The probable shape, size, and orientation of desmosomes of the cells comprising the secretory tubules in rat submaxillary gland was determined by statistical and algebraic methods applied to electron micrographs. It was concluded that these desmosomes are discrete ellipsoidal discs whose principal axes are in the order of 4100 and 2500 angstrom units, and that they are preferentially oriented with their long axis more or less parallel to the base-apex axis of the cell. Densitometric interpretation agrees with the statistically based reconstruction of desmosomal shape. By densitometric analysis it was also determined that the peak to peak distances between layers within these desmosomes are in essential agreement with other reported findings. The approach described may have general applications to problems in the analysis of submicroscopic morphology.

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