We study one dimensional continuous loss networks with length distribution $G$ and cable capacity $C$. We prove that the unique stationary distribution $\eta_L$ of the network for which the restriction on the number of calls to be less than $C$ is imposed only in the segment $[-L,L]$ is the same as the distribution of a stationary $M/ G / \infty$ queue conditioned to be less than $C$ in the time interval $[-L,L]$. For distributions $G$ which are of phase-type ($=$ absorbing times of finite state Markov processes) we show that the limit as $L\to\infty$ of $\eta_L$ exists and is unique. The limiting distribution turns out to be invariant for the infinite loss network. This was conjectured by Kelly (1991). \\ {\bf Key words:} Loss networks, Poisson process, projection method, stationary distribution, quasi stationary distributions. \\ {\bf AMS Classification:} Primary: 60D05, Secondary: 60G55}