  The mass of gas in protoplanetary discs is a quantity of great interest for
assessing their planet formation potential. Disc gas masses are, however,
traditionally inferred from measured dust masses by applying an assumed
standard gas-to-dust ratio of $g/d=100$. Furthermore, measuring gas masses
based on CO observations has been hindered by the effects of CO freeze-out.
Here we present a novel approach to study the mid-plane gas by combining
C$^{18}$O line modelling, CO snowline observations and the spectral energy
distribution (SED) and selectively study the inner tens of au where freeze-out
is not relevant. We apply the modelling technique to the disc around the Herbig
Ae star HD 163296 with particular focus on the regions within the CO snowline
radius, measured to be at 90 au in this disc. Our models yield the mass of
C$^{18}$O in this inner disc region of
$M_{\text{C}^{18}\text{O}}(<90\,\text{au})\sim 2\times10^{-8}$ M$_\odot$. We
find that most of our models yield a notably low $g/d<20$, especially in the
disc mid-plane ($g/d<1$). Our only models with a more interstellar medium
(ISM)-like $g/d$ require C$^{18}$O to be underabundant with respect to the ISM
abundances and a significant depletion of sub-micron grains, which is not
supported by scattered light observations. Our technique can be applied to a
range of discs and opens up a possibility of measuring gas and dust masses in
discs within the CO snowline location without making assumptions about the
gas-to-dust ratio.
