The lower molars of toxodonts are all on the same plan, each tooth being composed of two crescents, the anterior and posterior. The ends of these crescents are referred to as the anterior, median and posterior horns. The bay in the anterior crescent is simple and usually disappears with the wear of the tooth without making a pit. In the centre of the posterior crescent is the pillar or posterior tubercle which Scott has found to be characteristic of these South American Ungulates. It is, to my mind, the same as the mesostylid of the Fayum hyracoids. Between the pillar and the median horn, I find a narrow vertical ridge, which I have termed the septum; and which tends to unite with the pillar inclosing a small bay, usually seen in worn teeth as a pit. The bay between the septum and the median horn is designated bay 2, and this quite generally appears in a worn tooth as a pit (2). The bay between the septum and pillar is designated bay 3, and is usually seen as a tiny pit, which however does not extend as deep into the crown as the other pits and is usually lost when the tooth is about half worn off. The bay between the pillar and the posterior horn is numbered 4, and is usually open, though in a worn tooth it also may appear as a pit. The effect of wear is shown by comparing B and C in fig. 52, the latter being the same tooth sectioned a little below the middle. I find in studying a lower molar of Coresodon that bay 3 becomes a pit after some 6 mm. are worn off, while bays 2 and 4 remain open until some 10 mm. are worn off when they also become pits. Pit 3 will disappear when 12 mm. are worn off, but pits 2 and 4 run to the base of the crown. The various genera of the _Toxodontia_ in the Deseado I would divide into four families as follows: =Rhynchippidae=: molars brachydont, secondary cristae lacking or little developed, none of the incisors caniniform, limbs slender, feet digitigrade, digits 3-3. =Leontinidae=: molars brachydont, secondary cristae lacking or little developed, upper inc. 2 and lower inc. 3 developed into caniniform teeth, limbs heavy, feet digitigrade, digits 3-3 (according to Gaudry). =Isotemnidae=: molars brachydont, secondary cristae more or less developed, crowns contracted at the top, congulum more or less developed into a platform, skeleton unknown. =Nesodontidae=: molars hypsodont, secondary cristae highly developed, upper inc. 2 and lower inc. 3 caniniform, limbs heavy, feet digitigrade, digits 3-3. =Rhynchippidae=