In 1761–1762, under the guidance of his friend and mentor John Stuart, the third Earl of Bute, the young George III acquired an extensive collection of philosophical instruments from the workshop of George Adams of Fleet Street.Footnote ¹ The Earl of Bute largely defined the scope of George III's education, and a related programme of patronage and acquisition, in the late 1750s and early 1760s.Footnote ² The purchase from Adams reflects the optimism of the two men's shared political vision during those years, and the confidence they shared in the moral and social utility of the practice of Newtonian natural philosophy. Bute and Prince George both aspired to a future reign in which George III, as a monarch guided by virtue and duty, would effect moral reformation on a national scale. The programme of education they undertook for this purpose partly comprised intense historical study of the British systems of government and taxation, as well as those of its neighbours, allies and enemies in Europe. It also involved studies and exercises directly concerned with shaping the moral faculties of the young prince. To this end, Bute combined the philosophy of Francis Hutcheson, which identified the benevolent passions as the source of human morality, with the conviction that ‘geometrical’ or ‘mathematical’ habits of mind were necessary for carrying through moral action in political life. The way to acquire these habits of mind was through practice with instruments. The papers relating to George III's education contain hundreds of sheets of exercises in geometry and perspective drawing, all performed with dedicated instruments, from a simple compass and straightedge to the more complex architectonic sector.Footnote ³ The philosophical instruments, paid for by Bute on the king's behalf in 1762–1763, were directly associated with this kind of geometrical, instrumental exercise, and can therefore be seen as contributing to the wider moral and political project.Footnote ⁴

As the prince's mentor, Bute drew on his own education at the University of Leiden, as well as his role as a leading patron of the Scottish Enlightenment. His views on education were shaped by these experiences, and he applied them within his own family, as well as in the royal household. He intended machine experiments, like geometrical constructions, to function in this context as exercises in sustaining attention, in following long chains of reasoning, and ultimately in recognizing truth. These exercises were not purely intellectual; they were also manual, and positively required instruments – from air-pumps and complex machines to simple drawing-boards and dividers. In the context of Bute's combined approach to moral development, the performance of experiments did not aim at the sociable and ostensive forms of self-transformation implied by ‘polite science’.Footnote ⁵ Rather, it contributed to a far more austere undertaking, framed by the imperatives of duty, and intensified by the prince's social singularity and the isolated conditions of his upbringing.Footnote ⁶

In terms of personnel, George III's education was punctuated by a series of upheavals and political conflicts. The Earl of Bute and the mathematician George Lewis Scott, who acted as the prince's sub-preceptor between 1750 and 1756, were arguably the two most important figures in a parade of men who instructed him in the 1740s and 1750s.Footnote ⁷ John L. Bullion has characterized the intense friendship between Bute and Prince George in the late 1750s as a mentor–protégé relationship, in which the older man served simultaneously as ‘teacher’, ‘counsel and support’, ‘guide’, and ‘exemplar’ to the younger.Footnote ⁸ For a few years, they worked towards an ideal of national, moral reformation under George's kingship, in which Bute, as First Lord of the Treasury, would encourage public virtue through selective patronage.Footnote ⁹ George's own letters to Bute reflect the emotional tenor of this relationship, with rebukes from Bute eliciting remorse and self-accusation from the prince, who professed himself ‘extrem’ly hurt’, ‘deeply afflicted’ by his mentor's criticisms of his conduct.Footnote ¹⁰ He made repeated, impassioned promises to throw off ‘indolence … this my greatest enemy’: ‘my duty to my Creator, to my country, to my friend, and to myself all combine in spurring me on in the strongest manner to throw off that incomprehensible indolence, inattention and heedlessness that reign within me’.Footnote ¹¹ These pleas combined distressed self-criticism with the consciousness on the prince's part that the improvement of his own character and conduct comprised part of the duties arising from his rank.

Bute, too, saw his position as one of grave responsibility, and his response was inflected by the moral philosophy and the cultural experiences of the Scottish Enlightenment. His own background provided models for a ‘philosophical’ approach to education and for the exercise of patronage. Both were central to the commission for George III's philosophical machines. Following the example of his uncle Archibald Campbell, third Duke of Argyll, Bute had travelled to the Netherlands to attend the University of Leiden, where he enrolled to study law in 1732.Footnote ¹² Between 1650 and 1750, great numbers of young Scottish men travelled to the Dutch universities to study both law and medicine, and Bute's experience followed a pattern of education that served as a direct model for the new schools of law that were established in the universities of Edinburgh and Glasgow in the eighteenth century.Footnote ¹³ The legal education he received at Leiden would have been ‘polite, gentlemanly, scholarly, the education of a legal virtuoso’; the Dutch ‘elegant’ school of law approached its subject philosophically, rooting it in history, philology and rhetoric, with students branching out into mathematics, logic and the natural sciences.Footnote ¹⁴ Prince George's studies of national finance in the late 1750s were directed by Bute in a way that perhaps reflects this Dutch ‘elegant’ approach – as historical studies, encompassing the history of revenues and taxation in England since the Norman Conquest.Footnote ¹⁵

Using networks of patronage and influence established by the Duke of Argyll, Bute also participated actively in the shaping of the Scottish universities by the ‘moderate literati’ in the middle decades of the century.Footnote ¹⁶ In the early 1760s, he engineered university appointments for the jurist John Millar, the Church of Scotland minister William Leechman, the critic and rhetorician Hugh Blair, the philosopher Adam Ferguson, and the surgeon and natural philosopher James Russell.Footnote ¹⁷ As he became increasingly involved with the Prince of Wales, Bute turned to philosophers for advice about education. In 1754, he consulted at length with the natural philosopher and inventor Stephen Hales about appropriate schools for his eldest son, and a few years later he engaged Adam Ferguson as a tutor.Footnote ¹⁸ Bute's preoccupation with the emotional bases of virtue clearly reflected the concerns of Ferguson and other Scottish moral philosophers of the eighteenth century.Footnote ¹⁹ In 1757 he wrote to his friend John Home concerning his own children,

Several ‘plans’ of education; hundreds of sheets of exercises in Latin, geometry and perspective drawing; and essays on history, government, national finance, chemistry, the arts and the moral sentiments, all written by or relating to George III, survive in the Royal Archives at Windsor Castle.Footnote ²¹ The underlying purposes of the education they comprised were moral ones, for this was education in the classical sense, of bringing up a youth to virtue. ‘Some short notes concerning the education of a prince’ have been attributed to Bute, and a close reading of their contents confirms the attribution.Footnote ²² This document reveals the seriousness and sense of occasion with which Bute viewed his own responsibilities:

The programme of education devised by Bute for Prince George in the 1750s was also a programme of acquisition, and one that continued after George's coronation in 1760. Over his lifetime, Bute built up a collection of machines and instruments that rivalled, and may have provided a direct precedent for, that of his pupil.Footnote ²⁴ Purchases of instruments for George III, starting in the late 1750s, included two-, three-, four-, six-, and eight-foot achromatic telescopes, and ‘a 10 foot achromatic object Glass with a Tube for the Day & three Different magnifiers for the Planets with Stands and Boxes’ from John Dollond.Footnote ²⁵ In 1757, ‘a Magazine case of Silver drawing Instruments’, along with drawing boards and a stand, pens, pencils, rulers and two instruments specifically for perspective drawing – ‘Mr Kirby's Instrum[en]t with Rack work’ and ‘Another Instrum[en]t with a frame for Demonstrating the Rules in perspective’ – were supplied by George Adams.Footnote ²⁶ These items by Adams would have equipped the prince not just to learn geometry and perspective drawing, which was taught to him by the draughtsman Joshua Kirby, but to study the principles of architecture, which he learned, partly through the practice of drawing, from the architect William Chambers.Footnote ²⁷

Bills from the late 1750s show multiple purchases of books at auctions as well as from booksellers such as Andrew Millar. Bute acquired works on British and European history, geography and maps, antique ruins, architecture, mechanics, experimental philosophy and gardening.Footnote ²⁸ The artist and antiquary Richard Dalton, who was appointed librarian to the Prince of Wales in 1755, travelled to the Continent in 1758–1759 and 1762–1763 to acquire drawings and paintings for the prince's collection and to negotiate the new king's purchase of Consul Joseph Smith's famous collection of art and antiquities.Footnote ²⁹ The cabinetmakers and upholders John Cobb and William Vile provided mahogany bookcases, drawing presses, tables, medal cases and desks as well as clothes presses, jewel cabinets, birdcages and candle stands at St James's Palace and Buckingham House between 1757 and 1763.Footnote ³⁰ The overall pace of acquisition rose in the early 1760s, with the refurbishment of Buckingham House, and then fell off after Bute's departure from government in 1764, confirming his influence on the king's desire to collect on a grand scale.Footnote ³¹ In the late 1750s and early 1760s, then, the instrument-maker George Adams was part of a network of elite tradesmen and professionals, assembled principally by the Earl of Bute. Some, such as Chambers and Kirby, were involved in teaching George III; others, such as Dalton, Adams, Cobb and Vile, in equipping him to be a ‘great and good Prince’.Footnote ³²

On 28 August 1762, the historian Thomas Birch sent one of a regular series of letters to his friend and employer Philip Yorke.Footnote ³³ Among other news and gossip, Birch reported that

When Birch wrote, with apparent amusement, of ‘writing out the King's Exercises’, he touched on an important distinction between two eighteenth-century modes of experiment: the making of experiments as a public performance, on the one hand, and the making of experiments as a participatory exercise, on the other. George Lewis Scott and the Earl of Bute both emphasized the lasting value of such exercises to form good habits of mind. In a letter written in 1752 to the prince's sub-governor, Andrew Stone, Scott remarked that although George and his younger brother Edward were becoming familiar with the various ‘States of Europe’, they required mathematical instruction in order to progress much further:

Scott, himself a mathematician, was convinced that the order of instruction often carried more weight in princely education than did its content – and, like Bute, that geometry and its instruments could provide the basis of ‘proper study’. In the context of George III's education, mathematics and experimental philosophy were viewed like the ‘scientifical part’ of geography, as exercises designed to habituate the mind to dealing with truth, and to following long chains of connected ideas. Both were considered necessary guides for virtuous action in the complex situations of political life.

George III's vast collection of philosophical instruments was integrated into a ‘mathematical’ system of knowledge, similar to that recommended by Scott, through its direct association with one particular printed book: Mathematical Elements of Natural Philosophy, Confirmed by Experiments: or, an Introduction to Sir Isaac Newton's Philosophy by the Dutch mathematician and natural philosopher Willem ’sGravesande.Footnote ³⁶ The physical apparatus included machines for performing experiments in mechanics and pneumatics, constructed from mahogany, brass, glass, steel, ivory, leather, silk thread and clay. Two objects dominate the rest of the collection by virtue of their size, but also because they provide the physical stage for most of the other apparatus: a large air-pump and a mahogany table, referred to by Adams as the ‘great Table’. Together with a detachable pillar, the ‘great Table’ supported an ensemble of modular attachments: the apparatus for ‘explaining the principles of mechanics’.Footnote ³⁷ Adams also provided the air-pump with a range of glass ‘receivers’ and other accessories for performing experiments. These included animal bladders, mercury barometers and gauges, truncated brass cones, Magdeburg hemispheres, a heavy brass vessel for condensing air, a spring-driven bell, an arrangement of vessels for isolating different kinds of air, apparatus for electrical and chemical experiments in vacuo, and a pneumatic gun.Footnote ³⁸

The mechanical apparatus, assembled by Adams from designs published in a number of different printed sources, and comprising hundreds of separate experiments, is united by a modular system that allows its components to be assembled, reassembled and combined on the basic, central structure of the table and pillar. It included experiments for illustrating the properties of extension and solidity; plates of glass, artificial magnets and vessels of mercury for illustrating attraction and repulsion; a variety of multi-use parts such as pulleys, cross-bars, balances and supporting arms; devices for showing the centre of gravity and the properties of the simple machines; other machines for illustrating Newton's laws of motion and the motion of pendulums; machines for central forces and collisions between elastic and inelastic bodies; and others for experiments measuring elasticity. The sheer scale of the collection is reflected in its 177 separate entries in the Science Museum's 1993 catalogue, Public & Private Science: 114 for the ‘great Table’ and its related mechanical apparatus, and sixty-three for the air-pump and apparatus for pneumatics experiments.Footnote ³⁹ During the early 1760s these machines were displayed in Buckingham House along with part of the king's growing library. When the French mathematician Jerome Lalande visited in 1763, he recorded having seen the air-pump among ‘many cabinets in two large rooms full of instruments, machines and books’.Footnote ⁴⁰ After being moved from Buckingham House to the Royal Observatory at Richmond, and thence to King's College London, the instruments were permanently loaned to the Science Museum in London in 1926, where a selection from the collection is on display in the ‘Science in the 18th century’ gallery.Footnote ⁴¹

George III's instruments and experiments were directly linked with ’sGravesande's Mathematical Elements and a group of over a dozen other books, through detailed citations in illustrated manuscripts. The ‘Discourses’ mentioned by Thomas Birch in his letter to Philip Yorke can be identified with these manuscripts, compiled by George Adams: ‘A description of the pneumatic apparatus made for His Majesty King George the Third … 1761’ and ‘A description of an apparatus for explaining the principles of mechanicks made for his Majesty King George the Third … 1762’.Footnote ⁴² Each is a compendium of experiments, drawn from books and periodicals, and full of citations allowing the machine experiments to be interpreted in light of selected passages in Mathematical Elements and other publications. In the twenty years before his death in 1742, ’sGravesande had built up a vast collection of instruments for use in his lectures, in which experiments ‘illustrated’ the abstract and difficult principles of nature.Footnote ⁴³ His book presented its readers with a system of natural philosophy, progressing from the properties of bodies and motion; through the simple and compound machines; and culminating with the motions of the comets, the planets and their moons. For the Earl of Bute and George III, the rigour of ’sGravesande's philosophical system made the same book an ideal source of exercises in tracing out long sequences of connected ideas – an activity that was central to Bute's plan for moral development.

Jessica Riskin has rightly emphasized the importance of visual exposition and entertainment in eighteenth-century courses of experimental philosophy. But ’sGravesande's Mathematical Elements cannot accurately be called ‘Newtonianism without geometry’.Footnote ⁴⁴ ’sGravesande was the most rigorously geometrical of his peers. Both he and his translator Desaguliers had stressed that in their lectures, experiments acted as ‘a Medium’ to illustrate ‘a Series of philosophical Propositions in mathematical Order’.Footnote ⁴⁵ Thus ’sGravesande's book, and the manuscripts and machines provided by George Adams for George III, provided a ‘system’ of experiments ideal for what Bute had called ‘the investigating truth through long trains of Ideas, and the deducing true consequences from … propositions well laid and precisely defined’.Footnote ⁴⁶ This rigour not only is apparent in terms of the organization of ’sGravesande's course, which progresses from simple definitions through more and more complex propositions, each building on the last in imitation of Euclid's Elements.Footnote ⁴⁷ It also is reflected in his comprehensive provision of geometrical demonstrations or quantitative calculations relating to individual experiments. Although Desaguliers had trumpeted the ‘mathematical’ order of his own two-volume A Course of Experimental Philosophy, it was, in practice, rather haphazardly assembled. ’sGravesande's chapter on the air-pump, for example, provides mathematical glosses for each experiment, and attempts to impose order on their sequence, in part by excluding some of the usual ‘repertoire’ of experiments in pneumatics.Footnote ⁴⁸ In contrast, Desaguliers composed the corresponding chapter of his own book by ‘pasting in’ verbatim a pamphlet published twenty-seven years earlier by the instrument-maker William Vream, in which the maximum number of experiments received minimal verbal description.Footnote ⁴⁹ The philosophical instruments of George III are impressive and ingenious artefacts, but the decision to tie them so closely to the Mathematical Elements, through design as well as manuscript citations, framed them for mathematical exercise, no less than display.

Eighteenth-century ideas concerning the use of mathematical practice to shape subjectivity followed broadly Lockean views on the formative power of repeated practice and habituation.Footnote ⁵⁰ These ideas linked mind, body and objects in two crucial ways. First, John Locke had modelled his view of the power of mathematics to make men into ‘reasonable creatures’ on a series of comparisons with bodily exercise and practice.Footnote ⁵¹ It was the same process by which dancing made men into dancing-masters, or playing music made them into musicians or, for that matter, turning on a lathe made them into turners.Footnote ⁵² Second, the mathematical sciences, especially geometry and experimental philosophy, were compound activities, with manual and intellectual components inextricably connected. Matthew Jones has shown that both René Descartes and Gottfried Wilhelm Leibniz designed instruments for the practice of mathematics as a spiritual exercise.Footnote ⁵³ Joshua Kirby, tutor in perspective drawing to Prince George, also recognized the interconnection of manual exercise and subjectivity. According to Kirby, making perspective drawings caused a beneficial and lasting change in the mind of the draughtsman: through regular practice, the student would be ‘taught to SEE’ with ‘exactness’ and ‘judgment’.Footnote ⁵⁴ Ann Bermingham has proposed that the gentlemanly practices of drawing in seventeenth-century England were ‘a disciplining of the hand by the mind’.Footnote ⁵⁵ But Kirby's remarks reveal that the inverse was also true: geometrical exercise disciplined the mind through the hand.

Perhaps the most concrete elements in this web of connections between the corporeal and the intellectual – and certainly its most durable artefacts – were mathematical and philosophical instruments. George III's papers demonstrate that to study even elementary geometry was not simply to memorize definitions and axioms, or to reason through problems. It was also to construct diagrams with a compass and straightedge: ‘To bisect a given line’ or ‘On a given line to desc[ribe] a reg[u]lar Hexagon’.Footnote ⁵⁶ George III's philosophical machines provided the material basis for the exercises recommended by Scott, Bute and others, for the gradual and painstaking cultivation of a person with a fixed attention, able to follow long chains of reasoning, and therefore familiar with truth – that is, a prince capable of moral action.

Sometime after 1765, George III sketched a ‘Plan of education’ in which ‘modern philosophy’ was given a similar role to that of geometry in the ‘Short notes’, indicating that he, too, considered ‘the cognitive grasp perfected through philosophy and mathematics as a resource for the sorts of cognitive grasp necessary for living well’ – and for fulfilling his duties as a monarch:Footnote ⁵⁷

Bute's plan of moral education did not depend solely on giving George III a mathematical mind. Rather, these exercises had a carefully delimited role within a larger scheme that drew heavily on the work of Francis Hutcheson, professor of moral philosophy at the University of Glasgow from 1729 until his death in 1746. Like Hutcheson, Bute ‘regarded the culture of the heart as the main end of all moral instruction’.Footnote ⁵⁹ But he also believed that while a benevolent heart was the true motor of moral action, the passions alone were an inadequate guide in the complex situations of political life. For that, mathematical exercises were key.

In ‘Some short notes concerning the education of a prince’, Bute considered this relationship between the passions and the understanding in detail, positioning the emotional and geometrical components of this composite approach to moral development:

The argument developed here, and put into action in the education of George III, was that the conduct of the understanding was a moral matter, and the geometrical mind was best equipped to discover the sources and practical consequences of moral obligation.

Concern with moral development was no novelty in the history of princely education. Nevertheless, texts associated with the education of Tudor and Stuart princes did not afford the mathematical sciences any special efficacy in this regard. Roger Ascham, tutor to Elizabeth I, warned that excessive mathematical study made men ‘unfit to live with others … unapt to serve in the world’.Footnote ⁶¹ James I and VI advised his eldest son that the useful study of mathematics, for a prince, extended only to military arts such as ballistics and fortification.Footnote ⁶² At the latter end of the seventeenth century, John Bettam, tutor to James Francis Edward Stuart, the Old Pretender, dismissed contemporary debates in astronomy as ‘vain curiosity’.Footnote ⁶³ By the mid-eighteenth century, however, the stance taken by Bute and Scott represented just one of many competing attitudes concerning the moral effects of mathematical exercise. A variety of views was expressed by authors, some writing in the seventeenth century, but all available to readers such as Bute and George III in the 1750s and 1760s. Philosophers on the Continent, such as Descartes and Leibniz, had argued that the practices of geometry produced virtuous qualities of mind.Footnote ⁶⁴ In the first decade of the eighteenth century, the French Cartesian Bernard Fontenelle thought, perhaps along more Lockean lines, that frequent exercise in the mathematical sciences ‘wou'd make Truth so familiar, that we might on other Occasions know it at first sight, and almost by Instinct’.Footnote ⁶⁵ The Dissenting minister and tutor Isaac Watts considered the mathematical sciences ‘happily useful’ for the cultivation of attention, and a ‘steady fixation of thought’ to be in itself a moral faculty.Footnote ⁶⁶ Indeed, his view of the matter was very similar to that expressed in ‘Some short notes concerning the education of a prince’. ‘The evidence of truth does not always appear immediately, nor strike the soul at first sight’, wrote Watts, and without the ability to direct and maintain our attention, ‘we judge falsly of many things’.Footnote ⁶⁷

Defences of mathematics on moral and spiritual grounds came from an ideologically diverse group of authors, including Descartes, Leibniz, Fontenelle, Watts and the Jacobite mystic Andrew Michael Ramsay.Footnote ⁶⁸ The question continued under debate for much of the century, in pedagogy, moral philosophy and reflection on human relationships more broadly speaking. In England, a group of High Church Tories, including Samuel Johnson, the anti-Newtonian natural philosopher and theologian John Hutchinson, and his supporter George Horne, denied any connection between moral subjectivity and the mathematical sciences.Footnote ⁶⁹ Others, such as the physician and one-time friend of Newton, George Cheyne, warned that absorption in advanced mathematics could breed sinful pride and contempt for one's fellow creatures.Footnote ⁷⁰ This discussion, about the effects that mathematical practice could have in shaping moral subjectivity, was joined by some of the parties to concurrent debates over the epistemological, political and theological validity of Newtonian experimental philosophy.Footnote ⁷¹ But those arguing for and against the idea that such exercise could help prepare the mind for moral action defy neat separation into ‘Newtonian’ and ‘anti-Newtonian’ camps.

In the education of George III, then, geometrical exercises were intended to play a vital but carefully delimited role in shaping the prince's moral character. His long, undated ‘Essay on duty’ made the position more explicit, with direct reference to the alternative views of specific moral philosophers. Adopting the notion of the ‘moral sense’ proposed by Francis Hutcheson, the prince primarily condemned Thomas Hobbes for having ‘drawn a very odious picture of us’ by rooting human morality in self-interest.Footnote ⁷² But neither did he follow Samuel Clarke in arguing that moral relationships were analogous with proportional relationships in mathematics; after considering this position he rejected it. In his Boyle lectures, delivered in 1704, Clarke had argued that ‘the Original Obligation of all … is the eternal Reason of Things’.Footnote ⁷³ According to this eternal reason,

In his response to Clarke, Prince George explicitly refuted this geometrical model, writing that some philosophers

Returning to ‘Some short notes concerning the education of a prince’, we can clearly distinguish its attitude towards geometry from that of Clarke. Geometry prepared the mind for ‘the discovery of those sources from which all our moral obligations flow, and the pursuit of these obligations in all the parts to which they extend’.Footnote ⁷⁶ But it was not, in itself, the source or model of those obligations. Instead, Bute's concern for the ‘culture of the heart’ stemmed from his Hutchesonian view of moral obligation, which derived from the benevolent passions and affections, and from an internal, naturally operating, ‘moral sense’.Footnote ⁷⁷ Here the mental faculty shaped by geometry was conceived as an instrument of the benevolent passions, ensuring their efficacy in practice.

In the complex form of pedagogy adopted by the Earl of Bute in the late 1750s, each type of study aimed at forming a specific part of the prince's moral subjectivity. Sensitivity to the passions and affections, and the ability to conceptualize their operation, were complemented by exercises in the mathematical sciences. The latter were intended to habituate the mind to pursuing and identifying the truth ‘latent under every disguise’ – and thus to enable the prince to act as well as to feel virtuously.Footnote ⁷⁸ With direct concern for cultivating this ‘moral sense’, Bute drew on other branches of learning, such as history and moral philosophy. He attempted both to sensitize the young prince to his own passions and affections and, on a more general level, to illustrate the importance of their proper management for the happiness and virtue of individuals and societies. In one of his earliest letters explicitly regarding Prince George's education, the earl used a historical ‘abstract’ to show the prince how far his own moral character and education were implicated in the survival of the British Empire. In the great empires of the past (Egypt, Assyria, Babylon, Persia, Greece and Rome), ‘effeminacy and corruption’ led to eventual decline and defeat.Footnote ⁷⁹ This was a natural result of the accumulation of wealth and trade, and the consequent softening of manners in these ruling nations. Another reason for the ruin of ancient empires, however, was the depravity of their princes, and this Bute painted in the highest terms of condemnation, as resulting directly from bad education. ‘From their tender years’, wrote Bute, ‘they were surrounded by the basest flatterers, men who paid a servile court to their passions, cultivated with the utmost care every vicious inclination and laughed at honor, honesty, and every virtue’.Footnote ⁸⁰ The result was personal and national misery. Bute deployed these examples as a warning to the young Prince of Wales – to fear flatterers, and above all to preserve the warmth of his filial affection and regard for his mother:

Bute used history to make the prince aware of his own attachments and desires, as well as their social and political consequences. He also used contemporary moral philosophy to equip him with a conceptual model of virtue, the passions and affections. Prince George's ‘Essay on duty’ is a reworking of Hutcheson's An Essay on the Nature and Conduct of the Passions and Affections (1728), arguing in favour of the moral sense against philosophers, such as Clarke, who based the principles of virtue in reason; and, more importantly, against those, such as Hobbes, who understood human beings as fundamentally motivated by self-interest.

Following Hutcheson closely, the prince's ‘Essay on duty’ argued that human beings are endowed by God with a moral sense which naturally, and previously to ‘instruction, art, or Volition’, perceives virtue and vice.Footnote ⁸² He also proposed that noble, generous or benevolent actions are motivated by ‘Publick Affections’ (according to Hutcheson, ‘Love, Congratulation, Compassion, natural Affection’), rather than reason or self-love.Footnote ⁸³ The public affections operating unchecked, however, could be harmful to the individual and are moderated by ‘ye Private passions’ (‘Ambition, Covetousness, Hunger, Lust, Revenge, Anger’).Footnote ⁸⁴ Again, these ‘violent’ or ‘particular’ passions and affections alone cannot provide steady, moral direction; they are ideally dominated by ‘general’ or ‘calm’ desires of the same type.Footnote ⁸⁵ As the prince explained, ‘a calm self love is plac’d at ye head of ye Private passions, to direct their attractions & Repulsions. ye Publick Affections are controul'd by a dispassionate Benevolence, which in ye same manner ought limit their motion’.Footnote ⁸⁶

As Bute pictured it, the primary benefits of geometry in moral education would come from practical exercises, training the understanding to work in tandem with the passions. Hutcheson's system of counterbalancing passions and affections allowed the dynamics of emotional life to be figured mechanically, and in doing so Hutcheson used the intermediary image of the human body. The passions and affections ‘are by Nature balanced against each other, like the Antagonist Muscles of the Body … jointly, they form a Machine, most accurately subservient to the Necessities, Convenience, and Happiness of a rational System’.Footnote ⁸⁷ The prince chose instead to compare the passions and affections directly to a machine:

The instruments of natural philosophy played a complex role here: they simultaneously acted as the basis for moral exercise and provided a powerful analogy for Hutcheson's system of counterbalancing passions and affections.

This recurring emphasis on the efficacy of machines in moral life, present at diverse material and cognitive levels in the education of George III, raises the question whether virtue was conceived by him and Bute as mechanical, in the radical sense proposed by eighteenth-century French thinkers such as Julien Offray de La Mettrie. La Mettrie, rejecting Christian metaphysics, reduced the body and the soul to a single, physical substance. His moral philosophy was mechanical in that it held individuals' virtue or vice to be determined by the qualities of their physical constitutions; it also regarded standards of virtue and vice to be wholly conventional, constructed for the benefit of societies rather than for that of individuals in their natural state.Footnote ⁸⁹ In contrast, Hutcheson explicitly framed his moral sense as a faculty of the soul, and he considered the ‘public passions’, as the springs of social virtue, to be wholly natural.Footnote ⁹⁰ Adopting Hutcheson's philosophy, Bute and Prince George sidestepped the question whether the corporeal training implicit in geometrical practice contributed to its psychological effects. They juxtaposed, without attempting to integrate conceptually, the Hutchesonian analogy between moral affect and mechanics, on the one hand, and mechanical practice as moral exercise, on the other. By declining to draw any explicit, physiological relation between the two, the earl and the prince also avoided the suggestion that virtue itself might be mechanical, in La Mettrie's sense of being physiologically determined.

Bute's confidence in the moral utility of mathematical practice seems to represent a novel development in the history of princely education in Britain. Tudor and Stuart treatises on the subject, while concerned with virtue as one of the pillars of monarchical rule, considered the mathematical sciences injurious, indifferent, or useful only in the arts of war.Footnote ⁹¹ Nonetheless, the moral education of George III does speak to a broader context in which the Newtonian philosophy was used to secure the legitimacy of Hanoverian rule in Britain. Historians recognize a number of distinct modes of Newtonian apologetics for the Hanoverian succession. Steven Shapin has described disputes over the nature, sources and limits of monarchical power extending from the Exclusion Crisis into the 1720s, in which Newtonian doctrines formed part of the complex alignments among political parties, High and Low Church factions, and court and country interests.Footnote ⁹² Concerned to protect their standing at court and to quash perceived doctrinal threats to the Established Church, Newtonian Whigs made attacks on Leibniz abroad and freethinkers at home, in which natural-philosophical questions became virtually coextensive with questions over the nature of monarchical power.Footnote ⁹³

Allegorical and iconographic modes of association between Newtonianism and the Hanoverian regime are also well known. John Theophilus Desaguliers's allegorical poem The Newtonian System of the World, the best Model of Government (1728) argued by analogy with law-governed, planetary motion for the natural legitimacy of Hanoverian rule in a system of ‘limited Monarchy’.Footnote ⁹⁴ An iconographic mode of argument, using portrait busts to assert national, intellectual and moral affiliation with her adopted country, was deployed with apparent success by Queen Caroline in the early 1730s. Caroline's Hermitage at Richmond housed the busts and written works of the English philosophical and theological ‘worthies’, Isaac Newton, John Locke, Robert Boyle, William Wollaston and Samuel Clarke. As a widely publicized space for solitary retirement and contemplation, Caroline's Hermitage announced her identification with British virtues and achievements, in large part through association with Newton.Footnote ⁹⁵

Caroline's grandson, George III, was the first Hanoverian monarch born and raised in England. By the time of his succession, the last Jacobite rebellion had been suppressed; public anxiety over the foreignness of the Hanoverians, and the legitimacy of their succession, had largely subsided.Footnote ⁹⁶ In the context of his education, the question of legitimate rule was posed to him not as a dynastic concern, but rather as a matter of personal character. Here the Newtonian philosophy, deployed by previous generations as a ‘resource’ in political conflict, as a naturalizing allegory or as a nationalistic emblem, accrued a further role: that of providing exercises for transforming a self-confessed ‘indolent’ youth into a virtuous – and therefore morally legitimate – monarch.Footnote ⁹⁷ As a material basis for geometrical practice, the instruments now on display at the Science Museum in London played a tacit but crucial role in this undertaking.