The majority of the preceding families are more or less clearly represented by fossil remains, either in the younger strata of the earth’s crust, or in those cave-deposits of comparatively recent date which have furnished so many interesting relics of the Mammals of former days. It must be remarked, however, that while a considerable number of fossil Rodents have been named and described by palæontologists, the materials upon which many of them have been established are very imperfect; in a great number of cases isolated molar or even incisor teeth furnish the sole evidence of the existence of creatures which were manifestly Rodents, but of which the other characters are rather difficult to divine from such scanty material. Still, imperfect as may be “the record of the rocks” in this as in other instances, it is in some parts sufficiently complete to enable us to trace back the existence of many forms of gnawing Mammals through a long period of geological time. Of the SCIURIDÆ a considerable number of fossil species have been recorded. Species of the genera _Sciurus_, _Arctomys_, and _Spermophilus_, some of them identical with those still existing, have left their remains in Post-Tertiary deposits and in bone-caves in various parts of Europe; while species belonging to the first two genera, and to the American genus _Tamias_, have been detected in similar situations in North America. A few forms referred to the same genera go down still lower in the series of geological formations. True Squirrels are recorded from Miocene and Upper Eocene deposits in France, and a single species from the Tertiaries (probably Miocene) of Colorado; Marmots from Pliocene and Miocene beds in the South of France, and from a Pliocene deposit in Nebraska; and a Spermophile from the Miocene of Weisenau in Germany. Besides these examples of known types, several fossils have been obtained both in Europe and America, which are regarded as indicating genera distinct from any now living. _Plesiarctomys Gervaisii_ is founded on a fragment of jaw with four molars, obtained from Upper Eocene beds near Apt, Vaucluse. In its characters it appears to be intermediate between Squirrels and Marmots. _Pseudosciurus suevicus_, from the Upper Eocene (Bohnerz) of Würtemberg, seems to differ from all other Sciuridæ in the form of the molar teeth of the lower jaw, which are somewhat elongated, and have four tubercles arranged in two pairs, each pair being connected by a ridge. From the Tertiary deposits of the western territories of the United States, Professors Cope, Marsh, and Leidy have described several Sciurine Rodents as belonging to genera now extinct: thus _Paramys_ has five species; _Sciuravus_ (perhaps identical with the preceding), three; _Heliscomys_, _Mysops_, _Colonymys_, _Taxymys_, and _Tillomys_, one or two species each.