The thermal expansivity α(p) is related to isothermal compressibility κ(T) at various pressures for constant temperatures of 254.6, 274 and 297.5 K close to the melting pressure in ammonia solid III. By analyzing the experimental data for κ(T) according to a power-law formula, a linear variation of α(p) with the κ(T) is established here close to the solid-liquid transition in ammonia. Anomalous behavior of thermal expansivity α(p) and the isothermal compressibility κ(T) near the melting pressure is indicative of the λ-type transition in ammonia solid III.