  The multi-planetary system HD 106315 was recently found in K2 data . The
planets have periods of $P_b \sim9.55$ and $P_c \sim 21.06\,$days, and radii of
$ r_b = 2.44 \pm 0.17\, $ and $r_c = 4.35 \pm 0.23\, $ $R_{\oplus}$. The
brightness of the host star (V=9.0 mag) makes it an excellent target for
transmission spectroscopy. However, to interpret transmission spectra it is
crucial to measure the planetary masses. We obtained high precision radial
velocities for HD~106315 to determine the mass of the two transiting planets
discovered with Kepler K2. Our successful observation strategy was carefully
tailored to mitigate the effect of stellar variability. We modelled the new
radial velocity data together with the K2 transit photometry and a new
ground-based partial transit of HD 106315c to derive system parameters. We
estimate the mass of HD 106315b to be 12.6 $\pm$ 3.2 $M_{\oplus}$ and the
density to be $4.7 \pm 1.7\, g\,cm^{-3}$, while for HD 106315c we estimate a
mass of 15.2 $\pm$ 3.7 $M_{\oplus}$ and a density of $1.01 \pm 0.29\,
$g\,cm$^{-3}$. Hence, despite planet c having a radius almost twice as large as
planet b, their masses are consistent with one another. We conclude that HD
106315c has a thick hydrogen-helium gaseous envelope. A detailed investigation
of HD 106315b using a planetary interior model constrains the core mass
fraction to be 5-29\%, and the water mass fraction to be 10-50\%. An
alternative, not considered by our model, is that HD 106315b is composed of a
large rocky core with a thick H-He envelope. Transmission spectroscopy of these
planets will give insight into their atmospheric compositions and also help
constrain their core compositions.
