guyana, while Jean Picard and Cassini made measurements in Paris. From their data the first accurate value of the solar parallax was found, giving the distance from the Earth to the sun. Another measurement made by Jean Richer, namely that a pendulum with a period of one second is shorter in Cayenne than Paris, led him to explain this by suggesting that the Earth was flattened at the poles. This supported theoretical proposals by Newton and Huygens, but Cassini did not accept Jean Richer's explanation. He sought another experiment to determine whether the Earth was a perfect sphere.
In order to determine the shape of the Earth, Cassini proposed measuring an arc of the meridian from the north of France to the south. The project was begun in 1683 with Cassini making measurements from Paris towards the south, while Philippe de La Hire began making measurements north from Paris. The project was cancelled for financial reasons in 1684 when Cassini had reached Bourges, which is almost exactly in the centre of France.
In 1695 Cassini travelled in Italy. He took his eighteen year old son Jacques Cassini with him and they made numerous geodesic observations, as well as returning to Bologna where they repaired the gnomon at the Church of San Petronio in Bologna which Cassini had designed nearly thirty years before. In 1700 the meridian project was revived and now, in addition to a number of other scientists, Cassini had his son Jacques to assist him. They made measurements of the meridian from Paris to Perpignan, which is 13 km west of the Mediterranean coast. He obtained results which wrongly suggested that the Earth was elongated at the poles. As someone who rejected Newton's theory of gravitation, this result was rather pleasing since Newton's theory led him to a theoretical proof that the Earth would be flattened at the poles. However, having observed the flattening of Jupiter at its poles, it is surprising that he should have been such a strong advocate of the elongation of the Earth.
In 1680 he studied the Cassinian curve which is the locus of a point the product of whose distances from two fixed foci is constant. He worked on this as part of a study of the relative motions of the Earth and the sun and proposed this as the curve for planetary orbits rather than the ellipse as proposed by Kepler. The lemniscate of Jacob Bernoulli is a member of the Cassinian curves but this was not realised for 100 years.
From around 1709 Jacques Cassini gradually took over his father's duties as head of the Paris Observatory. Cassini's health began to deteriorate, in particular his eyesight became poor so that by 1711 he was nearly completely blind. Fontenelle [4] says that Cassini's calm and gentle character, coming from a deeply religious belief, allowed him to bear nearly total blindness with good cheer.
Taton gives this assessment of Cassini in [1]:-
Judgements on Cassini's work vary greatly. While many historians, following Delambre, accuse him of having found his best ideas in the writings of his predecessors and of having oriented French astronomy in an authoritarian and retrograde direction, others insist on the importance of his work as observer and organiser of the research at the Observatory. Although Cassini's control did restrict the Observatory's studies and although he did fight against most of the new theories, his behaviour does not seem as uniformly tyrannical and baleful as Delambre described it. He was not a theoretician; he was, however, a gifted observer and his indisputable discoveries are sufficient to win him a high position among the astronomers of the pre-Newtonian generation.
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