Perimeter data, obtained from structured walks performed upon straight chains of circles and displayed in Richardson plots, reveal two distinct classes of discontinuities: textural and structural. Textural discontinuities contain information about the surface features of the profile, while structural discontinuities reveal the profile＇s overall shape. The origins of both types of discontinuities have easy explanations. The highly predictable behavior of the structural discontinuities serves as the basis of a newly proposed method of analysis for perimeter data. The number of structural discontinuities is equal to N, the number of circles in the chain; furthermore, the value of the step size <(lambda)under bar>* associated with the first structural discontinuity is inversely related to N. These properties seem to be retained when the circles slightly intersect and also when the circles vary in diameter. Analysis of the structural discontinuities may provide a new method suitable for automated examination of chain-like agglomerate particles.