One of the enduring puzzles about Leibniz’s metaphysics is how Leibniz could claim that his monads, understood as essentially immaterial, could constitute the material bodies of experience. In this talk, Arthur sketches how he thinks Leibniz intended this to be understood. First, Arthur situates Leibniz's introduction of his monads as a solution to the problem of the composition of the continuum. With this in place, Arthur distinguishes Leibniz’s notion of constitution from composition, and shows how this can be construed to deliver his conclusions by constructing a kind of "characteristic” using his definitions and symbols.