Experiments were performed which demonstrate some of the length-measuring characteristics of a grid consisting of two sets of parallel lines crossing each other at right angles. If lines of various shapes are repeatedly superimposed at random on such a grid, the mean number of intersections each of these lines makes with the lines of the grid is directly proportional to the length of the line. There is a property of two-dimensional curves, which may be called directional bias, the presence of which in a test curve will increase the variability of the number of intersections made with the grid lines and skew the frequency distribution curve to the right. This effect is markedly reduced by taking the mean of three measurements if the second and third are taken with the grid rotated 30 degrees and 60 degrees respectively from its original position in relation to the test curve. Information gained from these experiments can be applied to stereological problems such as the estimation of particle densities in histological sections.
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