## Abstract

The extent to which the `splay', `bend' and `twist' constants (K$_{1,2,3}$) of a nematic liquid crystal differ from one another and the way in which they depend upon the degree of alignment (as characterized by the nematic order parameter S$_2$) are determined by the interaction responsible for alignment, V$_{ij}$. Priest (1973) has already shown that if V$_{ij}$ is expanded in products of spherical harmonic functions such as Y$_{l$_i$, m}$ Y$_{l$_j$,m}$ the contributions made to K$_1$, K$_2$ and K$_3$ by successive terms in the expansion are additive, and he has discussed the relative magnitude of these contributions for l$_i$ = l$_j$ = 2 and l$_i$ = 2, l$_j$ = 4. Priest's results in the limit S$_2$ = 1 are here confirmed, and they are extended to the case l$_i$ = l$_j$ = 4. To obtain results for the range 0.7 > S$_2$ > 0.4 which is of interest experimentally, however, Priest invoked the mean field approximation, and his conclusion that the contributions he considered are proportional to S$^2_2$ and S$_2$S$_4$ respectively is invalid for that reason. Methods of analysis developed in previous papers of this series are here used to show that Priest's S$^2_2$ should be replaced over the range of interest by say AS$^n_2$, where both A ($\approx$ 1) and n ($\approx$ 1.35) depend in principle on m and on whether it is K$_1$, K$_2$ or K$_3$ that interests us, though the variations are not great in practice. The same expression (AS$^n_2$ with A $\approx$ 1) may be used to describe the order-dependence of (l$_i$ = 2, l$_j$ = 4)- and (l$_i$ = 4, l$_j$ = 4)-contributions to K$_{1,2,3}$, with n $\approx$ 3.25 (\pm 0.25 say) and n $\approx$ 4.2 (\pm 0.4 say) respectively. The revised results can be fitted to recent data for nematic 5CB, but it would be premature to draw firm conclusions about the nature of V$_ij$ in this substance, because several approximations are still present in the theory. A conjecture made in earlier papers in the series concerning \langle P$_4$(cos $\beta_ij$)\rangle (alias $\sigma_4$) is here confirmed.