The title of Miranda Seymour’s vastly enjoyable new book is misleading. It suggests that Byron’s wife and daughter tumbled about in the slipstream of a volcanic genius. Yet although there was no escaping the blaze and shadow of Byron’s brilliance, the persona that he created and the fame that followed his life and death, their own lives were themselves rich in intellectual adventure. In very different ways, they were brave, bold, often hopelessly naive and sometimes maddening. It is one of the many pleasures of this book that Seymour makes the reader warm to their inconsistencies, to all the inexplicable oppositions of character and action that make them so familiar and human.

In Seymour’s account, angled to put the women centre stage, Byron is vain, narcissistic and self-pitying, his shallow affections most comfortably absorbed by Augusta, the half-sister even he called a ‘ninny’. He exits the scene early in the book, exiled from his wife and baby daughter in a sulphurous cloud of scandal. The courtship of Byron and Annabella Milbanke has been picked over by scholars for two hundred years; most have concluded that whichever way you look at it they made an odd couple. The doted-on only child of elderly Unitarians with progressive ideas, Annabella was clever, confident and allergic to criticism. She had a pronounced tendency to self-righteousness. At twenty-two and an heiress, she had many suitors but fell for Lord Byron. Well of course she did! And because she was probably too high-minded to read the cheap novels that would have taught her a thing or two, her heart, as Seymour puts it, was ‘obstinately set upon the reformation of a rake’. And Byron, sometimes, wanted to be saved – from the tormenting relationship with Augusta, his amorous ideal whose physical features resembled his own. Furthermore, at twenty-six, he was hopelessly in debt and Annabella had money. He proposed, she refused, and then, sitting at her parents’ home in Richmond, wrote to graciously extend the hand of mere friendship. Back and forth they went, she poring over every word he wrote, he mostly lukewarm but respectful too: he liked her rational, clear-sighted intelligence, though he mocked her as ‘the princess of parallelograms’. She tried to manipulate him by hinting at another admirer, but he was simply better at this game and tormented her by taking her at her word. By the time his financial circumstances compelled him to propose again, he was already bored. And yet Seymour’s account covers the contradictions too: there was something there between the two of them, sometimes.

The marriage, formalised in 1815, was ‘a sojourn in hell’, lasting barely a year. Byron drank, had liver problems and a pet squirrel. He veered between wallowing in guilt and cruelly dangling his infidelities before his wife, between dieting and stuffing himself with food. All unknowing, Annabella wrote to Augusta, married to George Leigh, for advice and they went to live with her. At night, Annabella was forced to retire early and listen to the siblings giggling downstairs; by day, Byron made Augusta read out the rude things he had written to her about Annabella before they married.

The following year it was all over. Annabella was back at home with her parents and Ada, away from the public gaze, agog with the rumours of incest and sodomy that followed Byron into exile. But if Annabella and Ada are the main subjects of this book, silly, pliant, morally vacuous Augusta played a crucial part in their lives as they subsequently unfolded. Annabella, for reasons that seem mostly inexplicable, for many years professed affection for Augusta, milking her for news of Byron. In a sitcom, the imprudent, impecunious, scandal-prone Leighs would be the embarrassing family members who turn up at awkward moments hoping for a loan. Years after her feelings for Augusta had curdled to loathing, Annabella supported members of her family – most strikingly her third daughter, the duplicitous, greedy Elizabeth Medora, believed (by Annabella and Medora at any rate) to have been fathered by Byron, and who had run off with her sister’s husband.

The Leighs are the comic counterweight to Annabella and Ada, whose intellectual excursions are at the centre of this book. Annabella developed a passionate interest in educational reform, opening several successful schools dedicated to technical education for the poor. The principles she laid out for them seem startlingly sensible. There would be no religious teaching and not too much sedentary work; expectations would not be set too low but there would be no prizes, ‘no definite boundary between work and play’, no corporal punishment and not too much ‘legislation’.

Her own daughter was hot-housed: intellectually precocious, exceptionally imaginative, Ada was a voracious reader and learner; at seven, she had a good word for her passion – ‘gobblebook’. At eleven, she experimented with flight by building a set of wings based on close study of the skeleton of a bird. She was lucky in her mother’s friends and was introduced by the mathematician Mary Somerville to the polymath and maverick Charles Babbage. Now she is best known (indeed rightly celebrated) for her translation of Luigi Menabrea’s article on Babbage’s Analytical Engine, supplemented with her own notes. These include this extraordinarily prescient description of the possibilities, intuitively grasped if not fully comprehended, of such a machine: ‘A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.’

Brilliant, ebullient, eccentric, vivacious, egocentric and oddly dressed, Ada had her mother’s discipline and her father’s volatility. Her husband, William King, Earl Lovelace, spent much of his time obsessively creating ornate architectural fantasies and she was prone to sudden passions (at sixteen she had briefly tried to elope with her shorthand tutor), including an unfortunate affair with a Somerset science enthusiast called John Crosse, who drained her of money, forcing her to pawn the Lovelace diamonds. But Ada’s relentless, awe-inspiring curiosity enchants. She numbered among her interests mathematics, the science of electricity and, at the end of her life, horse-racing odds, a passion that left her addicted to gambling. Even when felled by pain from the cancer that would kill her at thirty-six, she chose to see the illness as an opportunity to learn, to see her body as a molecular map, to create, as she put it, ‘a calculus of the nervous system’.

Annabella, whose reputation as a prig, a humbug and a tyrant is overturned in Seymour’s subtle, sympathetic examination, outlived her daughter, seeing the descendants of her short union with the 19th century’s most glittering celebrity go their own way into adulthood. Most intriguing was Ada’s eldest child, Lord Ockham, who turned his back entirely on the grand life, the big estates, high benevolence and intellectual endeavour. He went to sea with the Royal Navy, deserted, then became a worker in a shipyard. He was dead by the age of twenty-six. His burial place is unrecorded.