Barron, Stephanie. Jane Austen mystery #15

"March 1817: As winter turns to spring, Jane Austen's health is in slow decline, and threatens to cease progress on her latest manuscript. But when her nephew Edward brings chilling news of a death at his former school, Winchester College, not even her debilitating ailment can keep Jane from seeking out the truth. Arthur Prendergast, a senior pupil at the prestigious all-boys' boarding school, has been found dead in a culvert near the schoolgrounds--and in the pocket of his drenched waistcoat is an incriminating note penned by the young William Heathcote, the son of Jane's dear friend Elizabeth. Winchester College is a world unto itself, with its own language and rites of passage, cruel hazing and dangerous pranks. Can Jane clear William's name before her illness gets the better of her?" --Goodreads