It is known that if θ θ ( ξ ξ ) is a solution of the Lane–Emden equation, then so is C 2 / n + 1 θ θ ( C ξ ξ ) . Solutions that are related in this way are called homologous ; the process that transforms them is homology. If one chooses variables that are invariant to homology, then we can reduce the order of the Lane–Emden equation by one.