A refinement of two effective inequalities of A. Baker

A refinement is made of A. Baker's effective estimates for $|\alpha-p/q|$, where $\alpha$ is algebraic of degree $\ge3$ and $p/q$ is a rational fraction, and for the boundary of the integral solutions of the Diophantine equation $f(x,y)=m$, where $f$ is an irreducible form with integral coefficients of degree $\ge3$, and $m$ is a rational integer.