@Lordyaswas,
I don't know about the princes, but Austin refers to it as baseball (one word) in her
juvenilia, in the uncompleted
Catherine, or the Bower, which she wrote in the 1790s. Every year, when the
New York Times would have their annual spring baseball frenzy, they would often trot out references to base ball (two words) from documents as early the 1830s. For many years, i would send off letters to them, pointing out that Miss Austin was writing about baseball about 40 years before that. I eventually gave up the effort, because the editorial staff, apparently, found my letters beneath their notice.