|William John Wills|
William turned out to be Dr. William Wills, the brother of Les Vesconte's mother Sarah -- and the reason he wanted to sell was because he'd decided he wanted to emigrate to Australia! It seems, however, that his wife was initially unwilling to go, and so their sons headed out ahead of them; the stratagem worked, and the Willeses followed them a few months later. The family ended up in Ballarat in Victoria, where the father set up a new medical practice.
And it was there that his son William John Wills began a series of pursuits that would soon lead him to become, as had his cousin, an explorer. He'd had medical training with his father, and the younger William showed a gift for natural history reminiscent of Harry Goodsir's. He also became an avid outdoorsman, and learned the art of surveying; it was in this capacity that he was engaged by Robert O'Hara Burke, who had conceived of the almost-unheard-of idea of crossing the entire Australian continent on foot. The expedition departed in August of 1860, and endured almost unimaginable difficulties, primarily with a shortage of rations and the lack of other edible food sources. With the dismissal of the expedition's second-in-command, Wills became Burke's lieutenant. As they neared their final goal, though, Will's health declined steadily. Their only food at this point was the occasional fish and great heaps of nardoo -- a sort of Australian aquatic four-leaf clover. It was far from lucky for them -- instead, it became their "tripe de roche."
Finally, when it was clear he could go on no longer, Williams voluntarily stayed behind in their hut when Burke went to gather more nardoo. Fittingly, he wrote a final letter to his father before he died, and it's there that his thoughts turned to his cousin Henry:
Cooper's Creek, 27 June, 1861.
MY DEAR FATHER,
These are probably the last lines you will ever get from me. We are on the point of starvation, not so much from absolute want of food, but from the want of nutriment in what we can get. Our position, although more provoking, is probably not near so disagreeable as that of poor Harry and his companions.
He died the next day, followed soon after by Burke himself. It was to be William's letters and journals, posthumously edited by his father, that became the best-known account of the journey. You can read them in full here. The expedition has many other similar aspects to Franklin's -- numerous searchers were sent, but mis-read the clues and narrowly missed rendering aid, and the exact cause of Wills and Burke's deaths is disputed even to this day, with some blaming the improper preparation of the nardoo, some blaming scurvy, and some pointing to beri-beri (caused by a deficiency of Vitamin B1) as the main culprit.