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Eurypterids were an extinct group of aquatic chelicerate arthropods which originated in the mid-Ordovician and persisted until the late Permian. Being character-rich organisms with a well-resolved and robust phylogeny, eurypterids are an excellent study group for exploring evolutionary mechanisms and processes, such as trends in diversity and disparity and drivers of morphological change. Here, we use eurypterids as a case study for exploring mosaic evolution and the role of functional constraints in limiting disparity through an emphasis on the morphological diversity of the prosomal appendages and differences in somatic variation in the prosoma and opisthosoma. A dataset comprising 122 characters coded for 39 taxa (selected for completeness) was compiled in order to explore patterns of complexity in eurypterid tagmata over the course of their evolutionary history. The matrix, while comprised of discrete characters, is explicitly distinct from the kind of matrices employed in phylogenetic analysis, with prosomal appendage armature and tergite pleural structures being coded somite by somite. In total, 62 characters are coded for the prosoma (16 of which relate to the prosomal carapace and 46 of which relate to the prosomal appendages) and 60 are coded for the opisthosoma (55 for the tergites and 5 for the telson). From this dataset Euclidean pairwise distances between all taxa were generated and subjected to ordination through principal coordinates analysis (PCO), generating a theoretical morphospace. We compare metrics for disparity(as summarized by the Sum of Ranges and Sum of Variance of occupied morphospace)and appendage differentiation (limb tagmatization as defined by Cisne 1974) to explore patterns in complexity and disparity across eurypterids. Prosomal and opisthosomal disparity was analysed together and separately, in order to test for mosaicism across the eurypterid tagmata, with eurypterids grouped according to either environmental occupation, the form of the chelicera, and the morphology of appendage VI. These analyses explore whether limb complexity correlates with different life habits, the impact of increasing cheliceral size on limb complexity, and whether the advent of swimming in the group resulted in a functional release for appendage specialization.