  The chromatic spectral sequence is introduced in \cite{mrw} to compute the
$E_2$-term of the \ANSS\ for computing the stable homotopy groups of spheres.
The $E_1$-term $E_1^{s,t}(k)$ of the spectral sequence is an Ext group of
$BP_*BP$-comodules. There are a sequence of Ext groups $E_1^{s,t}(n-s)$ for
non-negative integers $n$ with $E_1^{s,t}(0)=E_1^{s,t}$, and Bockstein spectral
sequences computing a module $E_1^{s,*}(n-s)$ from $E_1^{s-1,*}(n-s+1)$. So
far, a small number of the $E_1$-terms are determined. Here, we determine the
$E_1^{1,1}(n-1)=\e^1M^1_{n-1}$ for $p>2$ and $n>3$ by computing the Bockstein
spectral sequence with $E_1$-term $E_1^{0,s}(n)$ for $s=1,2$. As an
application, we study the non-triviality of the action of $\alpha_1$ and
$\beta_1$ in the homotopy groups of the second Smith-Toda spectrum V(2).
