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Italian Cosimo Alessandro Collini (1727-1806), at the time chairman of the Cabinet of Curiosities of the principality of Pfalz (Germany), was the first naturalist to speculate about pterodactyls in 1784.
Fig.1. Pterodactylus antiquus (Upper Jurassic, Eichstätt, Bavaria), specimen studied by Cosimo Collini in 1784 and copper engraving of the fossil to illustrate his scientific study (image in public domain).
Based on a strange fossil found in a limestone quarry near the town of Eichstätt, with exceptional large fin-like arms and also associated with petrified remains of fishes and crustaceans, he proposed that these creatures once lived swimming in the sea.
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French-German naturalist Johann Hermann (1738-1800), observing the drawings made by Collini, also concluded that the elongated fourth finger of the creature supported a membrane of soft tissue, however he believed that this membrane formed a wing-like feature and pterodactyls therefore were able to fly! In March 1800 he contacted the French paleontologist Cuvier, presenting to him one of the first soft tissue reconstructions of an extinct animal: a body covered by fur (which, even if Hermann had studied the original specimen, is not preserved), large wings that resemble those of a bat - especially the part between the neck and the limbs of the animal - Hermann was even able to reconstruct the (obviously male) gender of the fossil specimen.
Fig.2. First life restorations of Pterodactylus antiquus by Jean Hermann of Strasbourg, from a letter send to George Cuvier in 1800 (image in public domain).
Studying Hermann´s description and drawings in 1801, but not the actual fossil, Cuvier confirmed the presence of the membranous wings and reclassified the creature tentatively as a flying reptile - adding to his classification the note, that this animal was for sure the strangest of all prehistoric creatures he had ever seen (and he had seen a lot!).
British paleontologist Richard Owen also classified pterodactyls as reptiles, but noted that the metabolism of these reptiles only enabled them to an unsafe flight and their possible maximum size would not exceed those of modern vertebrates. Already in 1847 this conclusion was refuted by the discovery of "Pterodactylus giganteus", an animal with a wingspan of over 4,7m (15 feet).
The naturalist and entomologist Edward Newman (1801-1876) published in 1843 his theory on the pterodactyl-problem, where he dared to contradict mighty Cuvier and Owen. Given the similarity of the skeleton with today's bats and the need for an efficient metabolism, pterodactyls must, so Newman, be mammals.
Fig.3. Reconstruction according to Newman´s pterodactyls-must-be-a-sort-of -mammal hypothesis of "Pterodactylus crassirostris" and below "Pterodactylus brevirostris", from NEWMAN 1843 (image in public domain).
Despite Newman´s effort, in the following decades the classic reptilian reconstruction will prevail, with pterodactyls resembling large winged, scaly, somehow sluggish lizards, most time seen resting on ground or hanging from rocky cliffs or trees. Only in Germany, where paleontologist Georg August Goldfuss (1782-1848) interprets minute pits found along the fossilized wing membranes as hair follicles, flying reptiles can be reconstructions as more dynamic and "evolved" creatures.
Modern research has finally established that pterosaurs are closely related to the archosaurs and some species were definitely covered by a sort of fur, but the onset of these "hairs", or better "bristles", in the outer epidermis makes these structures only superficially similar to mammalian hairs. The fur of pterodactyl is an example of convergent evolution, where features supposedly useful for thermoregulation were evolved independently in very different animal groups.
Fig.4. Specimen of Rhamphorhynchus muensteri (Upper Jurassic, Eichstätt Bavaria) with preserved imprints of flying membranes.
Fig.5. Left arm with imprints of the membrane of Rhamphorhynchus muensteri (Upper Jurassic, Eichstätt Bavaria). On this specimen, nicknamed "Zittel-wing", the German paleontologist Karl Alfred von Zittel in 1882 described the true shape and the structure of the pterosaur-wings.
Bibliography:
HUTCHINSON, H.N. (1897): Extinct monsters: A popular account of some of the larger forms of ancient animal life. Chapman & Hall, ld. London
NEWMAN, E. (1843): Note on the Pterodactyle Tribe considered as Marsupial Bats. The Zoologist 1: 129
SEELEY, H.G. (1901): Dragons of the air, an account of extinct flying reptiles. Appleton. New York
TAQUET & PADIAN (2004): The earliest known restoration of a pterosaur and the philosophical origins of Cuvier's Ossemens Fossiles. Comptes Rendus Palevol, 3(2): 157-175