  There are numerous examples of continuity in the mathematical structure of successive scientific theories. Indeed Niels Bohr and others explicitly applied the methodological principle known as the ‘correspondence principle’, according to which quantum-mechanical models ought to mathematically reduce to classical models in the limit of large numbers of particles, or the limit of Planck's constant becoming arbitrarily small. There are many cases in quantum mechanics where the Hamiltonian functions that represent the total energy of mechanical systems imitate those of classical mechanics, but with variables like those that stand for position and momentum replaced by Hermitian operators. Simon Saunders (1993a) discusses the structural continuities between classical and quantum mechanics and also shows how much structure Ptolemaic and Copernican astronomy have in common.  Harvey Brown (1993) explains the correspondence between Special Relativity and classical mechanics. Jonathan Bain and John Norton (2001) discuss the structural continuity in descriptions of the electron, as does Angelo Cei (2004). Votsis (2011) considers examples of continuity and discontinuity in physics.  Robert Batterman (2002) discusses many examples of limiting relationships between theories, notably the renormalization group approach to critical phenomena, and the relationship between wave and ray optics. Holger Lyre (2004) extends Worrall's original example of the continuity between wave optics and electromagnetism by considering the relationship between Maxwellian electrodynamics and Quantum Electrodynamics. Saunders (2003c and d) also criticises Tian Cao (1997) for underestimating the difficulties with a non-structuralist form of realism in the light of the history of quantum field theory.