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A statistical model of the successive locations of an animal in the plane induces a statistical model of the relative positions of successive locations. A common locational model is that the Cartesian coordinates of successive locations in the plane are independent bivariate normal random variables. This note gives the statistical properties of the direction and length of the vector joining successive locations.

Przibram's Rule states that the ratio of the mean weights in successive instars of hemimetabolous insects is 2.09. Faber (1994) described a two‐stage approach to testing Przibram's Rule when the instars of the measured individuals are unknown. In the first stage, individuals are assigned to one of the instars on the basis of their weights. In the second stage, a test of the null hypothesis that the means of logarithmic weight in the two groups differ by the logarithm of 2.09 is performed. This approach suffers from two problems. First, errors in assigning individuals to instars will exaggerate the difference between instars. Secondly, the validity of the test in the second stage is based on the implicit assumption that the variance of logarithmic weight in the two groups is equal. This note describes a test of Przibram's Rule that avoids these problems.