The distinctions between art and science, and arts and crafts, were unknown before the 17th century. "Arts" simply implied skills, whether in painting and music, or in glass-making, furniture-making or even magic. The division between the "fine arts" and the lower "mechanical arts" came later and, with that separation, and the post-romantic downgrading of science, much was lost.

In this wide-ranging survey of the aesthetics and practice of innovation and design from the 17th to the 19th centuries, Celina Fox sets out to recreate that vanished, unified sensibility. To do so she examines the progress and perception of industry from different perspectives, providing a detailed account while remaining alert to the piecemeal process and regional differences of the industrial revolution.

Her undertaking is complicated by the inbuilt links between technical innovation on the one hand and entrepreneurship and commerce on the other. The first significant attempt to study the "history of the trades" was made by the newly formed Royal Society in 1660. The research was conceived both as a study of the curiosities of the artificial, as opposed to the natural, world, and as a means of enriching the national coffers. But Fox notes the distorting impact of cultural background and ideology.

On the one hand, John Evelyn's eager, scatter-gun approach and classifying of trades as "Useful and mechanical", "Mean trades", "Servile", "Rusticall" and "Curious" (which included his beloved arts) displayed an intellectual and social stratification typical of the dilettanti. On the other, William Petty's account was dominated by economic concerns, stressing the importance of mathematics and engineering  his own interests. Meanwhile, Robert Hooke's more down-to-earth approach was governed by a determination "to facilitate and improve the present way of manual arts".

Despite good intentions, the project faltered and died, partly because of these divergent interpretations, but also because many craftsmen proved understandably reluctant to divulge their precious techniques. This clinging to trade secrets would dog similar projects until the breakthrough made in the 1750s by John Hinton's splendidly illustrated Universal Magazine of Knowledge and Pleasure. This was aimed squarely at the "middling classes", and was published, Fox notes dryly, while Diderot was still struggling with the famous Encyclopédie, which had yet to publish any plates.

In her central chapters, Fox looks at the means that those involved in technical and industrial work, particularly civil and mechanical engineering, used to communicate experiments and plans, inventions and achievements. These include drawing, models, societies, and publications such as technical manuals where "rational explanation" and "visual exposition" are complementary  or should be. The study of societies embraces the long-lasting, fruitful collaborations of small groups such as the Lunar Society of Birmingham. But Fox's main concern is with the aims and activities of the Society for the Encouragement of Arts, Sciences and Manufactures, founded in 1754, and the fierce arguments that raged about its procedures, especially its wooing of well-born amateurs as opposed to genuine artisans.

The book also offers insights into areas that are not usually covered in surveys of the growth of industry, such as naval surveying and shipbuilding, from Edward Dummer's exquisitely presented surveys of Britain's harbours and dockyards in the 1690s to the achievements  and unfulfilled visions  of Samuel Bentham (Jeremy's younger brother) and Simon Goodrich during the Napoleonic wars. But Fox's fine understanding of technical innovation is always combined with a shrewd awareness of financial and political manoeuvring. Bentham returned from a trip to Russia in 1807, for example, to find that his post as inspector general of naval works had been abolished, because the navy board was allegedly so "exasperated by the disruptions caused by his mechanical and managerial innovations at a time of war".

The difficulties were not always of official making  sometimes the engineers themselves were to blame. The technical instructions for assembly that often baffle us today presented equal difficulties in the 18th century, when the problem was not a flat-pack wardrobe but a towering, snorting steam engine. The elegant drawings of James Watt and other engineers are often admired for their clarity and logic, but the view was not so rosy on the ground. The Creighton brothers, in charge of building many Boulton and Watt engines, took to calling the Soho foundry "Pandemonium". Their task was bedevilled by drawings arriving in the wrong order and hopeless measurements. "Most drawings of parts are wrong for all engines," William Creighton lamented, adding that he had "tried to scrape some drawings into shape but 'tis a vile job and temporary joins exist in abundance". The achieving of Britain's industrial might is not always a tale of grand heroism.

Yet many entrepreneurs did feel they were engaged on a heroic project of national importance. In her later chapters Fox explores the way that industrialists and the public saw the projects and the projectors through paintings and portraits. It is fascinating, in this respect, to note how an artist such as Paul Sandby, who began as a surveyor and mapmaker and is best known for his topographical prints, also produced vivid scenes of industry, and to see too how the portrayal of industrial sites moves from the meticulously technical to the light-filled scenes of Joseph Wright and fiery romanticism of Loutherbourg. At the same time, portraits of industrialists such as Richard Arkwright, posing beside their machines, radiate a pride that the spectator is clearly supposed to share.

Fox has raided innumerable archives for new material, but her meticulous scholarship never swamps her sensitivity to the constraints under which people worked as well as the visions to which they aspired. Copiously illustrated and lavishly produced, The Arts of Industry is a notable contribution to the interdisciplinary studies of this area that have appeared increasingly in recent years, drawing attention to aspects of British history, skills and art that have been too long overlooked.

Jenny Uglow's A Gambling Man: Charles II and The Restoration is published by Faber.