He laughed. ‘It might be easier, aboard a small vessel, to obtain a fish eye, don’t you think?’

I scanned the room again. ‘What are the jars for?’

‘Preserving spirits. Anything of significance that I can procure on our voyage will be fixed in fluid and sent to London for… greater minds to work on. You can imagine, Miss Grayling, how heavy those jars are. It took me forever to get them down here.’

‘And this?’

I pointed at a strange object that stood on the floor in the gloom beside the far end of the desk. A glass orb, not quite a sphere, around a foot in diameter. It stood atop a brass cylinder, with a valve between the sphere and the cylinder operated by a small brass tap. The apparatus stood on a wooden tripod, and between the legs of the tripod there was a crank handle. The glass of the orb gleamed: in that dull interior plenty of things gleamed, but only this object did so in a way that suggested conceit.

‘That? That is an air pump. I had it made from Robert Boyle’s drawings. Are you familiar with them?’

I came closer. Peered into it. ‘No. What does it do?’

He smiled. ‘Perhaps we will have an opportunity to use it in our travels.’

My eyes roved further. Two pictures on the bulkhead behind him. The first was a lithograph depicting some terrible armoured monster: a bulbous abdomen and a narrow, pointed head lending it a shape like a comma lying on its side. Its backswept legs and mouth parts bristled with hairs like a fly, but it had no wings. In place of feet it had gleaming claws that hooked forward. It had a fierce, determined eye and what seemed to be a moustache.

‘What on earth?’

He laughed. ‘That, Miss Grayling, is a flea. It’s a page from Hooke’s Micrographia: I had it cut from the book and framed, I loved it so. The world we reveal with the microscope: all that power and rage in such a tiny creature.’

‘A doctor with a penchant for fleas at close quarters. Nice.’ Again he looked wounded and I wondered if I’d gone too far. ‘And the chart? Why have you drawn on it?’

A long spiral had been traced over the map, its origin somewhere near Sydney, leading south-west then curving anticlockwise, gently at first, through the south and then the east as it passed through the archipelago, becoming tighter and tighter as it wound its way into the heart of the speckling islands.

He waved the backs of his fingers at it. ‘A fancy of mine…’

‘What kind of fancy?’ I had him now. I’d found a deeper topic, where he’d be unable to condescend.

‘Spiral geometry. Sequences. Are you familiar with Euclid’s golden ratio?’

‘Not freshly.’ I gave him half a smile. ‘Remind me.’