The author commences by a brief statement of the facts and conclusions recorded in a paper by Sir Ev. Home on the dentition of the Sus Æthiopicus , in the Philosophical Transactions for 1799, p. 256; and gives the results of an examination of the original specimens described and figured by Home, and of other specimens showing earlier stages of dentition, which lead to the following conclusions as to the number, kinds, and mode of succession of the teeth in the genus Phacochœrus . The tooth answering to the first milk-molar and first premolar in the upper jaw, and those answering to the first and second milk-molars and corresponding premolars in the lower jaw of the common Hog are not developed. Eight successive phases of development of the grinding teeth of the African Wart-hogs are described and expressed by the following notation:— Phase. No. of grinding teeth. Kinds of teeth. I. 5-5/4-4 viz. { d 2, d 3, d 4, m 1, m 2. d 3, d 4, m 1, m 2. II. 6-6/5-5 viz. { p 2, p 3, p 4, m 1, m 2, m 3. p 3, p 4, m 1, m 2, m 3. III. 5-5/4-4 viz. { p 3, p 4, m 1, m 2, m 3. p 4, m 1, m 2, m 3. IV. 4-4/4-4 viz. p 4, m 1, m 2, m 3. V. 4-4/3-3 viz. { p 3, p 4, m 2, m 3. p 4, m 2, m 3. VI. 3-3/3-3 viz. p 4, m 2, m 3. VII. 2-2/2-2 viz. p 4, m 3. VIII. 1-1/1-1 viz. m 3. These observations prove that, contrary to the opinion of Home and Cuvier, the Wart-hogs have deciduous teeth, succeeded vertically by premolar teeth; in the Phacochœrus Æliani , at least, three deciduous teeth are, in some individuals, succeeded by as many premolar teeth; and, as a general rule, two deciduous teeth are displaced vertically by two premolars. The first true molar is remarkable for its unusually early development, which is followed by an unusually early abrasion and expulsion, when its place is obliterated by the second true molar being pushed forwards into contact with the last premolar. This tooth is as remarkable for its longevity, and remains after the wearing away and shedding of the second true molar, when the last true molar advances into contact with the last premolar, and the place of both the previously intervening true molars is obliterated. This unusual order of shedding of the molar teeth has given rise to the idea of the last large and complex true molar of the Phacochœrus being the homologue of both the last and penultimate grinders of the common Hog, which the author’s observations refute; and he, also, is able to point out, by re-examination of the original specimen figured by Home in the Phil.Trans., the source of the erroneous idea that the common Hog had an additional true molar behind the large one symbolised by m 3, in the author’s system of dental notation.