Quoting those passages may not be fair to Frost. Elsewhere in this beautifully produced study, he is so steadfastly the empirical professional historian. And the story he tells is as complex an account as any historian might care to undertake. Because Britain’s was the global reach of empire, Frost’s scholarship must be global as well. And we as readers must think globally, too: of Trincomalee and Penang, Nootka Sound, Egypt and Port Jackson. The voyage to all these places and to the ocean seas that bound them into meaning because they bound them into empire is demanding.

More demanding: we need to think like maritime imperialists. We need to recast our assumptions about space, need to read the relationship of land to sea differently. For years I have studied the great trading companies of the seventeenth-century Dutch seaborne empire. The West India Company’s vision of Manhattan Island startled me. The company completed the hydrographic mapping of the harbour and raks (reaches) of the Hudson River eight years before turning to a survey of the land. They said things that I once found strange: if we lose this shore fort, ‘the country and all is lost, and if held … the country also is held’. They thought in terms of archipelagos, searching for islands, not rolling prairielands. They privileged navy over army. In 1619 men of the East India Company came ashore at Djkatra (Batavia) as sea voyagers, not landsmen. They wanted its harbour and the control it gave of the Sunda Strait.

The Netherlands skippers told their stories in marvellous logs that take us to sea: to a ship’s deck covered with snow, hospital ships, an island in the narrows of an Indies strait called Right in the Way. Some narratives are printed in the Linschoten Collection. The University of Melbourne library has it. I am the only one who ever consults the volumes.

Alan Frost knows this strange world well. He is taking soundings of another empire, that of the British from 1764 to 1815. He is writing about the men who added the Indian and Pacific oceans to that imperial structure. The task he has set himself is a large one: how, between 1764 and 1815, did the Royal Navy ‘encompass the world’?

In the first of three sections, Frost begins his own exploration. He means to account for the integration into Europe’s ‘intellectual, political and economic system of a third of the world’s surface’. By 1783 the discovery voyages of explorers such as Samuel Wallis and James Cook had inaugurated a knowledge explosion of immense significance. The expansion of Cook’s imagination – in many ways unanticipated in the reach of its humanism – the paralleled the imaginative grasp of Britain’s policy makers, entrepreneurs and scientists. The new navigations put the French and Spanish on notice that Britain, already a presence in India and the Indies, would be a major player in a new zone of competition.

Frost’s reference to Europe’s systems is important. Throughout these decades, the interests of the European powers were singular but also interconnected. War entangled them continually. Rivalries for overseas trading spheres ensured that the integration of the newly discovered oceans would require years of naval contests. And Frost is an incisive reader of the diplomatic correspondence, the paper trail that marks the manoeuvres and occasional visions of this contestation.

To me, such correspondences are deeply depressing stuff: contrived half-truths; watching your back. Frost works carefully with it – indeed, is himself diplomatic. Not, I hasten to say, duplicitous, but careful in suggesting that, under the churning surf of the deceptions, miscalculations and sometimes sheer dottiness of officials were the currents of a plan, or a sequence of coherent plans. The Brits did not tumble into empire. They built up a navy, they searched for way-stations to impossibly distant places, they kept an eye out for naval materials (yes, trees for masts!) They waited to take the fine harbour of Trincomalee facing the Bay of Bengal – and it came to them. When they could not provide silver for the China trade, they traded furs from the Canadian Pacific coast. I say Frost is diplomatic in piecing together this overarching plan. Diplomats, like empire-builders, don’t leave behind smoking guns. So he needs to acknowledge conclusions that other historians have contested. This he does honestly but swiftly. And he is undeterred.

In the tightly argued middle section, Frost portrays Britain contending with continental powers for a very large world indeed. By 1783 she had lost her American colonies and was determined to avoid a similar fate in the East. But the shores and oceans of Ceylon, India and the Philippines were not easily won. Nor were strategic stations such as the Cape of Good Hope. A seemingly insignificant island such as Ache became important: think of its ‘Centrical Situation for a General Asiatic Commerce’.

‘Such an encompassing vision,’ Frost writes, ‘tends to leave the modern reader somewhat incredulous, but it was by no means uncommon at the time.’ And into this vision of centrical points for an all-Asian commerce fitted Botany Bay at Port Jackson. As Frost moves to the commercial and naval systems of the years from 1790 to 1815, we see schemes intersecting official policy and both, as during the administration of William Pitt the Younger, woven into vision and achievement. Nootka Sound, Penang, New Zealand: the Pacific Rim we know begins to emerge.

Frost’s British empire of the eighteenth century may not be the one that others prefer to write about. He doesn’t take naked imperialism to task as others do. He doesn’t make it his job to look closely at the other side of the beach. He is concerned with the terrible personal cost – to sailors, whalemen, soldiers – of trafficking imperialism. And he reflects on empire and loss. ‘Let the story of George Bass,’ he writes, ‘evoke the lives of all these agents of empire.’ And some paragraphs later: ‘Bass set out for South America on 5 February, 1803. Somewhere in the amplitudes of the great ocean, he disappeared.’