威廉・赫歇尔：从音乐家到天文学家的转型 —— 18 世纪科学学习的隐性能量

注：本文为 “自学转型的隐性能量” 相关翻译。
英文引文，机翻未校。

---

PHILOMATHS, HERSCHEL, AND THE MYTH OF THE SELF-TAUGHT MAN

爱智者、赫歇尔与自学成才者的神话

by EMILY WINTERBURN*
作者：艾米丽·温特本（*）

School of Philosophy, Religion and History of Science, University of Leeds, Leeds LS2 9JT, UK
英国利兹大学哲学、宗教与科学史学院，利兹，LS2 9JT

NOTES& RECORDS THE ROYAL SOCIETY JOURNAL OF THE HISTORY OF SCIENCE
《笔记与记录——英国皇家学会科学史期刊》

CrossMark
CrossMark 标识（用于追踪文献更新）

dick for updates
查询更新

Notes Rec. (2014) 68, 207–225
《笔记与记录》（2014），第 68 卷，207-225 页

doi:10.1098/rsnr.2014.0027
数字对象标识符：10.1098/rsnr.2014.0027

Published online 25 June 2014
在线出版时间：2014 年 6 月 25 日

The role of technicians and background characters in the historical practice of science is slowly gaining recognition. This paper looks at the collective effort involved in learning science, using as my case study the eighteenth-century musician turned astronomer, William Herschel. Lacking a university education, Herschel, like many contemporaries, presented himself as self-taught, thereby hiding his engagement with a rich network of didactic resources. Placing Herschel’s story within the history of pedagogy, I argue that this network, previously discussed only in the context of popular or marketplace science, was an important resource for science education at its highest level.
在科学的历史实践中，技术人员与幕后人物的作用正逐渐获得认可。本文以 18 世纪从音乐家转型为天文学家的威廉·赫歇尔（William Herschel）为案例，探讨科学学习过程中所涉及的集体努力。由于未接受过大学教育，赫歇尔与许多同时代人一样，将自己塑造为“自学成才者”，但这一身份掩盖了他对庞大教学资源网络的利用。将赫歇尔的经历置于教育学史背景下分析可发现，这一此前仅被视为大众科学或市场科学范畴的资源网络，实则是高层次科学教育的重要支撑。

Keywords: Herschel; education; philomath; fluxions; instrument maker
关键词：赫歇尔；教育；爱智者（philomath）；流数术（fluxions）；仪器制造者

The heroic tale of William Herschel the musician, who taught himself astronomy, discovered Uranus and founded modern sidereal astronomy, is well known.¹ Nevertheless, recent work in the history of pedagogy, and in particular recent analysis of the work carried out by technicians and assistants, suggests new ways of understanding the claim that William Herschel was self-taught in astronomy.
音乐家威廉·赫歇尔自学天文学、发现天王星（Uranus）并创立现代恒星天文学的英雄叙事广为人知。¹ 然而，近年来教育学史领域的研究——尤其是对技术人员与助手工作的最新分析——为理解“赫歇尔天文学自学成才”这一说法提供了新视角。

Eighteenth-century practitioners of science such as the instrument maker James Ferguson, and members of the Lunar Society such as James Watt are, like Herschel, often described as self-taught.² In this paper I question what such claims meant in practice by looking in detail at the way in which William Herschel used resources at his disposal to become an accomplished practitioner in several different fields.
18 世纪的科学从业者，如仪器制造者詹姆斯·弗格森（James Ferguson）、月光学会（Lunar Society）成员詹姆斯·瓦特（James Watt）等，都与赫歇尔一样常被描述为“自学成才者”。² 本文通过详细分析威廉·赫歇尔如何利用可及资源成为多个领域的资深从业者，探究“自学成才”这一表述在实际中的含义。

The special edition of Notes and Records on ‘Technicians’ (volume 62, part 1; 2008) has revealed a rich hidden world behind each practitioner of science. In Hannah Gay’s article, for example, she identifies roles not only for collaborators and assistants but also for all those on the periphery: the tradesmen, technicians and outside contractors.³ A similar story of hidden contributors can be built around education. Already, some research has uncovered the complex processes involved in becoming a practitioner of science. The historians of scientific pedagogy Andrew Warwick and David Kaiser have shown some of the ways in which nineteenth-century and twentieth-century scientists and engineers were trained.⁴ That work, however, focused on formal training institutions and more specifically on university education.
《笔记与记录》杂志“技术人员”专题特刊（第 62 卷第 1 部分，2008 年）揭示了每位科学从业者背后庞大的隐性世界。例如，汉娜·盖伊（Hannah Gay）在其文章中不仅明确了合作者与助手的角色，还提及了所有外围参与者：商人、技术人员与外部承包商。³ 教育领域同样存在类似的“隐性贡献者”叙事。已有研究揭示了成为科学从业者所需的复杂过程：科学教育史学家安德鲁·沃里克（Andrew Warwick）与大卫·凯泽（David Kaiser）阐述了 19 至 20 世纪科学家与工程师的部分培养方式。⁴ 然而，这些研究聚焦于正规培训机构，尤其侧重于大学教育。

*ewinterburn1974@gmail.com
*电子邮箱：ewinterburn1974@gmail.com

Dr Winterburn’s article was the winner of the 2014 Notes and Records Essay Award, open to young researchers in the history of science who have completed a postgraduate degree within the past five years.
温特本博士的文章获得了 2014 年《笔记与记录》论文奖。该奖项面向过去五年内获得研究生学位的青年科学史研究者。

207 © 2014 The Author(s) Published by the Royal Society.
207 © 2014 作者。由英国皇家学会出版。

on March 29, 2015 http://rsnr.royalsocietypublishing.org/ Downloaded from
2015 年 3 月 29 日 从 http://rsnr.royalsocietypublishing.org/ 下载

208
E. Winterburn
E. 温特本

In the eighteenth century a university education was much less common and by no means the only route to becoming an active member of the scientific elite. Alternative resources were available for studying and participating in science, including books, journals, lectures and societies.⁵ This ‘marketplace’ for science has been the subject of several articles and monographs, but the emphasis in those studies was on science for public consumption rather than as a resource for training aspiring natural philosophers.⁶ Using the example of William Herschel I show how these resources could have been, and indeed were, used to fashion the education of a future astronomer, natural philosopher and instrument maker.
18 世纪的大学教育远不普及，且绝非成为科学精英核心成员的唯一途径。当时存在多种可供学习与参与科学的替代资源，包括书籍、期刊、讲座与学会。⁵ 这一科学“市场”已成为多篇论文与专著的研究对象，但这些研究多聚焦于“面向公众消费的科学”，而非将其视为培养未来自然哲学家的资源。⁶ 本文以威廉·赫歇尔为例，说明这些资源如何（且事实上确实）被用于构建一名未来天文学家、自然哲学家与仪器制造者的知识体系。

LEARNING HOW TO LEARN

学习如何学习

William Herschel gave several accounts of his childhood after his 1781 discovery of Uranus; he also kept a ‘memorandum of his life’. In addition, his sister Caroline gave various accounts of her and her brother’s lives, including their childhood together. From these records a picture emerges of a family conditioned to understand education as above all a means of social advancement. However, it was also a training that taught William how expertise is gained.
1781 年发现天王星后，威廉·赫歇尔多次提及自己的童年经历，还留存了一份“人生备忘录”（memorandum of his life）。此外，他的妹妹卡罗琳·赫歇尔（Caroline Herschel）也对兄妹二人的生活（包括共同的童年）进行了多方面记述。从这些资料中可看出，赫歇尔一家将教育视为社会阶层提升的首要途径。不仅如此，这种家庭环境还培养了威廉获取专业技能的能力。

William Herschel and his siblings grew up in Hanover. Although there are no extant records of their family finances, Caroline’s accounts cite several incidents that suggest they were not well off. They moved house frequently for financial reasons, often sharing with other families. She and her mother made the family’s clothes, bed linen, meals and so on, and took in sewing to supplement the family income. At the same time she recorded her parents’ refusal to allow her to train to become a lady’s maid, a fact that suggests a concern with appearances and status.
威廉·赫歇尔与兄弟姐妹在汉诺威（Hanover）长大。尽管没有现存的家庭财务记录，但卡罗琳的记述中提及多个事件，表明家庭经济并不宽裕：因经济原因频繁搬家，且常与其他家庭合租；卡罗琳与母亲需承担全家的衣物制作、床品缝制、膳食烹饪等事务，还需承接缝纫活补贴家用。与此同时，卡罗琳记载父母拒绝让她接受侍女培训——这一细节反映出家人对社会形象与地位的重视。

Their father, Isaac, had avoided following his own father into gardening by using education (learning music) to raise his status and change his opportunities. He became an army musician, for the Hanoverian Guards, but he had higher ambitions for his children. Caroline recalled that their father’s greatest hope was to ‘see his children arrive at that eminence in this his favourite science [music], which he himself had not had the opportunity or time to attain.’⁷ According to William it was ‘my father’s greatest attachment to music [which] determined him to endeavour to make all his sons complete Musicians.’⁸
他们的父亲艾萨克·赫歇尔（Isaac Herschel）通过教育（学习音乐）提升社会地位、改变人生机遇，避免了子承父业成为园丁的命运。艾萨克成为汉诺威卫队（Hanoverian Guards）的军乐手，但他对子女抱有更高期望。卡罗琳回忆道，父亲最大的愿望是“看到孩子们在他最喜爱的学科[音乐]领域达到他自己因缺乏机会与时间而未能企及的高度”。⁷ 威廉则表示，“父亲对音乐的极度热爱，促使他致力于将所有儿子培养成专业的音乐家”。⁸

Isaac’s ambition for his children meant that he taught music to his sons, Jacob, William, Alexander and Dietrich. William was taught ‘to play on the violin as soon as I was able to hold a small one made on purpose for me.’ When Isaac was at home he gave the boys lessons. When he was away (which was often and for long periods) Anna, their mother, ensured they practised. This arrangement taught William not merely how to play but also how to acquire expertise, and he soon realized that long intense periods of repetitive practice were essential. Aged 14 years, after an audition, William became a musician in the Hanoverian Guards.
艾萨克对子女的期望促使他亲自教授儿子们（雅各布、威廉、亚历山大与迪特里希）音乐。威廉回忆：“我刚能握住一把为我特制的小小提琴时，父亲就开始教我拉琴了。”艾萨克在家时会亲自授课；外出时（这种情况频繁且持续时间长），母亲安娜（Anna）则会监督孩子们练习。这种培养模式不仅教会威廉演奏技巧，更让他掌握了获取专业能力的方法——他很快意识到，长时间高强度的重复性练习至关重要。14 岁时，威廉通过试镜成为汉诺威卫队的军乐手。

Alongside music practice, William and his siblings went to the local garrison school to study ‘basic literacy, arithmetic and religion’.⁹ Towards the end of his schooling, William took additional private lessons in French. In some accounts he claimed that his father instigated and paid for the lessons to improve his prospects as a musician; in others of emphasized his own agency in the process.¹⁰ Either way, the lessons were encouraged. They were not useful for someone aiming at the status of army musician, but they were essential for an aspiring musician at Court, where French opera and singing lessons were popular.
除音乐练习外，威廉与兄弟姐妹还在当地卫戍学校（garrison school）学习“基础读写、算术与宗教知识”。⁹ 学业末期，威廉额外参加了法语私教课程。在部分记述中，他称是父亲提议并支付学费，以提升他作为音乐家的发展前景；而在另一些记述中，他则强调自己在选课过程中的主动性。¹⁰ 无论如何，家人对这些课程均持支持态度。对于目标是成为军乐手的人而言，法语或许无用，但对于渴望进入宫廷的音乐家来说，法语至关重要——当时宫廷中法语歌剧与法语声乐课程十分盛行。

Philosophy and instrument making were similarly non-vocational lessons encouraged in this family. William stated that it was his French teacher who encouraged ‘the taste he found in his pupil for the study of philosophy, especially logic, ethics and metaphysics which were his own favourite pursuits.’¹¹ According to Caroline these philosophical discussions were also encouraged at home, where their older brother and father often joined in. As Caroline (then aged 6 years) remembered: ‘the names of Leibnitz, Newton and Euler’¹² were often quoted.
哲学与仪器制作同样是这个家庭鼓励的非职业性学习内容。威廉表示，他的法语老师发现他对哲学研究的兴趣后，“鼓励他深入学习——尤其是老师自己最喜爱的逻辑学、伦理学与形而上学领域”。¹¹ 据卡罗琳回忆，家庭中也常开展哲学讨论，哥哥与父亲经常参与其中。正如当时 6 岁的卡罗琳所记：“莱布尼茨（Leibnitz）、牛顿（Newton）与欧拉（Euler）的名字”¹² 是家中的常用语。

Caroline also mentioned activities concerned with instrument making several times in her description of family life, referring to William’s ‘self constructed Globes &c &c’¹³. Elsewhere she wrote of their brother Alexander, who ‘often sat by us and amused himself with making all sorts of things on pasteboard, or contriving how to make a twelve-hour cuckoo clock go a week.’¹⁴ This occupation was by no means unusual. James Ferguson, James Watt, Alexander Cummings and David Rittenhouse all later recalled having pursued instrument making as a hobby in childhood.¹⁵ Like Herschel, they all developed this hobby professionally as adults, a fact that helps to explain the inclusion of these reminiscences in their biographical notes.
卡罗琳在描述家庭生活时，也多次提及仪器制作相关活动，提到威廉“自行制作地球仪等物品”¹³。在其他记述中，她写道弟弟亚历山大“常坐在我们身边，要么用纸板制作各种小物件，要么琢磨如何让一台 12 小时报时的布谷鸟钟能运行一周”。¹⁴ 这种爱好在当时并不罕见：詹姆斯·弗格森、詹姆斯·瓦特、亚历山大·卡明斯（Alexander Cummings）与大卫·里滕豪斯（David Rittenhouse）日后均回忆称，童年时曾将仪器制作作为爱好。¹⁵ 与赫歇尔一样，他们成年后都将这一爱好发展为职业——这也解释了为何他们的传记中会包含这些童年回忆。

All three subjects-French, philosophy and instrument making-were learned with the help and encouragement of teachers and family. They were valued in this family primarily because learning and education were seen as a means of facilitating social mobility. French was useful for teaching French opera, philosophy came from the interests of a teacher, and instrument making was perhaps just popular at the time. It may also have come out of skills they acquired repairing their own musical instruments.
法语、哲学与仪器制作这三门学科的学习，均得到老师与家人的帮助和鼓励。它们在家庭中受重视的核心原因在于：学习与教育被视为实现社会流动的途径。法语对教授法语歌剧有用；哲学学习源于一位老师的兴趣引导；仪器制作或许是当时的流行爱好，也可能源于他们修理自身乐器时掌握的技能。

William Herschel’s childhood, as seen through diaries and reminiscences, demonstrates the care that must be taken with terms such as self-taught and autodidact. This was no formal training designed to make him a practitioner of science; nevertheless he was being trained-in part at home-to become a professional musician. Through family and teachers he was taught to value education; he was also shown how to learn and gain expertise. It is in these lessons that we begin to see what he meant by self-taught. That is, that his agency in the process came about not through isolated study but through his choices and active pursuit of tutors.
从日记与回忆录中呈现的威廉·赫歇尔童年经历可看出，使用“自学成才者”（self-taught）与“自学者”（autodidact）这类术语时需格外谨慎。赫歇尔并未接受过旨在成为科学从业者的正规训练，但他确实在家庭等环境中接受了成为专业音乐家的培养。家人与老师不仅让他认识到教育的价值，还教会他如何学习与获取专业技能。正是从这些经历中，我们得以理解他所指的“自学”：这一过程中的主动性并非源于孤立学习，而是源于他对学习内容的选择与对导师的主动追寻。

PHILOSOPHY AND MUSIC AND PHILOMATHS

哲学、音乐与爱智者

One of the reasons I show here why William first began studying natural philosophy was that it was an interest of some of the employers he served as a musician. Natural philosophy was regarded as a polite topic of conversation in England throughout the eighteenth century.¹⁶
本文指出，威廉最初开始研究自然哲学的原因之一，是这一领域恰好是他作为音乐家所服务的部分雇主的兴趣所在。在整个 18 世纪的英国，自然哲学都被视为一种得体的交谈话题。¹⁶

Lawrence Klein has shown how Thomas Parsons studied polite topics to win over clients in his work as a maker and seller of luxury goods, and argued that this led Parsons to engage in a programme of self-education.¹⁷ As a musician, William was in a similar position, serving polite society as an employee, looking for exploitable areas of shared interest. Like Parsons, he found this in natural philosophy.
劳伦斯·克莱因（Lawrence Klein）的研究表明，奢侈品制作与销售商托马斯·帕森斯（Thomas Parsons）通过研究得体话题来争取客户，并认为这一需求促使帕森斯开展了自学计划。¹⁷ 作为音乐家，威廉处于类似处境：他以受雇者身份服务于上流社会，需寻找可利用的共同兴趣领域。与帕森斯一样，他在自然哲学中找到了这一领域。

William and his brother Jacob left Hanover for England in 1757 towards the beginning of the Seven Years’ War. William stayed to find work as a musician. Jacob returned home to a post in the Hanoverian Court Orchestra.¹⁸ There was a growing market for musicians in mid-eighteenth-century England as musical audiences expanded, no longer confined to Court circles. As Cyril Ehrlich has observed, this created a new breed of musician: a jobbing musician, playing concerts and at country homes and giving private music lessons rather than relying on a patron. It was a profession dominated by foreigners, mainly Italian and German, and was one of the few areas that allowed its members to mix in socially elevated circles.¹⁹ Like Thomas Parsons, musicians such as Herschel were dependent on members of this elevated class for work, meaning that there were sound professional reasons for learning their rules of etiquette.
1757 年七年战争（Seven Years’ War）即将爆发之际，威廉与兄长雅各布（Jacob）离开汉诺威前往英国。威廉留在英国寻找音乐相关工作，雅各布则返回故乡，在汉诺威宫廷管弦乐团任职。¹⁸ 18 世纪中期的英国，音乐受众不断扩大，不再局限于宫廷圈层，因此音乐家的市场需求日益增长。正如西里尔·埃利希（Cyril Ehrlich）所指出的，这催生了一种新型音乐家——零工音乐家（jobbing musician）：他们通过举办音乐会、在乡村宅邸演奏、提供私人音乐课程谋生，而非依赖赞助人。这一职业主要由外国人（以意大利人和德国人为主）主导，且是少数能让从业者跻身上流社交圈的领域之一。¹⁹ 与托马斯·帕森斯一样，赫歇尔等音乐家的工作依赖于上流阶层成员，这意味着学习上流社会的礼仪规范具有充分的职业必要性。

Although William makes no mention of how he learned the proper way to conduct himself within this polite society, his later account of training Caroline offers some clues. After William had finished her technical education, teaching her how to sing, how to read music, and so on, he employed a dance teacher to teach her deportment and sent her to London with a fashionable lady friend, Mrs Colebrook.²⁰ In both cases the intention was to teach her presentation skills: how to hold herself and how to act among his musical clients. As a performer and jobbing musician, William needed to learn similar skills.
尽管威廉未提及自己如何学会在上流社会中得体行事，但他日后培养卡罗琳的经历提供了一些线索。威廉完成对卡罗琳的音乐技能培训（教授演唱、识谱等）后，聘请了舞蹈教师教授她仪态，并安排她与一位时髦的女性友人科尔布鲁克夫人（Mrs Colebrook）一同前往伦敦。²⁰ 这两项安排的目的均是教授她社交展示技巧：如何保持体态，以及在威廉的音乐客户面前如何举止。作为表演者与零工音乐家，威廉自身也需要掌握此类技能。

William initially found work in a militia band run by Lord Darlington, but soon he became a jobbing musician, playing concerts and giving music lessons in country homes across the northeast of England. In William’s letters to his brother Jacob he expressed frustration with this role and its lack of security and regular income. When the possibility of a post in Edinburgh came up in 1761, William went to the audition. There he was introduced to and had dinner with the metaphysician David Hume.
威廉最初在达林顿勋爵（Lord Darlington）掌管的民兵乐队工作，但不久后便转型为零工音乐家，在英格兰东北部的乡村宅邸举办音乐会并教授音乐。在写给兄长雅各布的信中，威廉表达了对这份工作的不满——缺乏稳定性与固定收入。1761 年，爱丁堡出现一个职位空缺机会，威廉前往试镜，并在当地经人介绍与形而上学家大卫·休谟（David Hume）共进晚餐。

When William had first arrived in England he had read the philosopher John Locke’s Essay Concerning Human Understanding:²¹ ‘I applied myself to learn the English language and soon was enabled to read Locke on the Human Understanding.’²² Locke’s book described the process of learning and emphasized that it came from practice and repetition. This description, as we have seen, resonated with the way in which William had learned music. After his meeting with Hume, William began to read other philosophical works.
威廉初到英国时，阅读了哲学家约翰·洛克（John Locke）的《人类理解论》（Essay Concerning Human Understanding）：²¹ “我努力学习英语，很快便能阅读洛克的《人类理解论》了。”²² 洛克在书中描述了学习过程，并强调学习源于实践与重复。正如前文所述，这一观点与威廉学习音乐的经历产生了共鸣。与休谟会面后，威廉开始阅读更多哲学著作。

In the early 1760s William read, among others, Leibniz’s Théodicée, William King’s An Essay on the Origin of Evil and Robert Smith’s Harmonics, or the philosophy of musical sounds.²³ Although his correspondence gives us the titles he was reading, it does not explain how he came to acquire those books. By the second half of the eighteenth century a common way of accessing books, more popular certainly than buying them from a bookseller, was to rent them from circulating libraries.²⁴ This would make sense for William at this time, given that he had no permanent base (a point he complained about to his brother) and an uncertain income. By considering where he got his books from, we also get an indication of how he came to choose his titles. Libraries, and the booksellers and agents running them, could recommend titles; they also had catalogues to browse and had carefully organized display shelves.
18 世纪 60 年代初，威廉阅读的著作包括莱布尼茨的《神义论》（Théodicée）、威廉·金（William King）的《论恶的起源》（An Essay on the Origin of Evil）以及罗伯特·史密斯（Robert Smith）的《和声学，或音乐声音的哲学》（Harmonics, or the philosophy of musical sounds）等。²³ 尽管他的书信提及了这些书名，却未说明获取书籍的途径。18 世纪下半叶，获取书籍的常见方式是从流通图书馆（circulating libraries）租借——这种方式无疑比从书店购买更受欢迎。²⁴ 对当时的威廉而言，这一方式合情合理：他没有固定居所（这一点他在信中向兄长抱怨过），收入也不稳定。探究他获取书籍的途径，还能让我们了解他选择读物的方式：图书馆及其经营者（书商与代理人）会推荐书籍，馆内还提供目录供浏览，书架也经过精心整理。

After this reading, in 1764 William began to write his own Treatise on Music.²⁵ This treatise was never published and has never previously been discussed by historians, but in terms of his transformation from musician to natural philosopher it provides a useful insight. This treatise was the first piece of work that William produced that attempted to engage in any form of philosophical writing.
经过这段阅读时期后，威廉于 1764 年开始撰写自己的《音乐论》（Treatise on Music）。²⁵ 该著作从未出版，且此前从未被历史学家讨论过，但对于研究他从音乐家到自然哲学家的转型过程具有重要启示意义——这是威廉首次尝试进行哲学类写作。

The intended content (the contents list is complete but not the extant manuscript) suggests that this treatise was written for his music students. There are, however, aspects of the work that show an attempt to integrate music, with his developing interests in philosophy. Smith’s Harmonics is the only book cited in the treatise, cited once to tell readers where they might learn more on the mathematics of harmonics, and again a few pages later on: ‘For a mathematical Division and account of these intervals see Dr Smiths Harmonics, Art: 1. Sect. II.’²⁶ However, although he cited Smith, he also argued against Smith’s attempt to reduce music to mathematical rules:
从计划内容（目录完整，但现存手稿不完整）来看，这部著作是为他的音乐学生撰写的。然而，书中部分内容显示，威廉试图将音乐与自己日益增长的哲学兴趣相结合。史密斯的《和声学》是书中唯一引用的著作：第一次引用是为了告知读者可在何处深入学习和声学的数学原理，几页后再次引用：“关于这些音程的数学划分与说明，参见史密斯博士的《和声学》，第 1 章第 2 节（Art: 1. Sect. II）。”²⁶ 尽管引用了史密斯的著作，威廉却反驳了史密斯试图将音乐简化为数学规则的做法：

But let us even suppose (which wants confirmation) that the degrees of pleasure arising from musical sounds answer’d perfectly the order of the simplicity of the ratios . . . [still we do not know] why those ratios were agreeable and so forth . . . Music is a kind of natural philosophy where we reason best from Experience, and matters of fact are often the best and clearest arguments we can bring.²⁷
“即便我们假设（这一假设尚需证实）音乐声音所带来的愉悦程度与比率的简洁性顺序完全一致……[我们仍无法知晓]为何这些比率会令人愉悦，等等……音乐是自然哲学的一种形式，在这一领域中，我们通过经验进行推理最为有效，而事实依据往往是我们能提出的最有力、最清晰的论据。”²⁷

Here, his analysis has elements of Locke, such as his claim that the best way to appreciate music is from experience. Mostly, however, this passage shows William’s unwillingness to reduce music to mathematics.
此处的分析体现了洛克思想的影响，例如他认为欣赏音乐的最佳方式是通过经验。但更重要的是，这段文字表明威廉不愿将音乐简化为数学。

William’s correspondence with his brother over his Treatise on Music suggests that he was working on it around 1764. Up to this point, besides his meeting with Hume, he mentioned discussing philosophy with no one other than his brother. Then, in 1766, William made several references to people, books and activities suggesting he had come into contact with a group known to contemporaries as philomaths.
威廉在与兄长讨论《音乐论》的书信中提及，他在 1764 年前后致力于这部著作的撰写。截至此时，除与休谟会面外，他提及的哲学讨论对象仅有兄长一人。然而到了 1766 年，威廉在书信中多次提及一些人物、书籍与活动，表明他已接触到一个在当时被称为“爱智者”（philomaths）的群体。

Philomaths were the readers and contributors to journals such as the Ladies’ Diary and the Gentleman’s Diary. These journals, as Jon Topham has shown, came as a response to changes in the publishing trade, but also through the enthusiasm of their editors to collate and disseminate new knowledge.²⁸ These philomaths attended lectures and read books, and some owned telescopes with which they might hunt for comets. Shelley Costa has described the readership of the Ladies’ Diary in the mid eighteenth century as typically those from the leisured classes, with the time to ponder mathematical puzzles, and ‘also the luxury of using written correspondence as entertainment’.²⁹ Olaf Pedersen looked at the Gentleman’s Diary readership, concluding that they comprised mainly school teachers and ‘leisured country gentlemen.’³⁰
爱智者群体是《女士日记》（Ladies’ Diary）与《绅士日记》（Gentleman’s Diary）等期刊的读者与撰稿人。正如乔恩·托法姆（Jon Topham）所指出的，这类期刊的出现既是对出版行业变革的回应，也源于编辑们整理与传播新知识的热情。²⁸ 爱智者们会参加讲座、阅读书籍，部分人还拥有望远镜以用于彗星观测。雪莱·科斯塔（Shelley Costa）描述道，18 世纪中期《女士日记》的读者群体以有闲阶层为主，他们既有时间思考数学谜题，“也享有将书面通信作为娱乐方式的条件”。²⁹ 奥拉夫·佩德森（Olaf Pedersen）对《绅士日记》的读者群体进行研究后得出结论：其读者主要由教师与“有闲乡绅”构成。³⁰

Ruth and Peter Wallis’s analysis of eighteenth-century philomaths and philomath culture reveals not only the range of participants but also their broad interests. John Draper’s print (figure 1) gives an indication of the types of subject considered in the eighteenth century to be philomathematical.³¹
露丝·沃利斯（Ruth Wallis）与彼得·沃利斯（Peter Wallis）对 18 世纪爱智者及爱智者文化的分析表明，这一群体不仅参与者范围广泛，兴趣领域也十分多元。约翰·德雷珀（John Draper）的版画（图 1）展示了 18 世纪被视为“爱智学科”（philomathematical）的各类主题。³¹

The Wallises’ description is even more wide-ranging than this diagram suggests, because the range of activities covered includes music and instrument making. William’s journey through these different interests and specialisms places him very definitely in the philomath tradition. The Wallises’ description gives no indication of how homogeneous the philomaths were as a group. William Herschel’s example suggests that some, if not all, philomaths were selective. As we shall see, he moved slowly from one area to another, hesitant at each stage as to how much he could claim regarding his expertise in each new field.
沃利斯夫妇的描述比该图表所呈现的范围更广，因为爱智者的活动领域还包括音乐与仪器制作。威廉在这些不同兴趣与专业领域间的探索轨迹，明确表明他属于爱智者传统。沃利斯夫妇的研究并未说明爱智者群体的同质性程度，但威廉·赫歇尔的案例显示，即便不是全部，至少部分爱智者在兴趣选择上具有选择性。正如后文将提及的，他在不同领域间的转型十分缓慢，在每个阶段都对自己在新领域的专业能力宣称持谨慎态度。

In 1766 William formally acknowledged his engagement with the philomath community and their role in shaping his reading habits. His very first reference to the group was on 1 January:
1766 年，威廉正式承认自己与爱智者群体的关联，以及该群体对其阅读习惯的影响。他首次提及这一群体的记录日期为 1 月 1 日：

1766, Jan 1. Wheatley [near County Durham]. This was the country seat of Sir Bryan Cook, where every fortnight I used to spend two or three days. Sir Bryan played the violin and some of his relations generally came from Doncaster to make up morning concerts . . . .³²
“1766 年 1 月 1 日，达勒姆郡附近的惠特利（Wheatley）。这里是布莱恩·库克爵士（Sir Bryan Cook）的乡间宅邸，我过去每两周会在此度过两三天。布莱恩爵士会拉小提琴，他的一些亲属通常会从唐卡斯特（Doncaster）前来，共同组织晨间音乐会……”³²

Feb. 19. Wheatley. Observation of Venus.³²
“2 月 19 日，惠特利。观测金星。”³²

Bryan Cook, as far as can be deduced, was a philomath. Little is known of him, yet William’s reference here suggests that he had some interest in astronomy that he was keen to share.
据推断，布莱恩·库克是一名爱智者。尽管关于他的记载极少，但威廉的记录表明，库克对天文学抱有兴趣，且乐于分享这一兴趣。

Two weeks later William described receiving a letter from ‘Mr Grey, a philosophical Gentleman with whom I have corresponded. He was a brother of Sir Henry Grey of Northumberland and lived in Newcastle.’³³ Again, little is known of Mr Grey, though significantly William describes him as ‘a philosophical gentleman’, making Grey a possible source for William’s knowledge of whom and what to read. In both cases, Cook and Grey, these were highly significant social and intellectual connections made through music that helped William to start to shape his education in philosophy and astronomy.
两周后，威廉描述自己收到了“格雷先生（Mr Grey）的来信——他是一位与我有书信往来的学者绅士（philosophical Gentleman），是诺森伯兰郡亨利·格雷爵士（Sir Henry Grey）的兄弟，居住在纽卡斯尔（Newcastle）”。³³ 关于格雷先生的记载同样稀少，但值得注意的是，威廉将其描述为“学者绅士”，这意味着格雷可能是威廉获取“该向谁学习、该读什么书”这类信息的来源之一。无论是库克还是格雷，这些通过音乐建立的社会与知识关联，都对威廉构建哲学与天文学知识体系起到了关键作用。

Some time later in 1766 he described an audition:
1766 年晚些时候，他描述了一次试镜经历：

I was a candidate for the place of organist, which by the interest of the Messrs Bates and many musical families I attended, I had great hopes to obtain. About this time I was an inhabitant of Halifax. My leisure time was employed in reading mathematical books such as the works of Emerson, Maclaurin, Hodgson, Dr Smith’s Harmonics, &c. This happened to be noticed by one of the Messrs Bates who told his brother: ‘Mr. Herschel reads Fluxions!’³⁴
“我是管风琴师职位的候选人，凭借贝茨兄弟（Messrs Bates）及我所服务的多个音乐世家的支持，我对获得该职位抱有极大希望。当时我居住在哈利法克斯（Halifax），闲暇时会阅读数学书籍，如爱默生（Emerson）、麦克劳林（Maclaurin）、霍奇森（Hodgson）的著作，以及史密斯博士的《和声学》等。贝茨兄弟中的一人注意到了这一点，并对他的兄弟说：‘赫歇尔先生在阅读流数术（Fluxions）相关书籍！’”³⁴

These books are precisely those that were widely read by eighteenth-century philomaths, and they show a notable shift in William’s established reading patterns.³⁵ The books he discussed with his brother in the 1750s and early 1760s were famous books by well-known philosophers. They were books taking a philosophical look at subjects that William knew, such as Smith’s book on harmonics. The books he now perused were more technically demanding titles by less famous authors, and were specifically on fluxions. They show an attempt to master a new subject that might impress his social superiors rather than provide new angles on subjects already known.
这些书籍正是 18 世纪爱智者广泛阅读的著作，它们表明威廉的阅读模式发生了显著转变。³⁵ 18 世纪 50 年代至 60 年代初，他与兄长讨论的书籍多为知名哲学家的经典著作，且多是从哲学角度探讨他熟悉的领域（如史密斯关于和声学的著作）。而此时他阅读的书籍，作者知名度较低，但技术难度更高，且专门聚焦于流数术领域。这表明他试图掌握一门新学科——其目的在于给上流社会人士留下深刻印象，而非为已知领域寻找新视角。

The books that William now began to scrutinize were written by schoolteachers (Emerson and Hodgson) and professors (Maclaurin and Smith). Hodgson stated his audience to be ‘principally young Beginners’; Emerson’s writing style, and the context of his other books (on mechanics and on trigonometry), suggest a similar beginner/schoolteacher audience. Maclaurin’s is slightly different. His preface dwelt on the inadequacy of the existing literature on fluxions, stating that his book was written as a response. According to Niccolo Guicciardini, the market for these books was steadily growing in the eighteenth century, reaching its peak mid-century. William was therefore taking an interest just as these books were at the height of their popularity.
威廉此时深入阅读的书籍，作者身份分为两类：教师（爱默生、霍奇森）与教授（麦克劳林、史密斯）。霍奇森明确表示其读者群体“主要是年轻初学者”；爱默生的写作风格及其其他著作（关于力学与三角学）的背景，表明他的读者同样以初学者或教师为主。麦克劳林的著作略有不同：他在序言中指出当时流数术相关文献存在不足，并表示自己的著作正是为填补这一空白而作。据尼科洛·吉恰尔迪尼（Niccolo Guicciardini）研究，18 世纪这类书籍的市场需求稳步增长，并在世纪中期达到顶峰。因此，威廉对这类书籍产生兴趣的时机，恰好是它们最受欢迎的时期。

As the above quotation suggests, William was not only interested in learning fluxions, he was also keen for his educational pursuits to be witnessed. One of the ‘Messrs Bates’ mentioned has been identified as Joah Bates (1740–99), a musician, civil servant and key player in the organization of public music events in his home town of Halifax.³⁶ For the Bates brothers to know that William ‘reads fluxions’, William must have made this information public by talking of or demonstrating his reading.
如上文引文所示，威廉不仅热衷于学习流数术，还希望自己的学习行为被他人知晓。文中提及的“贝茨兄弟”之一，经考证为乔亚·贝茨（Joah Bates，1740-1799）——他既是音乐家、公务员，也是其故乡哈利法克斯公共音乐活动组织的核心人物。³⁶ 贝茨兄弟能够知晓威廉“阅读流数术书籍”，必然是因为威廉通过谈论或展示自己的阅读内容，主动公开了这一信息。

William was hardly alone in using philomath culture as a stepping stone to social and professional success. Although the term philomath is rarely used today as a description of a historical character, the journals they contributed to, the Ladies’ Diary and the Gentleman’s Diary in particular, crop up with remarkable regularity in the biographies of minor figures engaged in eighteenth-century scientific life. The silk weaver and amateur astronomer James Six, the self-taught mathematician John Dawson, and the clergyman and man of science George Walker, for example, were all contributors. William Wales went from contributor to the Ladies’ Diary to assistant at the Royal Observatory, Greenwich, without any apparent formal training and certainly without a university education.³⁷
以爱智者文化为跳板实现社会地位与职业成就提升的，并非只有威廉一人。尽管如今“爱智者”一词极少用于描述历史人物，但他们所投稿的期刊（尤其是《女士日记》与《绅士日记》），却频繁出现在 18 世纪科学领域次要人物的传记中。例如，丝绸织工兼业余天文学家詹姆斯·西克斯（James Six）、自学成才的数学家约翰·道森（John Dawson）、牧师兼科学家乔治·沃克（George Walker），均是这些期刊的撰稿人。威廉·威尔士（William Wales）从未接受过正规训练，更无大学教育背景，却从《女士日记》的撰稿人逐步成为格林威治皇家天文台（Royal Observatory, Greenwich）的助理。³⁷

William read books written for philomaths and advertised his understanding of these works. Further evidence of his involvement with philomath culture can be found 14 years later in the Ladies’ Diary for 1780, in which William’s solution to a problem incorporating both mathematics and music was published.³⁸ The Ladies’ Diary worked by setting problems in one edition and printing all the correct solutions in the next, complete with workings and a list of names of all who sent in correct answers by that method.³⁹
威廉阅读为爱智者撰写的书籍，并主动展示自己对这些著作的理解。14 年后，即 1780 年的《女士日记》中，出现了更多能证明他参与爱智者文化的证据——该期刊发表了威廉对一道融合数学与音乐的问题的解答。³⁸ 《女士日记》的运作模式是：在某一期中提出问题，在下一期中刊登所有正确解答，并附上解题过程及采用该解法的答题者名单。³⁹

William’s submitted answer was the first public demonstration of his abilities to a purely philosophical (as opposed to musical) audience. That he selected a problem incorporating both mathematics and music demonstrates his caution in claiming too much for his abilities. The problem asked for the number of vibrations of a musical string when the length, tension and weight are given, and a small given weight is ‘fastened to its middle and vibrates with it.’⁴⁰ William’s entry cautiously acknowledged that his answer was ‘not to be considered mathematically true, but as a practical solution approaching near the truth.’⁴¹ Whereas to other musicians, in the context of an audition or music lesson, he presented himself as a master of fluxions, to other philomaths he instead promoted his authority as a musician.
威廉提交的解答，是他首次向纯学术（而非音乐领域）受众公开展示自己的能力。他选择一道融合数学与音乐的题目，这一行为体现了他在宣称自身能力时的谨慎态度——不愿过度夸大。该问题要求：在已知琴弦长度、张力与重量，且琴弦中点“固定一个给定小重物并随琴弦一同振动”的情况下，计算琴弦的振动次数。⁴⁰ 威廉在解答中谨慎地承认，自己的答案“不应被视为数学意义上的精确解，而应被看作接近真相的实用解法”。⁴¹ 值得注意的是，在试镜或音乐课等场合面对其他音乐家时，他会将自己塑造为流数术专家；而在面对其他爱智者时，他则转而强调自己在音乐领域的权威性。

These early formative years of William’s life, when he was first introduced to natural philosophy and then spent years studying, have previously been ignored in all secondary literature. It is significant, however, in that it shows the resources available and how and why they may have been accessed. As a jobbing musician William had discovered a shared interest in natural philosophy with several of his employers. With that knowledge he set about developing his expertise, making himself their equal, by creating an education from available literature and through informal networks. His transition from music to philosophy was slow and cautious, and he took care to tailor his claims regarding expertise to his audience.
威廉人生早期这些受启发的岁月——从首次接触自然哲学到多年深耕该领域——此前在所有二手文献中均未被提及。然而，这一阶段具有重要意义：它揭示了当时可获取的资源，以及获取这些资源的方式与原因。作为零工音乐家，威廉发现自己与部分雇主在自然哲学领域存在共同兴趣。基于这一认知，他开始通过现有文献与非正式网络构建知识体系，逐步提升专业能力，以达到与雇主同等的水平。他从音乐领域向哲学领域的转型缓慢且谨慎，并始终注意根据受众调整对自身专业能力的表述。

ASSEMBLING HIS TEAM

组建团队

A crucial turning point in Herschel’s career came when he decided to make telescopes. Richard Holmes has already commented on the importance of Caroline’s arrival in Bath in enabling William to take up this new hobby.⁴² Equally important, I show here, was the arrival of their brother Alexander, and indeed it is only by recognizing the range of contributors to the Herschel project that a satisfactory role for Caroline can be understood. Although Caroline is always mentioned in accounts of William Herschel’s life and work, there is some debate regarding the exact nature of her contribution and why it might be considered significant to the history of science. Michael Hoskin suggests she was a ‘mere’ assistant and less talented than her brother. Others, meanwhile, have chosen to characterize her as an ambitious pioneer.⁴³ Here I introduce Caroline as part of a team that William put together. In this context, William and Caroline are presented not in competition but as part of a larger collective who made William’s telescope building and observing plans possible.
赫歇尔职业生涯的关键转折点，始于他决定自制望远镜之时。理查德·霍姆斯（Richard Holmes）已指出，卡罗琳抵达巴斯（Bath）对威廉开展这一新爱好起到了重要作用。⁴² 本文则认为，他们的兄弟亚历山大（Alexander）的到来同样关键——事实上，只有认识到赫歇尔科研项目背后众多贡献者的作用，才能准确理解卡罗琳的角色意义。尽管卡罗琳在所有关于威廉·赫歇尔生平与工作的记述中均会被提及，但学界对她贡献的具体性质，以及其贡献为何对科学史具有重要意义，仍存在争议。迈克尔·霍斯金（Michael Hoskin）认为她“仅仅是”助手，且天赋不及兄长；而另一些学者则将她描述为富有抱负的开拓者。⁴³ 本文将卡罗琳视为威廉组建的团队中的一员：在此框架下，威廉与卡罗琳并非竞争关系，而是共同构成一个更大集体的一部分——正是这个集体让威廉制造望远镜与开展观测的计划成为可能。

The word ‘team’ used in this sense is not a contemporary term. The Herschels, if they talked collectively about the people involved in their astronomy and instrument making activities at all, would have used family, household, or, if pressed to include the various outside contractors, workmen. They did not describe themselves as equal participants. Caroline in particular always emphasized her subordinate role, but that does not mean that we should accept that hierarchy uncritically. I have used the word ‘team’ here to allow all the participants in the work to be acknowledged.
此处所用的“团队”（team）一词并非当时的术语。赫歇尔一家在谈论参与其天文学与仪器制作活动的人员时，若涉及集体表述，会使用“家人”（family）、“家务人员”（household）等词；若必须纳入外部合作者，则会用“工匠”（workmen）。他们从不将自己描述为“平等参与者”，卡罗琳尤其总强调自己的从属地位——但这并不意味着我们应不加批判地接受这种等级关系。本文使用“团队”一词，旨在认可所有参与工作的人员的贡献。

In 1770 William’s younger brother Alexander arrived in Bath, hoping to find work as a musician. Alexander was a dedicated and skilful mechanic. When the brother-in-law of William’s son John went through William’s correspondence, he found ‘some curious ones of his brother Alex all confined to the subject of mechanics.’⁴⁴ The letters lacked the social niceties normally found in correspondence between siblings and were instead purely functional and technical in tone. When pushed further, John gave the following anecdote about his uncle Alexander:
1770 年，威廉的弟弟亚历山大抵达巴斯，希望找到音乐相关工作。亚历山大是一位专注且技艺精湛的机械师。威廉之子约翰（John）的姐夫在整理威廉的书信时，发现“一些与亚历克斯舅舅（指亚历山大）相关的有趣信件，内容均围绕机械学展开”。⁴⁴ 这些信件没有兄弟姐妹通信中常见的社交客套话，语气纯粹是功能性与技术性的。经进一步追问，约翰讲述了关于他舅舅亚历山大的一则轶事：

He never moved away from his own home, except to pay a yearly visit to his brother’s [i.e. William’s] family and then invariably came accompanied by his turning lathe and other implements, and getting himself & them established the moment of his arrival, in the workshop (now H’s observatory) scarcely left that apartment during the whole period of his stay. . . . He used to go away after his stated week of visitation had expired having scarcely seen his friends all the time, but declaring himself quite delighted with their society.⁴⁵
“他（亚历山大）从不出远门，只每年去一次他兄长（即威廉）家。每次去必定带着自己的车床与其他工具，一到就立刻在作坊（现为赫歇尔天文台）里安顿下来开始工作，整个拜访期间几乎从不离开那个房间……他通常在为期一周的拜访结束后离开，期间几乎没怎么与亲友见面，却称自己‘十分享受与他们的相处’。”⁴⁵

Letters between the brothers suggest that, while in Bath, William relied on the technical skills of Alexander.⁴⁶ Collectively, this archival material suggests that Alexander was not sociable but instead single-minded in his attention to technical and mechanical detail. In terms of learning how to build state-of-the-art telescopes, this was an extraordinary asset.
兄弟二人的通信表明，威廉在巴斯期间依赖亚历山大的技术能力。⁴⁶ 综合这些档案资料可知，亚历山大不善社交，但在关注技术与机械细节方面极为专注。对于学习制造最先进的望远镜而言，这种特质是极其宝贵的优势。

A second important factor was the arrival of Caroline in 1772, relieving William of many time-consuming activities including supervising household staff and, as her English and music improved, copying out musical scores and teaching the choir.⁴⁷ A third factor was the opportunity presented by a local man giving up his hobby making mirrors. William makes no reference to this man’s identity except to say that he lived in Bath and would sell him his tools and give him lessons.⁴⁸
第二个重要因素是卡罗琳于 1772 年抵达巴斯，为威廉分担了许多耗时的事务，包括管理家务人员；随着卡罗琳的英语与音乐能力提升，她还承担了抄录乐谱与教授唱诗班的工作。⁴⁷ 第三个因素是一位巴斯当地居民放弃了制作镜子的爱好，这为威廉提供了机会。威廉未提及此人的身份，仅表示他住在巴斯，愿意将制作镜子的工具卖给自己，并提供相关指导。⁴⁸

William’s tutoring under this local mirror-maker did not, according to his own testimony, last long: ‘going to work with these tools I found no difficulty to do in a few days all what he could show me, his knowledge indeed being very confined.’⁴⁹ William then continued in September 1773 ‘with the assistance of Dr Smith’s popular treatise.’⁵⁰ In the same year he bought and studied James Ferguson’s Astronomy,⁵¹ Emerson’s Trigonometry,⁵² Emerson’s Optics⁵³ and, around the same time, Emerson’s Mechanics.⁵⁴ Both Smith and Emerson were authors he had read before. James Ferguson wrote for a similar audience, and, as Anthony Turner has previously observed, was lecturing in Bath at around this time.⁵⁵
据威廉本人所述，他向这位当地镜匠学习的时间并不长：“使用这些工具操作后，我发现几天内就能掌握他所能教的全部内容——他的知识确实非常有限。”⁴⁹ 随后在 1773 年 9 月，威廉“借助史密斯博士的通俗专著继续学习（制作镜子）”。⁵⁰ 同年，他购买并研读了詹姆斯·弗格森的《天文学》（Astronomy）、⁵¹ 爱默生的《三角学》（Trigonometry）、⁵² 爱默生的《光学》（Optics），⁵³ 并在同期阅读了爱默生的《力学》（Mechanics）。⁵⁴ 史密斯与爱默生都是他此前读过的作者；詹姆斯·弗格森的著作受众与爱默生类似，且正如安东尼·特纳（Anthony Turner）此前所指出的，弗格森当时恰好在巴斯举办讲座。⁵⁵

Smith and Emerson gave clearly written advice for constructing different kinds of telescope. Smith, as Michael Hoskin and Reginald Jones have already shown (figure 2), provided step-by-step instructions on how to build a telescope very similar to the 7-foot reflector William eventually perfected (figure 3).⁵⁶ Emerson meanwhile provided more general mathematical tools with which to solve problems when varying the design of the telescope.
史密斯与爱默生在著作中为不同类型望远镜的制作提供了清晰的指导。正如迈克尔·霍斯金与雷金纳德·琼斯（Reginald Jones）所指出的（图 2），史密斯提供了分步教程，指导如何制作一台与威廉最终完善的 7 英尺反射望远镜（图 3）极为相似的仪器。⁵⁶ 而爱默生则提供了更通用的数学工具，用于解决望远镜设计方案调整时遇到的问题。

Although William is always named as the maker of this and all his later telescopes, each one was a team effort. William made, cast and polished the primary mirror. In the context of the instrument-making industry, this alone qualified him to be the named maker of the telescope.⁵⁷ However, Alexander made the eyepieces and micrometers, and a cabinet maker was called upon to build the wooden tube and stand. In fact, Caroline’s autobiographies suggest that even the mirrors were a team effort, with Caroline sometimes helping to make the moulds (out of manure and straw).⁵⁸ On another occasion, William and Alexander together were noted as having been present when a mould broke, causing molten metal to damage the kitchen floor.
尽管威廉始终被记载为这台望远镜及此后所有望远镜的制造者，但每一台望远镜的完成都是团队努力的结果。威廉负责主镜的制作、浇铸与抛光——在仪器制造行业的语境中，仅此一项工作就足以让他获得“望远镜制造者”的署名资格。⁵⁷ 然而，目镜与测微计由亚历山大制作，木制镜筒与支架则由一位家具木工负责。事实上，卡罗琳在自传中提到，即便主镜的制作也离不开团队协作：她有时会帮忙制作模具（用粪便与稻草制成）。⁵⁸ 另有记载显示，一次模具破裂导致熔融金属损坏厨房地板时，威廉与亚历山大均在现场。

Besides providing a basic telescope design, Smith’s book was also useful, as Hoskin and Schaffer have discussed, in providing William with descriptions of what he should be able to see through the telescope.⁵⁹ A further use not previously considered is that Smith’s book may have offered William a guide in how ‘to practice seeing’.⁶⁰
正如霍斯金与沙弗（Schaffer）所论述的，史密斯的著作除提供基础望远镜设计方案外，还为威廉提供了“通过望远镜应观测到何种景象”的描述，这同样具有重要价值。⁵⁹ 此外，该著作还可能为威廉提供了“练习观测”（to practice seeing）的方法指导——这一用途此前未被关注。⁶⁰

In addition to its section on instrument making, on mathematics and on telescopic discoveries, Smith’s Opticks contained a section entitled ‘A Popular Treatise’ within which was the chapter ‘Concerning our ideas acquired by sight’.⁶¹ This chapter’s arguments were framed within the context of Locke’s Essay Concerning Human Understanding and his views on learned knowledge. The chapter went on to describe William Cheselden’s work on cataracts. Cheselden was a famous surgeon from the early eighteenth century. His work on cataracts involved their surgical removal, followed by intensive training in which the patient was taught to see again (or for the first time). This showed that sight was not purely a function of the eye, but also of the brain learning to interpret what was seen. William had learnt music through concentrated repetitive solitary practice from an early age and here, described in Smith, presented as an application of Locke’s ideas, was that same practice applied to sight. William applied this technique to his own sight, describing the process to his friend Alexander Aubert, a businessman and astronomer with his own observatory:
史密斯的《光学》（Opticks）除包含仪器制作、数学与望远镜发现相关章节外，还设有一个名为“通俗论述”（A Popular Treatise）的部分，其中有一章题为“论通过视觉获得的观念”（Concerning our ideas acquired by sight）。⁶¹ 该章的论述以洛克《人类理解论》的思想及其关于“习得性知识”的观点为框架，进而介绍了 18 世纪早期著名外科医生威廉·切塞尔登（William Cheselden）在白内障治疗领域的工作。切塞尔登的治疗流程是：先通过手术移除白内障，再对患者进行强化训练，教他们重新（或首次）学会“看”。这一案例表明，“看见”并非纯粹的眼部功能，还依赖大脑学习如何解读视觉信号。威廉自幼通过专注、重复的独自练习学习音乐，而史密斯在书中将类似练习应用于“观测”的描述（被视为洛克思想的实践），恰好与他的学习经历契合。威廉将这一方法应用于自身的观测训练，并向友人亚历山大·奥伯特（Alexander Aubert）——一位拥有私人天文台的商人兼天文学家——描述了这一过程：

When you want to practice seeing (for believe me Sir,—to use a musical phrase—you must not expect to see at sight or a livre ouvert) apply a power something higher than what you can see well with, and go on encreasing it after you have used it some time.⁶²
“当你希望练习观测时（先生，请相信我——用音乐术语来说——你不能期望‘即兴视奏’（see at sight）或‘照着乐谱演奏’（a livre ouvert）），应使用比你当前能清晰观测的倍率稍高的镜片；使用一段时间后，再逐步提高倍率。”⁶²

By practising observing as he had practised music, William became an excellent observer. His instrument-making skills also improved as he practised and perfected the art of mirror making, experimenting with different alloy compositions and polishing techniques. Then in 1778 he read a paper on mirror making in Philosophical Transactions of the Royal Society. The paper was by John Mudge, a physician by profession, and a brother of the famous clockmaker; it described a technique that had won Mudge the Royal Society’s Copley Medal. William tried out the technique described and decided that his own method produced a better mirror.⁶³ This observation gave him renewed confidence in his abilities.
通过将音乐练习的方法应用于观测训练，威廉成为了一名出色的观测者。同时，他通过练习与完善制镜工艺（尝试不同合金成分与抛光技术），其仪器制作技能也不断提升。1778 年，他在《英国皇家学会哲学汇刊》（Philosophical Transactions of the Royal Society）上读到一篇关于制镜的论文。该论文作者是约翰·马奇（John Mudge）——职业为医生，且是著名钟表匠的兄弟——文中描述的技术曾为马奇赢得英国皇家学会的科普利奖章（Copley Medal）。威廉尝试了论文中描述的技术，最终认为自己的方法能制造出更好的镜子。⁶³ 这一发现让他对自身能力重拾信心。

Although membership of the Royal Society at this time included a large percentage of timeservers, rich gentlemen with no particular interest or talent for science, its Copley Medal was nonetheless a prestigious prize, awarded to those regarded as having made an outstanding achievement in science. If Mudge’s technique was regarded as outstanding, and William’s was better, that surely must be evidence that his efforts had paid off. When William had sent in his solution to Ladies’ Diary, he had explained his right to do so in terms of the question’s musical content, and his expertise in that field. After his reading of Mudge, William began a new tack: instead of claiming authority through his musical expertise, he would now claim it through the precision and quality of his astronomical instruments.
尽管当时英国皇家学会的成员中，有很大比例是“挂名成员”——即对科学无特殊兴趣与天赋的富裕绅士——但其科普利奖章仍是极具声望的奖项，授予被认为在科学领域取得杰出成就的人士。若马奇的技术被视为“杰出”，而威廉的技术更优，这无疑证明他的努力已见成效。此前，威廉向《女士日记》提交问题解答时，会以题目涉及音乐内容、且自己在该领域具备专业能力为由，证明自己提交解答的合理性。而在阅读马奇的论文后，威廉开始转变策略：不再通过音乐专业能力宣称权威，而是转而通过天文仪器的精度与质量来建立权威。

BATH PHILOSOPHICAL SOCIETY

巴斯哲学学会

In 1779 William began to get to know members of the Bath Philosophical Society, one of several regional philosophical societies to emerge in the late eighteenth century. These were societies in which the university-educated and the self-taught alike could come together to discuss the latest scientific thinking, and develop those ideas through experiment and discussion. They were also often a place for gaining access to otherwise prohibitively expensive literature through the formation of society libraries.⁶⁴
1779 年，威廉开始结识巴斯哲学学会（Bath Philosophical Society）的成员。该学会是 18 世纪晚期涌现的多个区域性哲学学会之一，其特点是：接受过大学教育者与自学成才者可在此平等交流，探讨最新科学思想，并通过实验与讨论深化这些想法。此外，这类学会通常会建立图书馆，让成员得以接触那些原本因价格高昂而难以获取的文献。⁶⁴

According to Klein, the Bath Philosophical Society was established in part to aid social mobility. The society’s president, Edmund Rack, was a weaver’s son, who worked as a draper while cultivating literary and intellectual friendships and interests. In 1777 he set up the Bath Agricultural Society. Two years later he joined with Thomas Curtis, a governor of the Bath General Hospital, to form the Bath Philosophical Society. This society was successfully designed to attract both gentry and the self-made such as Rack, Parsons and Herschel. Like the Agricultural Society, this society had a strong bias in favour of agricultural development and natural history, but it also encompassed more diverse scientific and literary interests.⁶⁵
据克莱因研究，巴斯哲学学会的成立部分旨在促进社会流动。学会主席埃德蒙·拉克（Edmund Rack）是织工之子，职业为布商，同时热衷于建立文学与学术领域的人脉，培养相关兴趣。1777 年，他创立了巴斯农业学会（Bath Agricultural Society）；两年后，他与巴斯综合医院（Bath General Hospital）董事托马斯·柯蒂斯（Thomas Curtis）共同组建了巴斯哲学学会。该学会的定位极具吸引力，既吸引了贵族阶层，也接纳了拉克、帕森斯（Parsons）与赫歇尔等“白手起家者”。与农业学会类似，巴斯哲学学会虽侧重农业发展与自然史领域，但也涵盖了更为多元的科学与文学兴趣方向。⁶⁵

By the end of 1779 William had successfully tested the quality of his telescopes and, as we have seen, recognized the value of public demonstrations of learning. With this in mind, he took his telescope into the street to observe the Moon:
截至 1779 年末，威廉已成功验证了其望远镜的质量；且正如前文所述，他深知“公开展示学习成果”的价值。基于这一考量，他将望远镜搬到街上观测月球：

I brought my seven feet reflector into the street, and directed it to the object of my observations. Whilst I was looking into the telescope, a gentleman coming by the place where I was stationed stopped to look at the instrument. When I took my eye off the telescope he very politely asked if he might be permitted to look in, and this being immediately conceded, he expressed great satisfaction at the view. Next morning the gentleman, who proved to be Dr Watson, jun. (now Sir William), called at my house to thank me for my civility in showing him the moon, and told me that there was a Literary Society then forming at Bath, and invited me to become a member of it, to which I readily consented.⁶⁶
“我将自己的 7 英尺反射望远镜搬到街上，对准观测目标（月球）。当我通过望远镜观测时，一位绅士经过我所在的位置，停下脚步观察这台仪器。我移开眼睛后，他礼貌地询问能否让他也观测一下——我立即同意了，他观测后对景象表示非常满意。次日早晨，这位绅士（后来得知是小沃森博士，即后来的威廉·沃森爵士）专程到我家拜访，感谢我客气地让他观测月球，并告知我巴斯当时正筹备一个‘文学学会’（Literary Society），邀请我成为会员——我欣然应允。”⁶⁶

This ‘literary society’ was the Bath Philosophical Society. Dr Watson was a member of this society and of the Royal Society; he was also a physician with an interest in botany and mineralogy. William was keen to make a good impression on both Watson and the society as a whole.
这里所说的“文学学会”正是巴斯哲学学会。小沃森博士既是该学会成员，也是英国皇家学会成员，同时还是一名对植物学与矿物学感兴趣的医生。威廉迫切希望给沃森博士及整个学会留下良好印象。

William chose to give his first paper not on mathematics, astronomy or instrument making, but on natural history.⁶⁷ This choice, so outside William’s normal areas of interest and research, suggests an eagerness to please his hosts. This first paper described his observations over a series of days of a branch of coralline and the apparatus he used, giving particular attention to the microscope’s magnifying power.⁶⁸ In his concluding remarks he made a throw-away reference to Leibniz, suggesting that if certain things were true ‘it would almost look something like an instance of Leibnitz’s pre-establish’d Harmony.’ In this one paper he introduced himself to the society and attempted to grab their attention with a topic from their, rather than his, field of expertise. At the same time, he tried to present himself as an expert on instrumentation, well informed in natural philosophy.
威廉选择的第一篇学会报告主题，并非数学、天文学或仪器制作，而是自然史。⁶⁷ 这一主题与他常规的兴趣及研究领域相去甚远，足见他渴望取悦主办方的心态。这篇报告描述了他连续多日对珊瑚藻（coralline）枝条的观测过程，以及所使用的仪器——尤其强调了显微镜的放大倍率。⁶⁸ 在结语部分，他顺带提及莱布尼茨，称若某些情况属实，“几乎可视为莱布尼茨‘前定和谐’（pre-establish’d Harmony）理论的实例”。在这篇报告中，威廉通过选择学会（而非自己）擅长的领域作为主题，实现了在学会的“亮相”并试图吸引成员关注；同时，他也借此展现自己在仪器使用方面的专业性，以及在自然哲学领域的广博知识。

Further evidence of William’s wish to ingratiate himself with the Bath Philosophical Society’s members can be found in his collaboration with Curtis. This is the only instance of William’s working on a project with anyone outside his immediate family, and it demonstrates his enthusiasm for fully engaging with the society. The papers themselves—all short descriptions of electrical experiments performed—came out of discussions after William’s paper on Joseph Priestley’s History of Vision.⁶⁹
威廉与柯蒂斯的合作，进一步证明了他希望融入巴斯哲学学会成员圈子的意愿。这是威廉唯一一次与直系亲属以外的人合作开展项目，体现出他积极参与学会活动的热情。他们合作的论文（均为电学实验的简短描述），源于威廉关于约瑟夫·普里斯特利（Joseph Priestley）《视觉史》（History of Vision）的报告引发的讨论。⁶⁹

In between his papers on natural history and electricity William began to report on observations made with his telescopes.⁷⁰ Two of these papers—one on a star in Collo Ceti, the other on lunar mountains—were later read to the Royal Society. The first of these was in essence an edited transcript of two years from his observing journal for Collo Ceti. The second was more ambitious. He began by explaining that his reason for observing the Moon was to repeat the observations of ‘Galileo, Hevelius, Kircher’ as ‘their instruments were far from being arrived to that degree of perfection we now have obtained.’ Like his first paper, his arguments and descriptions surrounding his observations centred on the quality of his apparatus and his breadth of reading.
在提交自然史与电学主题报告的间隙，威廉开始汇报通过自己的望远镜获得的观测结果。⁷⁰ 其中两篇报告——一篇关于鲸鱼座（Collo Ceti）某恒星，另一篇关于月球山脉——后来被提交至英国皇家学会宣读。前者本质上是他对鲸鱼座恒星两年观测日志的编辑整理；后者则更具野心：他在报告开篇解释，自己观测月球的原因是为了重复“伽利略（Galileo）、海维留斯（Hevelius）、基歇尔（Kircher）”的观测——“因为他们的仪器远未达到我们如今已实现的精度水平”。与第一篇报告类似，他围绕观测展开的论证与描述，核心仍聚焦于两点：自身仪器的高质量，以及自己的广博阅读量。

In William’s progression of papers to the Bath Philosophical Society there is a gradual shift in how he presented himself as he absorbed the culture, learning how ideas must be presented. His early papers simply flattered his host, while describing what he had done and seen. Gradually, however, he learned how to use his papers to present ideas, not just descriptions, and the correct way to incorporate references to his reading and the superiority of his telescopes. When he came to discover the planet Uranus in 1781, his involvement with the society meant he knew just how to word his announcement and whom to tell.
随着威廉向巴斯哲学学会提交的报告不断增多，他在“自我呈现”方式上发生了渐进式转变——这源于他对学会文化的理解，以及对“如何恰当呈现学术观点”的学习。早期报告仅通过选择主办方关注的主题表达善意，内容以描述自己的所作所为与所见所闻为主；但渐渐地，他学会了利用报告呈现观点（而非单纯描述事实），并掌握了“引用阅读成果”与“强调望远镜优势”的恰当方式。1781 年发现天王星时，正是这段学会经历让他明确知晓：该如何措辞发布这一发现，以及该告知哪些关键人物。

CALCULUS VERSUS FLUXIONS

微积分与流数术

William’s self-education had taught him to observe, to build telescopes, to write papers and to present himself and his work in a way that would get him noticed. However, this education had its limits. It was, as he was to find out, a very English education.
通过自学，威廉掌握了观测技能、望远镜制作方法、论文写作能力，以及如何以引人关注的方式呈现自我与工作成果。但这种自学存在局限性——正如他后来发现的，这是一种“极具英国特色”的教育。

In 1781 Nevil Maskelyne informed the French astronomer Charles Messier of William’s discovery of a new planet.⁷¹ Calculations on the planet’s orbit followed, performed by Messier, Lalande, Méchain and Dagelet, and were then communicated to William by Joseph Jérôme Lefrançois de Lalande in May 1782.⁷² This was the first letter in a longrunning—and previously unexamined—correspondence. Through this correspondence, we see the limits of William Herschel’s education.
1781 年，内维尔·马斯基林（Nevil Maskelyne）将威廉发现新行星（天王星）的消息告知法国天文学家夏尔·梅西耶（Charles Messier）。⁷¹ 随后，梅西耶、拉朗德（Lalande）、梅尚（Méchain）与达热莱（Dagelet）共同计算了这颗新行星的轨道，并由约瑟夫·热罗姆·弗朗索瓦·德·拉朗德（Joseph Jérôme Lefrançois de Lalande）于 1782 年 5 月将计算结果告知威廉。⁷² 这是两人长期书信往来（此前未被研究）的第一封信。透过这段通信，我们得以看到威廉·赫歇尔教育背景的局限性。

France and England were at war for much of the eighteenth century, establishing the boundaries of their new empires, and this had repercussions for the transmission of scientific and mathematical knowledge. The various attempts during the eighteenth century to introduce ideas from one nation to the other suggest that scientific activities in each country followed separate trajectories. The dispute between Maupertuis and Cassini during the 1730s over the shape of the Earth was in part an argument over English science, mathematics and instrumentation versus French alternatives.⁷³ Émilie du Châtelet’s reputation was built on bringing Newton’s ideas from England to France.⁷⁴ The Ladies’ Diary and Gentleman’s Diary were originally produced in part to introduce developments in French mathematics to the English. In each case, attempts were made to bridge a perceived gap between the science, philosophy and mathematics of the two countries.
18 世纪的大部分时间里，英法两国为确立新帝国的边界处于战争状态，这对科学与数学知识的传播产生了影响。18 世纪期间，双方多次尝试引入对方国家的思想，这一现象表明两国的科学活动遵循着不同的发展轨迹。例如，18 世纪 30 年代莫佩尔蒂（Maupertuis）与卡西尼（Cassini）关于地球形状的争论，部分本质是“英国科学、数学与仪器”与“法国对应体系”的对抗。⁷³ 艾米莉·杜·夏特莱（Émilie du Châtelet）的声望则源于她将牛顿思想从英国引入法国的工作。⁷⁴ 《女士日记》与《绅士日记》的创办初衷，也部分包括向英国人介绍法国数学的新发展。上述案例均表明，当时人们认为英法两国在科学、哲学与数学领域存在“鸿沟”，并试图弥合这一鸿沟。

Over the course of the eighteenth century, each country had developed its mathematics separately, with English fluxions becoming increasingly empirical, and Continental calculus increasingly abstract.⁷⁵ In England the work of Newton had evolved through the work of people such as Taylor, Maclaurin and Simpson. In contrast, in France, mathematics was moving forward through the work of d’Alembert, Lagrange and Laplace. For those engaged in mathematical study, this nationalistic divide meant that expertise could generally only be achieved in the mathematics of one country or the other. As Olaf Pedersen has observed, the sources that William was using to learn fluxions were loyal to the English side, completely ignoring French calculus.⁷⁶ William had studied fluxions, but he slowly discovered that this was of limited use in understanding the work of his French colleagues.
18 世纪期间，英法两国的数学发展路径逐渐分化：英国的流数术（fluxions）日益侧重经验主义，而欧洲大陆（以法国为代表）的微积分（calculus）则日益偏向抽象化。⁷⁵ 在英国，牛顿的数学思想通过泰勒（Taylor）、麦克劳林（Maclaurin）与辛普森（Simpson）等人的工作得到发展；与之相对，法国数学的进步则得益于达朗贝尔（d’Alembert）、拉格朗日（Lagrange）与拉普拉斯（Laplace）的贡献。对数学研究者而言，这种“国家性分化”意味着：通常只能在其中一国的数学体系内达到专业水平。正如奥拉夫·佩德森所指出的，威廉学习流数术时使用的资料完全“忠于英国体系”，对法国微积分体系完全忽略。⁷⁶ 威廉虽精通流数术，但他逐渐发现，这一知识在理解法国同行的研究工作时作用有限。

Lalande’s first letter contained results of calculations performed on William’s new planet, followed by a request for information about both William’s life and his telescopes. William’s reply began politely. He admired Lalande and thanked him for the results. In reply to his questions, he told him he had been born in Hanover and ‘brought up to Music; my leisure hours were generally devoted to mathematics and other studies.’ In other words, he had always been interested in mathematics. Lalande had expressed an interest in his telescopes; William presented himself not as an instrument maker but as a mathematician and philosopher.
拉朗德的第一封信中，包含对威廉发现的新行星的轨道计算结果，随后还请求威廉提供关于其个人经历与望远镜的信息。威廉的回信态度礼貌，他表达了对拉朗德的钦佩，并感谢对方分享计算结果。在回应问题时，他告知拉朗德自己出生于汉诺威，“以音乐为业，闲暇时间通常致力于数学及其他学科研究”。换言之，他试图塑造自己“始终对数学抱有兴趣”的形象。尽管拉朗德明确表达了对其望远镜的兴趣，威廉却并未将自己定位为仪器制造者，而是强调自己作为数学家与哲学家的身份。

For a time, the correspondence between William and Lalande followed a pattern. Lalande would relate the results of new calculations and introduce natural philosophers from across Europe. William, meanwhile, would discuss work that he was about to have published. Then, in the summer of 1788, not long after William had married Mary Pitt, Lalande visited England. William’s marriage to this rich widow had been the source of some unflattering gossip. Although he may have resented these slights, it was true that Mary had introduced a change of pace to the family. Money was no longer a concern. Family holidays were taken, a point that Watson observed, which made for a more measured, less fraught approach to working life. Lalande’s visit, then, must be seen in this light. Just as Caroline’s arrival gave William the freedom to begin telescope building, his marriage to Mary allowed him time to begin to understand French mathematics.
在一段时间内，威廉与拉朗德的通信遵循着固定模式：拉朗德会分享新的轨道计算结果，并介绍欧洲各地的自然哲学家；威廉则会讨论自己即将发表的研究成果。1788 年夏天，即威廉与玛丽·皮特（Mary Pitt）结婚后不久，拉朗德到访英国。威廉与这位富裕寡妇的婚姻曾引发一些负面流言，尽管他可能对这些非议感到不满，但玛丽确实为家庭生活带来了改变：经济压力不复存在，家人还会外出度假——沃森曾提及这一点，认为这让威廉的工作节奏更为从容，不再充满紧迫感。从这一背景来看，拉朗德的此次到访意义特殊：正如卡罗琳的到来为威廉提供了开展望远镜制作的自由，与玛丽的婚姻则让他有时间开始学习理解法国数学。

Lalande’s visit in 1788 marked a turning point in their correspondence: the letters that followed were filled with explanations and mathematical examples.⁷⁷ In one letter William asked for a paper to be shown to Jean-Baptiste-Joseph Delambre. Lalande’s reply related Delambre’s corrections line by line, ending that ‘if you had sent observations in more detail to De Lambre more rigorous determinations would have been attempted.’⁷⁸
1788 年拉朗德的到访，成为两人通信的转折点：此后的信件中充满了数学解释与实例。⁷⁷ 例如，威廉曾在一封信中请求拉朗德将自己的一篇论文转交让-巴蒂斯特-约瑟夫·德朗布尔（Jean-Baptiste-Joseph Delambre）。拉朗德在回信中逐行转达了德朗布尔的修改意见，最后还指出：“若你能向德朗布尔提供更详细的观测数据，他本可尝试进行更精确的计算。”⁷⁸

William’s response was defensive, and apologetic. He was embarrassed at having made the mistakes and was quick to explain them away, telling him:
William’s mathematical abilities had reached their limits, and he was embarrassed. Nevertheless he stayed friends with Lalande and continued to build contacts across the Channel. He passed papers to them, and they in turn sent back papers and books, making his library unusually diverse for an English philosopher. William’s education was made possible by his cultivation of useful, intellectually generous contacts, and by his ability to use other people and resources in his life to free up his time sufficiently to study and develop expertise. His contact with French mathematicians showed the limits of this process. Their mathematics was too different. Although he maintained an interest in French mathematics and astronomy, he decided to leave its mastery to his son, whose education in this area he would nurture and encourage.⁸⁰
威廉的回信态度带有防御性与歉意。他对自己犯下的错误感到尴尬，并急于解释：“我用于练习（数学）的时间太少，加之日常事务繁杂，计算时思绪常被干扰，即便出现更多失误也不足为奇……”⁷⁹ 此时，威廉的数学能力已达瓶颈，且他对此感到难堪。尽管如此，他仍与拉朗德保持友谊，并继续拓展与欧洲大陆的学术联系：他会将自己的论文寄给法国学者，对方则会回寄论文与书籍——这让他的藏书在英国哲学家中显得格外多元。威廉的知识积累，一方面得益于他主动维系“有用且乐于分享知识”的人脉，另一方面则在于他善于借助他人与资源为自己腾出时间，以投入学习并提升专业能力。但与法国数学家的接触，暴露了这种“自学模式”的局限性：两国数学体系差异过大。尽管威廉始终对法国数学与天文学保持兴趣，却决定将精通这一领域的希望寄托在儿子身上，并承诺会培养与支持儿子在该领域的学习。⁸⁰

CONCLUSION

结论

William Herschel was remarkable in coming to possess a serious expertise in practical astronomy from a background in music. It was not, however, uncommon for eighteenth-century children to make scientific instruments as a hobby. Nor was it unusual for those in professions that engaged with the leisured classes—as traders or tutors—to regard natural philosophy as a useful tool in developing their professional reputations. William’s use of philomath contacts and philomath literature followed similar patterns to those of many of his contemporaries. He also, like Thomas Parsons, Edward Rack, John Dawson and George Walker, found in his local philosophical society a means of mixing with and learning from individuals who could help him develop as a natural philosopher and ultimately become a Fellow of the Royal Society.
威廉·赫歇尔从音乐背景跨界，最终在实用天文学领域获得深厚专业造诣，这一经历固然非凡，但以下两点在 18 世纪并不罕见：其一，儿童将制作科学仪器作为爱好；其二，从事与有闲阶层打交道的职业（如商人或教师）者，会将自然哲学视为提升职业声望的有用工具。威廉对爱智者人脉与文献的利用方式，与同时代许多人相似；且和托马斯·帕森斯、爱德华·拉克（Edward Rack）、约翰·道森及乔治·沃克一样，他也通过地方哲学学会（巴斯哲学学会）结识并向能帮助自己的人学习——这些人助力他成长为自然哲学家，并最终成为英国皇家学会会员。

Scientific education in eighteenth-century England involved participation in several informal and ever-changing groups. These subsets of the scientific world—the philomaths, the lecturer/instrument makers, the philosophical societies and the Royal Society—all had different ways of engaging with scientific knowledge, but, as Herschel’s example has shown, they were interconnected. It was possible to move between groups and, in doing so, to learn not just the content and tacit knowledge involved in becoming a practitioner of science, but also how to construct and present an appropriate image.
18 世纪英国的科学教育，涉及参与多个非正式且不断变化的群体。这些科学领域的分支群体——爱智者、讲师/仪器制造者、哲学学会与皇家学会——虽以不同方式接触科学知识，但正如赫歇尔的案例所揭示的，它们彼此关联。人们可在不同群体间流动，在此过程中，不仅能学习成为科学从业者所需的知识与隐性技能，还能掌握如何构建并呈现恰当的个人专业形象。

A current trend in the history of science has been to focus on historical actors outside the world of elites. Herschel’s example shows this to be an artificial divide in the eighteenth century. Academicians wrote books read by philomaths; members of the Royal Society learned their science from travelling lecturers and regional philosophical societies. Although some men of science received a university education, many did not. In both cases, much of their scientific education came through the kinds of network described above.
当前科学史研究的一个趋势是关注精英圈层之外的历史参与者。但赫歇尔的案例表明，这种“精英与非精英的划分”在 18 世纪是人为的：院士会撰写供爱智者阅读的书籍；皇家学会成员会从巡回讲师与地方哲学学会中学习科学知识。尽管部分科学家接受过大学教育，但更多人并未接受过——无论是否有大学背景，他们的科学知识积累，很大程度上都依赖于前文所述的各类人脉网络。

The story of William Herschel’s education demonstrates the way in which these networks and resources were used, and how one might progress through them, rising through social as well as scientific ranks, to reach a position of prestige and authority. William was not simply a passive recipient of this education. He actively sought out networks, reading material and tutors, he acted on advice, and he applied his learning in imaginative ways. In that sense he was self-taught.
威廉·赫歇尔的知识积累历程，展示了人们如何利用这些网络与资源，如何在其中逐步进阶——既提升科学领域的地位，也实现社会阶层的上升——最终获得声望与权威。威廉并非这一教育过程的被动接受者：他主动寻找人脉网络、阅读材料与导师，积极采纳建议，并以富有想象力的方式应用所学知识。从这个角度而言，他确实是“自学成才”。

At the same time, William’s story also shows us the range of people involved in enabling his education. Although in a sense he was self-taught, he cannot take sole credit for his education. His education was made possible by mentors and tutors; he was also helped by his siblings, local craftsmen and his wife, who collectively freed up his time, shared his workload and added skills to his scientific enterprise. Without this extensive team around him, William would have been able to achieve very little. William’s story gives us a detailed glimpse of what was probably a common form of scientific education in eighteenth-century England. His encounter with French mathematics shows that it was a specifically English experience.
与此同时，威廉的经历也向我们揭示了助力他知识积累的众多参与者。尽管从某种意义上他是“自学成才”，但这份知识积累的功劳不能仅归于他一人：导师与教师为他提供指导；兄弟姐妹、地方工匠与妻子为他提供帮助——他们共同为他腾出时间、分担工作，并为他的科学事业补充所需技能。若没有身边这个庞大的团队，威廉几乎无法取得任何成就。威廉的故事让我们得以细致窥见 18 世纪英国可能普遍存在的一种科学教育模式，而他在法国数学面前的“力不从心”则表明，这种教育模式具有鲜明的“英国本土特色”。

ACKNOWLEDGEMENTS

致谢

This paper came out of my PhD thesis. I should therefore like to thank the National Maritime Museum for support and funding; my supervisors, Rob Iliffe and Andy Warwick at Imperial College, London, for their help and patience; and Patricia Fara, William Ashworth and Barbara Becker for their feedback on my overall thesis. On this paper specifically I should like to thank Jo Elcoat and Becky Bowd at Leeds, Hieke Huistra and Silke Fengler from my Summer Academic Working Group, and the judges for the Notes and Records Essay Award. I should also like to thank Bob.
本文源自本人的博士论文。在此，我要感谢英国国家海事博物馆（National Maritime Museum）提供的支持与资助；感谢我的导师——伦敦帝国理工学院（Imperial College London）的罗布·伊利夫（Rob Iliffe）与安迪·沃里克（Andy Warwick）——给予的帮助与耐心指导；感谢帕特里夏·法拉（Patricia Fara）、威廉·阿什沃思（William Ashworth）与芭芭拉·贝克尔（Barbara Becker）对整篇博士论文提出的反馈意见。针对本文，特别感谢利兹大学的乔·埃尔科特（Jo Elcoat）与贝基·鲍德（Becky Bowd）、暑期学术工作坊的希克·胡伊斯特拉（Hieke Huistra）与西尔克·芬格勒（Silke Fengler），以及《笔记与记录》论文奖的评委们。同时，也向鲍勃（Bob）表示感谢。

NOTES

1. Occasionally this narrative is questioned; see, for example, Schaffer on our understanding of Herschel’s novel approach to astronomy in Simon Schaffer, “Herschel in Bedlam: natural history and stellar astronomy,” Br. J. Hist. Sci. 13, 211–239 (1980); see also Holmes on the discovery of Uranus as no “Eureka moment” in Richard Holmes, Age of wonder (Harper Press, London, 2008), pp. 94–100.

2. Dictionary of national biography; Jenny Uglow, The lunar men: the friends who made the future (Faber & Faber, London, 2002), p. xiv.

3. Hannah Gay, “Technical assistance in the world of London science, 1850–1900,” Notes Rec. R. Soc. 62, 51–75 (2008).

4. Andrew Warwick, Masters of theory: Cambridge and the rise of mathematical physics (University of Chicago Press, 2003); David Kaiser (ed.), Pedagogy and the practice of science (MIT Press, Cambridge, MA, 2005).

5. Nicholas Hans, New trends in education in the eighteenth century (Routledge & Kegan Paul, London, 1951); Peter and Ruth Wallis, Mathematical tradition in the north of England (NEBMA, Durham, 1991); A. Musson and E. Robinson, Science and technology in the industrial revolution (Manchester University Press, 1969).

6. Most notably Aileen Fyfe and Bernard Lightman (eds), Science in the marketplace: nineteenth-century sites and experiences (University of Chicago Press, 2007).

7. Michael Hoskin, Caroline Herschel’s autobiographies (Science History Publications Ltd, Cambridge, 2003), p. 19.

8. William Herschel, “Memorandums from which an historical account of my life may be drawn,” Royal Astronomical Society (hereafter RAS): WH.7/8, p. 6.

9. Ibid.

10. William Herschel to Charles Hutton, 1784, Harvard: MS Eng 1414 F(29); British Library (hereafter BL): microfilm M/541.

11. Herschel, op. cit. (note 8), p. 7.

12. Constance Lubbock, The Herschel chronicle: the life-story of William Herschel and his sister Caroline Herschel (Cambridge University Press, 1933), p. 7.

13. Caroline L. Herschel to John F.W. Herschel, 8 May 1827, BL: Eg.3761 f. 64.

14. Mrs. J. Herschel (ed.), Memoir and Correspondence of Caroline Herschel (London, 1876), p. 6. Account, and further extended memoir (reprint by Cambridge University Press, 2010); Andrew Carnegie, James Watt (Forgotten Books, 2012 reprint). See also Dictionary of national biography entries for Ferguson, Watt, Cummings and Rittenhouse.

15. Lawrence E. Klein, “Politeness and the interpretation of the British eighteenth century,” Hist. J. 45, 869–898 (2002); Alice Walters, “Conversation pieces: science and politeness in eighteenth-century England,” Hist. Sci. 35, 121–154 (1997).

16. Lawrence E. Klein, “An artisan in polite culture: Thomas Parsons, stone carver, of Bath, 1744–1813,” Huntington Library Q. 75, 27–51 (2012).

17. Michael Hoskin, The Herschel partnership: as viewed by Caroline (Science History Publications Ltd, Cambridge, 2003), p. 17.

18. Cyril Ehrlich, The music profession in Britain since the eighteenth century: a social history (Oxford University Press, 1985), pp. 31–32.

19. Lubbock, op. cit. (note 12), p. 55.

20. John Locke, An Essay Concerning Human Understanding, in four volumes (Glasgow, 1759).

21. Herschel, op. cit. (note 8), pp. 7–8.

22. Robert Smith, Harmonics, or the Philosophy of Musical Sounds (Cambridge, 1749).

23. Edward H. Jacobs, “Buying into classes: the practice of book selection in eighteenth-century Britain,” Eighteenth-Cent. Stud. 33, 1, 43–64 (1999).

24. Estimated date of authorship from reference in Lubbock, op. cit. (note 12), p. 16.

25. William Herschel, Theory of Music, Edinburgh: Ms. No. Dk.2.35, Book C, Chapter V, p. 9.

26. Ibid., p. 13.

27. Jon Topham, “Anthologizing the book of nature: the origins of the scientific journal and circulation of knowledge in late Georgian Britain” in The circulation of knowledge between Britain, India and China: the early-modern world to the twentieth century (ed. B. Lightman, G. McOuat & L. Stewart), pp. 119–153 (Brill, Leiden, 2013).

28. Shelley Costa, “The ‘Ladies’ Diary’: gender, mathematics, and civil society in early-eighteenth-century England,” Osiris 17, 49–73 (2002), at p. 56.

29. Olaf Pedersen, “The ‘Philomath’ of 18th century England,” Centaurus 8, 238–262 (1963), at p. 250.

30. Wallis and Wallis, op. cit. (note 5).

31. Lubbock, op. cit. (note 12), p. 35. Sir Bryan Cook here is plausibly Sir Bryan Cooke (1717–69), a baronet.

32. Herschel, op. cit. (note 8), p. 19.

33. Herschel, op. cit. (note 8), p. 20.

34. Niccolo Guicciardini, The development of Newtonian calculus in Britain 1700–1800 (Cambridge University Press, 1989), p. 56 lists 12 frequently reprinted books on fluxions from 1736 to 1758; Maclaurin, Hodgson and Emerson are all on the list.

35. Fiske and Johnstone, Blackwell history of music in Britain, eighteenth century (Blackwell, Oxford, 1988), p. 246.

36. The role of philomath culture in the education of British mathematicians in the eighteenth century is referred to in Warwick, op. cit. (note 4), pp. 34–35.

37. Herschel, op. cit. (note 8), p. 83.

38. Guicciardini, op. cit. (note 35), pp. 115–117.

39. From Ladies’ Diary 1779, reproduced in John Louis Emil Dreyer, The scientific papers of Sir William Herschel (Royal Society and the Royal Astronomical Society, London, 1912), p. xxviii.

40. William Herschel, “The same [solution to . . .] by Mr Wm. Herschel,” Ladies’ Diary 1780, pp. 46–47, at p. 47; reprinted in Dreyer, op. cit. (note 40), p. xxix.

41. Holmes op. cit. (note 1), p. 83.

42. Hoskin, op. cit. (note 18), p. 4; Claire Brock, The comet sweeper: Caroline Herschel’s astronomical ambition (Icon Books, London, 2007).

43. Anecdotes of John F.W. Herschel as noted down by James Stewart, September 1833, John Hers chel-Shorland’s private family archive papers ARM.

44. Ibid.

45. William Herschel to Alexander Herschel, 10 March 1785, RAS: WH.1/9.2.

46. Holmes op. cit. (note 1), pp. 83–86.

47. Dreyer, op. cit. (note 40), p. xxiv.

48. Ibid.

49. Lubbock, op. cit. (note 12), p. 66.

50. James Ferguson, Astronomy explained upon Sir Isaac Newton’s principles and made easy to those who have not studied mathematics (London, 1756), which he is quoted as having read in Dreyer, op. cit. (note 40), p. xxiv.

51. William Emerson, The elements of trigonometry (W. Innys, London, 1749), which he is quoted as having read in Dreyer, op. cit. (note 40), p. xxiv.

52. William Emerson, The elements of optics (London, 1768); Herschel, op. cit. (note 8), p. 30.

53. William Emerson and G. A. Smeaton, The principles of mechanics (W. Innys & J. Richardson, London, 1754).

54. Anthony Turner, Science and music in eighteenth century Bath: catalogue of an exhibition in the Holburne of Menstrie Museum, Bath, 22 September 1977–29 December 1977 (University of Bath, 1977), p. 53.

55. Reginald Victor Jones, “Through music to the stars: William Herschel, 1738–1822,” Notes Rec. R. Soc. 33, 37–56 (1978), at p. 42. See also Michael Hoskin, William Herschel and the construction of the heavens (Oldbourne, London, 1963), p. 20.

56. G. L’E. Turner, “James Short, F.R.S., and his contribution to the construction of reflecting telescopes,” Notes Rec. R. Soc. Lond. 24, 91–108 (1969). See also Allan Chapman, Dividing the circle. The development of critical angular measurement in astronomy 1500–1850, 2nd edn (John Wiley, Chichester, 1995), pp. 139–145.

57. Hoskin, op. cit. (note 7), p. 63.

58. Schaffer, op. cit. (note 1), p. 222; Michael Hoskin, “William Herschel’s early investigations of nebulae: a reassessment,” J. Hist. Astron. 10, 165–176 (1979), at p. 167.

59. William Herschel to Alexander Aubert, 28 January 1782, in Lubbock, op. cit. (note 12), p. 104.

60. Robert Smith, A Compleat System of Opticks (1738), pp. 42–43.

61. Lubbock, op. cit. (note 12), pp. 104–105.

62. Joachim Rienitz, “William Herschel’s mirror test and its consequences,” Bull. Scient. Instrum. Soc. no. 6, p. 5 (1985); also in Jones, op. cit. (note 56), p. 39.

63. Ma´ire Kennedy, “Reading the Enlightenment in eighteenth-century Ireland,” Eighteenth-Cent. Stud. 45, 355–379 (2012).

64. Klein, op. cit. (note 17); Rack’s background is also mentioned in Turner, op. cit. (note 55), pp. 82 and 91.

65. Lubbock, op. cit. (note 12), p. 73.

66. William Herschel, “Observations on the Growth and Measurement of Corallines,” read to Bath Philosophical Society on 18 February 1780; reprinted in Dreyer, op. cit. (note 40), p. lxvi.

67. He does not say who made the microscope.

68. All reprinted in Dreyer, op. cit. (note 40): the initial paper on electricity was William Herschel, “Propositions and Queries,” read to the Bath Philosophical Society on 23 March 1780; William’s collaboration resulted in two papers, both read to the Bath Philosophical Society: William Herschel and Thomas Curtis, “Electrical Experiments,” read on 7 April 1780, and William Herschel and Thomas Curtis, “Experiments in Electricity continued,” read on 21 April 1780.

69. All reprinted in Dreyer, op. cit. (note 40): “Observations on the Mountains of the Moon”; “Continuation of the Observations on the height of the lunar Mountains”; “Astronomical Observations on the Periodical Star in Collo Ceti”; “Communication of my letter to the Rev Dr Maskelyne, On the Measurement of the Lunar Mountains”; “Observations on the Occultation of Gamma Virginis, made with a view to determine whether any Effect of a Lunar Atmosphere could be perceived”; “On the periodical star Collo Ceti”; “Account of a Comet”.

70. Lubbock, op. cit. (note 12), p. 86.

71. Joseph-Je´roˆme Lalande to William Herschel, 1 May 1782, RAS: WH. 1/13.L.1.

72. Mary Terrall, “Representing the Earth’s shape: the polemics surrounding Maupertuis’s expedition to Lapland,” Isis, 83, 218–237 (1992).

73. Judith Zinsser, “Mentors, the marquise Du Chaˆtelet and historical memory,” Notes Rec. R. Soc. 61, 89–108 (2007).

74. Guicciardini, op. cit. (note 35), pp. 37–39.

75. Pedersen, op. cit. (note 30).

76. Joseph-Je´roˆme Lalande to William Herschel, 9 September 1788, RAS: WH. 13.L.12.

77. “Si vous aves rapporte´ les observations avec plus de de´tail au De Lambre on aurait essaye´ des de´termination plus rigoureuse.” Joseph-Je´roˆme Lalande to William Herschel, 2 October 1788, RAS: WH. 1/13.L.13.

78. William Herschel to Joseph-Je´roˆme Lalande, 17 October 1788, RAS: WH. 1/1 p. 168.

79. Emily Winterburn, The Herschels: a scientific family in training (PhD thesis, Imperial College London, 2011).

---

本文简读

1. William Herschel’s Journey from Musician to Astronomer: Uncovering the Hidden Resources of 18th-Century Scientific Learning
   威廉·赫歇尔：从音乐家到天文学家的转型——18世纪科学学习的隐性能量

2. Beyond the “Self-Taught” Narrative: William Herschel’s Scientific Education Through Philomath Networks and Collaborative Teams
   超越“自学成才”叙事：威廉·赫歇尔通过爱智者网络与协作团队实现的科学教育

章节主题

1. 学习基础与家庭影响

• PHILOMATHS, HERSCHEL, AND THE MYTH OF THE SELF-TAUGHT MAN: Learning How to Learn in Herschel’s Childhood
  爱智者、赫歇尔与自学成才者的神话：赫歇尔童年时期的“学习如何学习”
• Family, Music, and Early Education: The Foundations of William Herschel’s Scientific Pursuits
  家庭、音乐与早期教育：威廉·赫歇尔科学探索的根基

2. 爱智者群体与知识积累

• Philomath Culture and Herschel’s Reading: How Journals, Books, and Networks Shaped His Scientific Education
  爱智者文化与赫歇尔的阅读：期刊、书籍与人脉如何塑造其科学知识体系
• From Ladies’ Diary to Fluxions: William Herschel’s Engagement with 18th-Century Philomath Communities
  从《女士日记》到流数术：威廉·赫歇尔与18世纪爱智者群体的关联

3. 团队协作与望远镜制作

• Assembling the Herschel Team: Siblings, Craftsmen, and the Collective Effort Behind Telescope Building
  组建赫歇尔团队：兄弟姐妹、工匠与望远镜制作背后的集体努力
• From Mirror-Making to “Practicing Seeing”: How Collaborative Skill-Building Fueled Herschel’s Astronomy
  从制镜到“练习观测”：协作式技能培养如何推动赫歇尔的天文学研究

4. 学术圈层与身份构建

• The Bath Philosophical Society: Herschel’s Gateway to Scientific Prestige and Community
  巴斯哲学学会：赫歇尔通往科学声望与学术圈层的门户
• Crafting a Scientific Identity: How Herschel Adapted His Expertise Claims for Different Audiences
  构建科学身份：赫歇尔如何针对不同受众调整专业能力表述

5. 教育局限性与结论

• Calculus vs. Fluxions: The Limits of Herschel’s “English” Scientific Education
  微积分与流数术：赫歇尔“英国式”科学教育的局限性
• Rethinking 18th-Century Scientific Education: Herschel’s Story as a Model of Network-Driven Learning
  重思18世纪科学教育：赫歇尔的经历作为“人脉驱动型学习”的范例

---

via:

• Philomaths, Herschel, and the myth of the self-taught man | Notes and Records: the Royal Society Journal of the History of Science
  https://royalsocietypublishing.org/doi/10.1098/rsnr.2014.0027