The Argument of the Riemann Zeta Function on the Critical Line

The following assertion is proved: If $N_1(T)$ is the number of sign changes of the argument of the Riemann zeta function $\zeta (s)$ on the interval $0<\operatorname{Im}s\le T$ of the critical line$\operatorname{Re}s=1/2$, then, for any $a$ such that $27/82<a\le 1$, $T\ge T_1(a)>0$, and $H=T^a$, the inequality $N_1(T+H)-N_1(T) \ge H\log T\exp \bigl (-\frac {c\log \log T}{\sqrt {\log \log \log T}}\bigr )$ holds with a constant $c=c(a)>0$.