  This paper is a first step in order to extend Kummer's theory for line
congruences to the case $\lbrace x, \xi \rbrace $, where $x: U \rightarrow
\mathbb{R}^3$ is a smooth map and $\xi: U \rightarrow \mathbb{R}^3$ is a proper
frontal. We show that if $\lbrace x, \xi \rbrace$ is a normal congruence, the
equation of the principal surfaces is a multiple of the equation of the
developable surfaces, furthermore, the multiplicative factor is associated to
the singular set of $\xi$.
