So how do I know this figure is Melpomene? A clever friend of mine did the work by doing what I should have done: he referred to James Hall's Dictionary of Subjects & Symbols in Art. This is a great reference, and I do use it often. Hall tells that Melpomeme is one of nine muses, each with her own sphere of influence over learning and the arts.
Classical figures compel me to learn about the classics, and this makes them especially intriguing. And now that I know there are nine muses, I shall be watching for figures depicting the remaining eight, not to mention other figures on this same base. I giggle inwardly when I am dubbed an 'expert' on early Staffordshire figures. In reality, I am a student, forever learning. And that's so exciting.