  On the basis of the result obtained by applying Baxter's exact perturbative
approach to the dilute A_3 model to give the E_8 mass spectrum, the dilute A_L
inversion relation was used to predict the eigenspectra in the L=4 and L=6
cases (corresponding to E_7 and E_6 respectively). In calculating the
next-to-leading term in the correlation lengths, or equivalently masses, the
inversion relation condition gives a surprisingly simple result in all three
cases, and for all masses.
