dg.differential geometry - Example for an integral, rectifiable varifold with unbounded first variation

I'm just looking for an example of an integral, rectifiable varifold, which has no locally bounded first variation.

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Recapitulation

for every $m$-rectifiable varifold $mu$ exists a $m$-rectifiable set $E$ in $mathbb R^n$, meaning $E=E_0 cup bigcup_{kinmathbb N} E_k$ with $mathcal H^m(E_0)=0$ and $E_ksubseteq F_k$ for some $mathcal C^1$-manifolds $F_k$ of dimension $m$, and a non-negativ function $thetain L^1_{text{loc}}(mathcal H^m|_E)$ such that $mu=theta mathcal H^m|_E$. This is a characterisation of $m$-recitifiable varifolds.
The first variation $deltamu$ of a varifold $mu$ is for $etainmathcal C^1_c(mathbb R^n;mathbb R^n)$ given by
$$deltamu(eta)=int div_mueta,dmu,$$
where $ div_mu(eta)(x) = sum_{i=1}^n tau_i^T(x)cdot Deta(x)cdot tau_i(x)$ where $tau_i(x)$ is a orthogonal basis of the tangentspace of $mu$ in $x$, which coinsidence $mu$-almost everywhere with $T_xF_i$ for $xin E_isubseteq F_i$ as above. So $div_mueta(x)$ is just the divergence in the manifold $F_i$, with $xin E_isubseteq F_i$.

We say $mu$ has an locally bounded first variation, if for all $Omega'subseteq Omega$ there exists $c(Omega')<infty$ such that
$$ deltamu(eta) le C(Omega',Omega) Vert etaVert_{L^infty(Omega)} qquadforall;etainmathcal C^1_c(Omega'). $$
See for more explanation for example http://eom.springer.de/G/g130040.htm.

For a $mathcal C^2$-manifold $M$ in $mathbb R^n$ with mean curvature $H_M$ the first variation is
$$ delta M(eta)=-int_M H_M cdot eta ,dvol_M -int_{partial M} tau_0 cdot eta ,dvol_{partial M} qquadforall;etainmathcal C_c^1(mathbb R^n)$$
with the inner normal $tau_0in T_xMcap(T_xpartial M)^bot$ and where the mean curvature is the trace of the second fundamental form $A$ by the meaning of $H_M(x)=sum_{i=1}^m A_x(tau_i,tau_i)$ in the normal space of $M$. As obviouse in this case the first variation is locally bounded.