Melting curve of ${}^4$He: no sign of the supersolid transition down to 10 mK

We have measured the melting curve of ${}^4$He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 $\mu$bar. Crystals of different quality show the expected $T^4$-dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid ${}^4$He and on the Debye temperature of solid ${}^4$He. Below 80 mK we have observed a small deviation from $T^4$-dependence which however cannot be attributed to the supersolid transition because instead of decrease the entropy of the solid rather remains constant, about $2.5\times {10}^{-6}$ $R$