  We have determined the magnetic phase diagram of the quasi-one-dimensional
$S=$ 1 Heisenberg antiferromagnet $Ni (C_5 H_{14} N_2)_2 N_3 (PF_6)$ by
specific heat measurements to 150 mK in temperature and 32 T in magnetic field.
When field is applied along the spin-chain direction, a new phase appears at
$H_{c2}\approx 14$ T. For the previously known phases of field-induced order,
accurate determination is made of the power-law exponents of the ordering
temperature near the zero-temperature critical field $H_c$, owing to the
four-fold improvement of the minimum temperature over the previous work. The
results are compared with the predictions based on the Bose-Einstein
condensation of triplet excitations. Substituting deuterium for hydrogen is
found to slightly reduce the interchain exchange.
