It is shown that all the normals drawn from any point in the plane to the members of a family of equiangular spirals may be simply located geometrically. The locus of all the end points of the normals is a circle. It is also shown that the standing wave pattern in a uniformly attenuating medium may in simple cases (as with an attenuating transmission line) be represented by a vector diagram using a symmetrical pair of spirals. Then the foregoing theorem makes it possible to determine the voltage and current maxima and minima by constructing the locus circle referred to. This is illustrated by several examples. Finally it is pointed out that the locus circle may also be projected into the ``Smith Chart.''