As before, the three dimensional density of the disc is given by We modify the GalactICS model accordingly to generate this density. If Type II profiles are instead assumed to be due to dust extinction, Eq. 10 holds for the disc density, and only the light follows an inner truncated profile (Eq. 1). The KD disc employs two integrals of motion: the energy E and the angular momentum L$_{z}$ , and an approximate third integral describing the energy in the vertical motions, E$_{z}$ . By the Jeans theorem, any function of three isolating integrals of motion in a given potential will exactly solve the CBE (Binney & Tremaine 2008). The third integral allows for σ$_{z}$ = σ$_{R}$ ; observations of the solar neighbourhood suggest that σ$_{z}$/σ$_{R}$ = 0 . 6 (Wielen 1974), which would be impossible if the DF were a function of only two integrals of motion. The GalactICS model decouples the vertical and radial dispersion of the disc. The vertical dispersion is given by the vertical potential gradient and scale height. The radial velocity dispersion is given by and the tangential dispersion is given by the epicycle equations, i.e. Here, Ω = v/R is the angular rotation speed and the epicycle frequency κ is given by κ 2 = [ R ( d Ω $^{2}$/dR ) + 4Ω $^{2}$]. By design, the velocity ellipsoid in the GalactICS disc is cylindrically aligned. Note that Eq. 13 includes a parameter to control the scale length of the velocity dis- persion profile. Although observations by Bottema (1993) suggest that R$_{d}$ = R$_{σ}$ , there is no clear theoretical reason why this should necessarily be the case. Here we treat R$_{d}$ and R$_{σ}$ independently to provide maximum flexibility in fitting all data sets. The GalactICS model, modified to include inner truncation, has two further parameters for the disc; the turnover radius R$_{h}$ and the cutoff index α . We complete the parameter 3.2. Summary of the GalactICS model 11 σ$_{φ}$ = κ 2Ω σ$_{R}$. (14) σ 2 R = σ 2 0 exp( − R/R$_{σ}$ ) (13) ρ ( R, z ) = ρ$_{0}$ exp [ − ( R/R$_{d}$ − ( R$_{h}$/R ) $^{α}$)] sech $^{2}$( z/z$_{d}$ ) . (12) 3.1.3. The dynamics