de Gennes gave a three-parameter representation of strain energy in a cholesteric liquid crystal that is second order on the $Q$ tensor, and hence in order parameter. He discarded a term involving an elastic constant ${K}_{24}$ which is relevant at surfaces and disclinations. The splay and bend elastic constants ${K}_{11}$ and ${K}_{33}$ are alike in the second-order theory. The complete Oseen-Frank expression in terms of a director has five parameters, including ${K}_{24}$. If uniaxiality, which is implicit in the director theory, is imposed on the $Q$ tensor, five independent third-order tensor functions are found. These differentiate between ${K}_{11}$ and ${K}_{33}$ and show the third-order dependence of the Oseen-Frank elastic constants on order parameter. Numerical values of these second- and third-order elastic coefficients of 4-methoxybenzylidene-4\ensuremath{'}-$n$-butylaniline (MBBA), $p$-azoxyanisole (PAA), and E-7 (British Drug House designation of a cyano-biphenyl mixture) are obtained from published values of the dependence of Oseen-Frank elastic constants and various anisotropies on temperature, and from a relation of Nehring and Saupe.