Successful missionaries in 19th-century Africa required certain attributes: burning religious passion, a firm if dubious belief in Western cultural superiority and a robust constitution headed the list.

Other assets were deemed to be desirable but not absolutely necessary: these included a wife.

As Julie Davidson explains in her delightful new book, the organisations that supervised missionary activity preferred their agents to be married. Wives provided companionship, they could help with pastoral chores, and they made their husbands much less threatening to the locals. A missionary who brought the family along on his evangelical adventure was less likely to cause trouble – he would not want to endanger his nearest and dearest. It therefore came as no surprise when David Livingstone married Mary Moffat in 1845.

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Many of Livingstone's biographers have assumed that this was a marriage of convenience. There's compelling evidence to back this up, including the famous letter Livingstone wrote at the time of his engagement. He described Mary in pragmatic terms: she was "a matter-of-fact lady, a little thick, black-haired girl, sturdy, and all I want".

Not much sign of Eros there, but then again Livingstone was not one who often exposed his soul in his correspondence and, crucially, we have no idea how Mary felt about the match. In any event, a genuine devotion developed during their marriage and Davidson discerns moments of playfulness and even "some joy and laughter". She also points out that the hectic rate at which Mary fell pregnant indicates that the couple enjoyed a suitably healthy sex life.

Unfortunately, the marriage also had more than its share of dark days. Livingstone was the most restless of missionaries and his wanderlust routinely put his wife in troublesome situations. Crossing the Kalahari while pregnant cannot have been pleasant for Mary and, on one occasion, her mother sent Livingstone a very stern letter. He was planning another of his jaunts and Mrs Moffat was scandalised by the prospect of "a pregnant woman with three little children trailing about in the company of the other sex, through the wilds of Africa, among savage men and beasts". Assuredly, she wrote, "All the world will condemn the cruelty of the thing to say nothing of the indecorousness of it."

The alternative was for Livingstone to leave his wife behind for a while. This happened quite frequently, too, but the results were no more satisfactory. Mary hated being apart from her husband and often felt "wretched and vulnerable". At no time did this become more apparent than during the 1850s, when Mary was sent to languish in the UK for several years while her husband concentrated on becoming one of the most celebrated figures of the Victorian era. It was an awful period for Mary. She sank into depression, squabbled with the in-laws, struggled with debts and, so rumour whispered, became overly fond of the demon drink. Most devastatingly of all, she began to question her religious faith.

It is a poignant tale but anyone who seeks to tell it faces a mighty obstacle. Mary left behind no journals and only a handful of letters: the remainder may well have been destroyed by Livingstone or his heirs and trustees. A comprehensive biography of this fascinating woman is therefore out of the question. Davidson realises this: as she puts it, Mary is a "phantom in her own story". It is still possible, however, to produce a convincing sketch, and that's what Davidson sets out to do. The result is a compelling blend of verifiable fact and, for the most part, reasoned speculation.

Mary's pluck is hard to miss. She was terrified of lions, but that was eminently sensible, and she seems to have taken other dangers in her stride. She was never afraid of hard work, whether this involved planting turnips, making soap from animal fat or mastering the local languages. Above all, this book challenges the stereotypical image of Mary as nothing more than a "steadfast and solid" wife. Davidson suspects that "a searching intelligence was trapped inside the carapace of obedience and reserve". We'll never know, but given all that Mary endured, I'd like to think Davidson is correct.

This volume knows its limits, but when the facts run out, Davidson wisely inserts stories of her own exciting journeys in search of Mary's deeds. Here we encounter the author's profound love for her subject and Africa. Davidson travelled to Mary's grave on the banks of the Zambezi and laid down a few flowers. Some might say Mary deserved a dozen bouquets, but I found Davidson's gentle, heartfelt tribute both touching and appropriate. I felt much the same about this wonderful book.

Looking For Mrs Livingstone

Julie Davidson

Saint Andrew Press, £24.99