  We study spectral properties of Hamiltonians $\rH_{X,\gB,q}$ with
$\delta'$-point interactions on a discrete set
$X={x_k}_{k=1}^\infty\subset\R_+$. %at the centers $x_n$ on the positive half
line in terms of energy forms. Using the form approach, we establish analogs of
some classical results on operators $\rH_q=-d^2/dx^2+q$ with locally integrable
potentials $q\in L^1_{\loc}(\R_+)$. In particular, we establish analogues of
the Glazman-Povzner-Wienholtz theorem, the Molchanov discreteness criterion,
and the Birman theorem on stability of an essential spectrum. It turns out that
in contrast to the case of Hamiltonians with $\delta$-interactions, spectral
properties of operators $\rH_{X,\gB,q}$ are closely connected with those of
$\rH_{X,q}^N=\oplus_{k}\rH_{q,k}^N$, where $\rH_{q,k}^N$ is the Neumann
realization of $-d^2/dx^2+q$ in $L^2(x_{k-1},x_k)$.
