数学家传记
内维尔·马斯基林是一位英国天文学家,他在希哈利恩进行了一项著名实验,测量了地球的密度。
内维尔·马斯基林的父亲Edmund Maskelyne是一位执业出庭律师和国务卿办公室的法律顾问。他住在英格兰威尔特郡的珀顿唐。Edmund Maskelyne于1724年2月4日与伊丽莎白·布斯结婚,她是弗瑞兹·约翰·布斯和伊丽莎白·普罗杰的女儿。他们有四个孩子:William Maskelyne(1725-1772)、Edmund Maskelyne(1728-1775)、马斯基林(本传记的主人公)和Margaret Maskelyne(1735-1817)。马斯基林在1800年写下了自传笔记,其中提供了一些关于家族起源的信息。他说他是(例如见[1]):-
……一个古老家族的最后一位男性继承人,该家族长期定居在威尔特郡的珀顿,从姓氏来看可能来自诺曼底,那里在50年前还有或曾有一个姓马斯克林的家庭。
四个孩子都出生在肯辛顿,但在1736年,全家搬到了威斯敏斯特的托特希尔街。这意味着两个最大的男孩威廉和埃德蒙离他们就读的威斯敏斯特学校很近,他们的父亲老埃德蒙也离工作地点很近。1741年1月,马斯基林开始在威斯敏斯特学校接受教育。老埃德蒙于1744年3月去世,当时马斯基林12岁,这使得家庭相当贫困。1748年母亲伊丽莎白去世时,马斯基林仍在威斯敏斯特学校接受教育。此后,马斯基林寄宿在威斯敏斯特的文森特·伯恩家中,同时继续他的学业。就在母亲去世前不久,他在看到1748年7月25日的日食后,对天文学产生了兴趣。马斯基林在谈到自己的学校教育时写道(例如见[1]):——
伟大的数学家们之所以成为天文学家,是因为数学为他们掌握天文学提供了便利;但在这里,对天文学的热爱成了致力于数学的动机,没有数学,我们的天文学家很快就发现他无法在自己喜爱的科学中取得所期望的进展;几个月内,在没有任何帮助的情况下,他就掌握了几何学和代数学的基础。借助这些帮助,他很快阅读了天文学和光学方面的主要著作,以及……力学、气体力学和流体静力学方面的著作。他在这些科学中取得的可观进展自然而然地把他引向了剑桥大学……
马斯基林于1749年11月进入剑桥大学圣凯瑟琳学院。次年夏天,他转到彭布罗克学院,1752年再次转学,这次转到三一学院,在那里学习数学荣誉学位考试课程,并于1754年获得文学学士学位。他在数学荣誉学位考试中排名第七数学荣誉学位考试一等及格者(Wrangler)。为了获得 fellowship,他于1755年被任命为牧师,成为赫特福德郡奇平巴尼特的助理牧师。然后,他于1756年成为剑桥大学三一学院的 fellow。此时,他与詹姆斯·布拉德利保持着密切联系,后者是牛津大学的萨维尔天文学教授和皇家天文学家。马斯基林在与詹姆斯·布拉德利共事中学到了很多,并协助他制作了一份折射表。
在詹姆斯·布拉德利作为其支持者之一的情况下,1758年4月27日,马斯基林被接纳加入伦敦皇家学会,他的推荐信描述他为
……一位精通数学学习和自然哲学的人……
1760年7月14日,Royal Society同意派遣马斯基林前往圣赫勒拿岛观测将于1761年6月6日发生的金星中天。马斯基林此前曾提议同一探险队应尝试测量天狼星的视差。
马斯基林视差提案的摘录见THIS LINK
这次金星凌日很重要,因为精确的测量将使得地球到太阳的距离能够被精确测量,并确定太阳系的尺度。他于1761年1月18日乘坐亨利王子号船启航。在航行期间,他使用托比亚斯·梅耶制作的月球表,试验了通过月球位置确定经度的方法。他于1761年4月6日抵达圣赫勒拿岛,有充足的时间寻找良好的观测地点并架设仪器。遗憾的是,6月6日多云,他无法对凌日进行测量。他在圣赫勒拿岛花了几个月时间试图计算天狼星的视差,但最终认定他的仪器有故障。失望之余,马斯基林于1762年2月乘坐沃里克号船启航返回英格兰。5月15日抵达普利茅斯后,他回到奇平巴尼特,在那里担任助理牧师,并致力于出版一本书。他在The British Mariner's Guide(1763年)中发表了通过月球距离确定经度的方法,其中还收录了托比亚斯·梅耶的表。
1763年,他乘船前往巴巴多斯,对约翰哈里森的计时器H4进行测试。马斯基林虽然不是经度委员会的成员——该委员会负责评估计算经度的方法,并为此提供巨额奖金——但被认为是一位合适的评判者,因为他能够利用木星的卫星精确计算巴巴多斯的经度,并将这一精确结果与哈里森的H4所给出的结果以及他的月距法所给出的结果进行比较。马斯基林于9月23日作为随船牧师乘坐HMS Princess Louisa号航行,于11月7日抵达巴巴多斯的布里奇敦。威廉·哈里森,即约翰哈里森之子,于1764年5月13日携计时器H4抵达。他反对马斯基林参与H4的测试,因为马斯基林正在推崇他自己的月距法。他们就由谁进行测量达成了妥协,测试得以进行。哈里森的H4表现最佳,误差约为10英里,而月距法产生的误差约为30英里。回到英格兰后,他于1764年12月20日向皇家学会提交了结果。1765年2月9日,经度委员会批准了哈里森的H4和月距法。
返回后不久,于1765年2月26日,他被任命为皇家天文学家,接替纳森尼尔·布利斯,后者在任仅两年后于1764年9月去世。在马斯基林之前担任皇家天文学家的所有四人都以最低薪水担任此职,作为有独立收入的人。另一方面,马斯基林获得了薪水,使该职位成为他的主要职业(每年350英镑)。这产生了使他的观测成为公共财产的效果,而早期的职位持有者则认为他们的观测是私人财产。他于1766年12月出版了Nautical Almanac的第一卷,并继续从事这个项目直到去世。最初目的是提供表格,以便通过月距法计算经度[15]:-
[航海天文历]的基本特征是一张月球距离表,计算精度为1角秒,覆盖全年[1767年]每三小时间隔,并辅以马斯基林自己整理的其他必要表格、解释、说明和示例。困难由此减少到计算本地时间——相当于找到方位角——以及校正观测到的月球距离(通过天文历中描述的两种方法之一)以考虑折射和视差的影响。
马斯基林在格林尼治天文台担任皇家天文学家期间所做的工作,由Mary Croarken描述如下[8]:-
格林尼治的主要工作是观测太阳、月球、行星和恒星的位置,并公布这些数据。这是一项相当繁重的任务,因为不仅需要进行观测,而且常常是在夜间进行,还需要对观测数据进行归算,即修正折射、视差、仪器误差等等,并且必须誊写一份清稿。为了完成这些职责中的大部分,马斯基林雇用了一名助手。……马斯基林与他的许多科学界同代人一样,是英格兰教会按立的牧师,每年都要去他在威尔特郡的教区住所,并定期参加皇家学会以及伦敦的其他会议,他在那里是科学界体制内的重要一员。实际上,这意味着他的助手要承担大部分观测工作,尽管平心而论,观测记录簿显示马斯基林在驻地时也经常进行观测。
同样在[18]中,还有一段关于马斯基林对其助手所要求技能的有趣描述,这是他在1787年写下的:-
要懂得算术、几何、代数、平面三角学和球面三角学以及对数;要有好的眼力和好的听力,发育良好,体格健壮,使他能够在白天花几个小时进行计算,并能起床进行深夜发生的观测。要写得一手好字,并且是一名敏捷而稳定的算术计算者。如果他懂一些天文学并且有机械方面的才能,那就更好了。要清醒勤勉,能够忍受禁闭。年龄在20到40岁之间。
当然,马斯基林被任命为皇家天文学家对约翰 Harrison来说是一个打击,因为他认为马斯基林是他在经度奖上的主要竞争对手。成为皇家天文学家意味着马斯基林成为经度委员会[11]的成员:-
……由此产生的关于H4的报告完全是否定的。看来马斯基林在“精度”的含义上含糊其辞,以谴责Harrison的发明。在这个时代,所有时钟都会以某种速率走快或走慢,但只要该速率恒定且已知,人们就可以得出准确的时间。马斯基林拒绝允许这些修正。
哈里森于1776年去世,至死都认为马斯基林在对H4的评判中有失偏颇。
马斯基林于1772年向皇家学会提议,用铅垂线进行一项测定地球密度的实验。他并非第一个提出此类实验的人。皮埃尔·布格和夏尔·马里·德·拉孔达米纳在30多年前就尝试过这样的实验。Royal Society成立了山体引力委员会,派遣多位科学家在英格兰和苏格兰寻找合适的山体,这些山体必须:-
……高度足够,与其他山丘有一定距离,且东西向长度明显大于南北向。
马斯基林在获得国王乔治二世准许其离开格林威治的职务后,于1774年在苏格兰珀斯郡的希哈利恩山进行了实验。山体引力委员会之所以选择希哈利恩山,是因为它的形状出奇地规则且呈锥形,因此可以准确测定其体积。他在山的南侧建立了一座天文台,标定了一条子午线,架设了一条与望远镜相连的铅垂线,并在39颗恒星穿过子午线时进行了169次观测[5]:-
每颗恒星距“天顶”(由铅垂线指示)的角距离都被极为仔细地记录下来。
完成这些观测后,他在山的北侧建立了一座天文台,并进行了类似的一系列观测。根据这些必须经过折射、岁差、光行差、偏差和章动校正的观测,马斯基林计算出铅垂线被山体的引力吸引偏转了11.7″。由此他推断出地球的密度约为水的4.5倍。1775年,他因这项工作被授予皇家学会的科普利奖章:-
关于山体引力的奇特而费力的观测。
他关于这一主题的论文摘录见THIS LINK。
我们已经注意到,马斯基林于1755年被授予圣职。1768年,他被剑桥大学授予神学学士学位,并于1775年获得什罗普郡什拉沃丁的圣职俸禄。他的兄弟威廉于1772年去世,马斯基林此时继承了威尔特郡珀顿斯托克的庞德农场。1777年,他被剑桥大学授予神学博士学位,并于1782年由三一学院授予诺福克郡北朗克顿的圣职俸禄。他于1784年8月21日在霍尔本的圣安德鲁教堂与索菲亚·罗斯(1752—1821)结婚,她是北安普敦郡科特斯托克的约翰佩特·罗斯的次女。他们有一个女儿玛格丽特(1785年6月27日生于格林尼治)。婚后,马斯克林一家常把庞德农场用作乡间隐居之所。
我们提及马斯基林工作的另外几个方面:
至于他的性格,他被描述为[4]:-
……彬彬有礼、精明且讨人喜欢(尤其是当你恰好站在他一边时)。作为乡绅阶层的马斯基林家族中的一员,并且是印度克莱夫的妹夫,他深知自己在有序社会中的位置,并且在绅士科学家和水手的世界中是个机敏的推动者。
Derek Howse写道[1]:-
大量幸存下来的通信证据表明,尽管在有些人看来他可能显得浮夸且有点令人厌烦,但马斯基林几乎普遍受到同时代人的喜爱和钦佩——也许计时器制造商及其家人除外。在一些二十世纪的通俗书籍中,马斯基林被描绘成一个邪恶的天才,出于个人怨恨以及因为他自己参与了与之竞争的月距法测定经度,试图剥夺那位可怜的文盲木匠应得的奖励——这种名声在他自己的时代肯定不是普遍持有的,现代研究也完全不能证明其正当性:他是经度委员会的成员,由议会任命,负责就大笔公共资金的授予提供建议;没有任何证据表明他曾在任何时候滥用其公职身份,更不用说中饱私囊了。
马斯基林因其贡献而受到世界各地许多学会和科学院的荣誉。他当选为美国艺术与科学院、Paris Academy of Sciences、汉诺威科学院以及俄罗斯和波兰的科学院的成员。
Nevil Maskelyne's father, Edmund Maskelyne, was a practising barrister-at-law and Counsel to the Secretary of State's Office. He lived at Purton Down, Wiltshire, England. Edmund Maskelyne married Elizabeth Booth, daughter of John Booth and Elizabeth Proger, on 4 February 1724. They had four children, William Maskelyne (1725-1772), Edmund Maskelyne (1728-1775), Nevil Maskelyne (the subject of this biography), and Margaret Maskelyne (1735-1817). Nevil Maskelyne wrote autobiographical notes in 1800 in which he gave some information about the origins of the family. He said he was (see for example [1]):-
... the last male heir of an ancient family long settled at Purton in the County of Wiltshire, which from the name probably came from Normandy, where there is or was 50 years ago a family of that name Masqueline.
All four children were born in Kensington but, in 1736, the family moved to Tothill Street, Westminster. This meant that the two eldest boys, William and Edmund, were close to Westminster School where they were pupils and their father, Edmund Sr., was close to his place of work. In January 1741 Nevil began his education at Westminster School. Edmund Sr., died in March 1744 when Nevil was 12 years old leaving the family rather poor. Nevil was still being educated at Westminster School when his mother Elizabeth died in 1748. After this Nevil boarded at Vincent Bourne's house in Westminster while he continued his school education. Just before the death of his mother his interest in astronomy had begun after seeing the eclipse of 25 July 1748. Maskelyne writing about his school education said (see for example [1]):-
Great mathematicians have become astronomers from the facility mathematics gave them in the attainment of astronomy; but here the love of astronomy was the motive of application to mathematics without which our astronomer soon found he could not make the progress he wished in his favourite science; in a few months, without any assistance he made himself master of the elements of geometry and algebra. With these helps he soon read the principal books in astronomy and optics and also in ... mechanics, pneumatics and hydrostatics. The considerable progress he had made in these sciences led him naturally to the University of Cambridge...
Maskelyne entered St Catharine's College, Cambridge in November 1749. In the summer of the following year he moved to Pembroke College and in 1752 he moved again, this time to Trinity College where he studied the mathematical tripos and graduated with a B.A. in 1754. He was ranked as seventh wrangler in the mathematical tripos. As part of his move to gain a fellowship, he was ordained a minister in 1755, becoming a curate at Chipping Barnet in Hertfordshire. Then he became a fellow of Trinity College, Cambridge in 1756. By this time he was in close contact with James Bradley who was the Savilian professor of astronomy at Oxford and the Astronomer Royal. Maskelyne learned much from working with Bradley and assisted him in producing a table of refractions.
With Bradley as one of his supporters, on 27 April 1758 Maskelyne was admitted to the Royal Society of London, his recommendation describing him as
... a person well versed in mathematical learning and natural philosophy ...
On 14 July 1760 the Royal Society agreed to send Maskelyne to the island of St Helena to observe a transit of Venus which would take place on 6 June 1761. Maskelyne had earlier proposed that the same expedition should try to measure the parallax of the star Sirius.
An extract from Maskelyne's parallax proposal is at THIS LINK
This Venus transit was important since accurate measurements would allow the distance from the Earth to the Sun to be accurately measured and the scale of the solar system determined. He set sail on the ship Prince Henry on 18 January 1761. During the voyage he experimented with the lunar position method of determining longitude using the lunar tables produced by Tobias Mayer. He arrived in St Helena on 6 April 1761 in plenty of time to find a good site for observing and to set up his instruments. Sadly, the 6 June was cloudy and he was unable to make measurements of the transit. He spent several months on St Helena trying to compute the parallax of Sirius but eventually decided that his instruments were faulty. Disappointed, Maskelyne set sail for England on the ship Warwick in February 1762. Reaching Plymouth on 15 May, he went back to Chipping Barnet, where he was a curate, and worked on publishing a book. He published the lunar distance method for determining longitude in The British Mariner's Guide (1763) where he also included Tobias Mayer's tables.
In 1763 he went on a voyage to Barbados to carry out trials of John Harrison's timepiece H4. Maskelyne, although not a member of the Board of Longitude who were evaluating methods of computing longitude for which a large prize was on offer, was considered a suitable judge since he could compute the longitude of Barbados accurately using Jupiter's satellites, and compare this accurate result with that given by Harrison's H4 and also the result given by his lunar distance method. Maskelyne sailed on the HMS Princess Louisa on 23 September as the ship's chaplain reaching Bridgetown, Barbados, on 7 November. William Harrison, John Harrison's son, arrived with the timepiece H4 on 13 May 1764. He objected to Maskelyne's involvement in the H4 trials since Maskelyne was championing his own lunar distances method. They agreed a compromise in terms of who made the measurements and the trials were carried out. Harrison's H4 came out best with an error of around 10 miles, with the lunar distance method producing an error of around 30 miles. Back in England, he presented the results to the Royal Society on 20 December 1764. On 9 February 1765 the Board of Longitude gave its approval to both Harrison's H4 and to the lunar distance method.
Soon after his return, on 26 February 1765, he was appointed Astronomer Royal to succeed Nathaniel Bliss who had only held the post for two years when he died in September 1764. All four men to hold the post of Astronomer Royal before Maskelyne had done so with minimal salary as people of independent means. Maskelyne, on the other hand, was given a salary to make the post his main occupation (£350 per annum). This had the effect of making his observations public property whereas the earlier holders of the post considered their observations their private property. He published the first volume of the Nautical Almanac in December 1766 and continued to work on this project up to the time of his death. The original purpose was to present tables to allow longitude to be computed by the lunar distance method [15]:-
[The Nautical Almanac's] essential feature was a table of lunar distances computed to a nominal precision of 1" for three-hourly intervals throughout the year [of 1767], supplemented by additional requisite tables, explanations, instructions and examples worked out by Maskelyne himself. The difficulties were thereby reduced to the computation of local time-equivalent to finding an azimuth - and the correction of the observed lunar distances (by means of either of two methods described in the almanac) for the effects of refraction and parallax.
The work that Maskelyne carried out as Astronomer Royal at the Greenwich Observatory is described by Mary Croarken [8]:-
The principal work at Greenwich was to observe the positions of the Sun, Moon, planets and stars and to publish these data. This was a considerable undertaking because not only did the observations need to made, frequently at night, but they also needed to be reduced, i.e. corrected for refraction, parallax, instrument error, and so on, and a fair copy had to be made. To perform most of these duties Maskelyne hired an assistant. ... Maskelyne, like many of his scientific contemporaries an ordained minister of the Church of England, annually visited his parish living in Wiltshire and regularly attended Royal Society and other meetings in London, where he was very much part of the scientific establishment. In practice this meant that his assistant was expected to carry most of the observing load, although in fairness the observing books show that Maskelyne also regularly observed when in residence.
Also in [18] there is an interesting description of the skills Maskelyne required of his assistants, set down by him in 1787:-
To understand Arithmetic, Geometry, Algebra, Plane and Spherical Trigonometry, and Logarithms; to have a good eye and good ears, be well grown, and have a good constitution to enable him to apply several hours in the day to calculation, and to get up to the observations that happen at late hours in the night. To write a good hand, and be a ready and steady arithmetical computer. If he know something of Astronomy and had a mechanical turn so much the better. To be sober and diligent, and able to bear confinement. Age from 20 to 40.
Of course, Maskelyne's appointment as Astronomer Royal was rather a blow to John Harrison who considered him his major competitor for the longitude prize. Being Astronomer Royal meant that Maskelyne became a member of the Board of Longitude [11]:-
... the resulting report on H4 was entirely negative. It seems Maskelyne prevaricated over the meaning of "accuracy" to condemn Harrison's creation. In this era, all clocks gained or lost time at some rate, but so long as that rate was constant and known, one could derive an accurate time. Maskelyne refused to allow these corrections.
Harrison died in 1776 believing to the end that Maskelyne was biased in his judgement of H4.
Maskelyne proposed to the Royal Society in 1772, an experiment for determining the Earth's density with the use of a plumb line. He was not the first to suggest such an experiment. Bouguer and La Condamine had tried such an experiment over 30 years before. The Royal Society set up the Committee for the Attraction of Mountains which sent various scientists to seek suitable mountains in England and Scotland which had to be:-
... of sufficient height, tolerably detached from other hills, and considerably larger from East to West than from North to South.
Maskelyne, after seeking permission from King George II to be absent from his duties at Greenwich, carried out the experiment in 1774 on Schiehallion, a mountain in Perthshire, Scotland. Schiehallion was chosen by the Committee for the Attraction of Mountains because it was surprisingly regular and conical in shape so its volume could be determined accurately. He set up an observatory on the south side of the mountain, marked a meridian line, set up a plumb-line linked to a telescope and observed 39 stars with 169 observations as they crossed the meridian [5]:-
The angular distance of each star from the "zenith" (as indicated by the plumb-line) was noted with great care.
After making these observations, he set up an observatory on the north side of the mountain and made a similar series of observations. From his observations, which had to be corrected for refraction, precession, aberration, deviation and nutation, Maskelyne computed that the plumb-line was pulled 11.7" by the gravitational attraction of the mountain. From that he deduced that the Earth's density is approximately 4.5 times that of water. He was awarded the Copley medal of the Royal Society in 1775 for his:-
Curious and Laborious Observations on the Attraction of Mountains.
Excerpts from his papers on this subject are given at THIS LINK.
We have noted that Maskelyne was ordained in 1755. In 1768 he was awarded the degree of bachelor of divinity by the University of Cambridge and, in 1775, he was given the living of Shrawardine in Shropshire. His brother William died in 1772 and Maskelyne inherited Pond's Farm, Purton Stoke, Wiltshire at this time. In 1777 he was awarded the degree of doctor of divinity by the University of Cambridge and, in 1782, he was given the living of North Runcton, Norfolk by Trinity College. He married Sophia Rose (1752-1821), the second daughter of John Pate Rose of Cotterstock, Northamptonshire, on 21 August 1784 in St Andrew's, Holborn. They had a daughter Margaret (born at Greenwich on 27 June 1785). After their marriage, the Maskelynes made much use of Pond's Farm as a country retreat.
We mention a few other aspects of Maskelyne's work:
As to his character he is described as [4]:-
... urbane, shrewd and likeable (especially if one happened to be on his side). As one of a line of squirearchial Nevil Maskelynes and brother-in-law to Clive of India, he knew his place in an ordered society and was an adroit mover in a world of gentlemen scientists and sailors.
Derek Howse writes [1]:-
The evidence from the large body of correspondence that has survived proves that, pompous and a bit of a bore as he might have seemed to some, Maskelyne was almost universally liked and admired by his contemporaries - except perhaps by some chronometer makers and their families. The reputation that survives in some popular twentieth-century books of Maskelyne as the evil genius who tried to deprive the poor illiterate carpenter of his just rewards-out of personal spite and because of his own involvement in the rival lunar-distance method of finding longitude-was certainly not one that was held generally in his own day, nor is it in any way justified by modern research: he was a member of the board of longitude, appointed by parliament to advise on the award of large sums of public money; there is no evidence whatsoever that he at any time abused his position as a public servant, still less lined his own pocket.
Maskelyne was honoured for his contributions by many societies and academies throughout the world. He was elected to the American Academy of Arts and Sciences, the Paris Academy of Sciences, the Hanover Academy of Sciences and academies in Russia and Poland.
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