Magnetic Field Dependence of $T_{AB}$ in Superfluid $^3He$

The magnetic field dependence of the $A\to B$ transition temperature $T_{AB}$ in the superfluid $^3He$ is reconsidered in order to take into account the linear-in-field contribution beyond the approximation used in Ref.[7]. In the high field region, where the quadratic-in-field contribution prevails, the well known answer is restored. On the other hand,it is pointed out that the Fermi liquid effects shift the observability of the linear-in-field region to rather low magnetic fields.