Let $\mathcal W$ be the classical Wiener measure on $C_0 = \bracs{f \in C([0, \infty)): f(0) = 0}$. Let $ H_0^1 = \bracs{f \in C^1 \cap C_0: Dh \in L^2} $ For every $f \in C_0([0, \infty))$, define $ S_f: C_0 \to C_0 \quad \theta \mapsto S_f\theta = \theta + f $ as the translation map. Let $\mathcal W_f$ be the distribution of $S_f$. If $f \in H_0^1$, then $\mathcal W_f \ll \mathcal W$, with $ \frac{d\mathcal W_f}{d\mathcal W} = \exp\braks{\mathcal I(Df)_\infty(\theta) - \frac{\norm{Df}_2^2}{2}} $ where $ \mathcal I(Df)_\infty = \int_0^\infty f(r)d\theta(r) $ If $f \not\in H_0^1$, then $\mathcal W_f \perp \mathcal W$.