With regard to the lower teeth the difficulties are greater, owing to the absence of any suture corresponding to that which defines the incisors above; but since the number of the teeth is the same, the corresponding teeth are preceded by milk-teeth, and in the large majority of cases it is the fourth tooth of the series which is modified in the same way as the canine (or fourth tooth) of the upper jaw, it is quite reasonable to adopt the same divisions as with the upper series, and to call the first three, which are implanted in the part of the mandible opposite to the premaxilla, the incisors, the next the canine, the next four the premolars, and the last three the molars. It may be observed that when the mouth is closed, especially when the opposed surfaces of the teeth present an irregular outline, the corresponding upper and lower teeth are not exactly opposite, otherwise the two series could not fit into one another; but as a rule the points of the lower teeth shut into the interspaces in front of the corresponding teeth of the upper jaw. This is seen very distinctly in the canine teeth of the Carnivora, and is a useful guide in determining the homologies of the teeth of the two jaws. Objections have certainly been made to this view, because, in certain rare cases, the tooth which, according to it, would be called the lower canine has the form and function of an incisor (as in Ruminants and Lemurs), and on the other hand (as in _Cotylops_, an extinct Ungulate from North America) the tooth that would thus be determined as the first premolar has the form of a canine; but it should not be forgotten that, as in all such cases, definitions derived from form and function alone are quite as open to objection as those derived from position and relation to surrounding parts, or still more so. _Dental formulæ._—For the sake of brevity the complete dentition, arranged according to these principles, is often described by the following formula, the numbers above the line representing the teeth of the upper, those below the line those of the lower jaw:—incisors ³⁻³⁄₃₋₃, canines ¹⁻¹⁄₁₋₁, premolars ⁴⁻⁴⁄₄₋₄, molars ³⁻³⁄₃₋₃ = ¹¹⁻¹¹⁄₁₁₋₁₁; total 44. Since, however, initial letters may be substituted for the names of each group, and it is quite unnecessary to give more than the numbers of the teeth on one side of the mouth, the formula may be conveniently abbreviated into— _i_ ³⁄₃, _c_ ¹⁄₁, _p_ ⁴⁄₄, _m_ ³⁄₃ = ¹¹⁄₁₁; total 44. The individual teeth of each group are always enumerated from before backwards, and by such a formula as the following— _i_ 1, _i_ 2, _i_ 3, _c_, _p_ 1, _p_ 2, _p_ 3, _p_ 4, _m_ 1, _m_ 2, _m_ 3 ------------------------------------------------------------------------- _i_ 1, _i_ 2, _i_ 3, _c_, _p_ 1, _p_ 2, _p_ 3, _p_ 4, _m_ 1, _m_ 2, _m_ 3 or more briefly— 1,2,3 1 1,2,3,4 1,2,3 _i_ ------ _c_ -- _p_ -------- _m_ -----. 1,2,3, 1, 1,2,3,4, 1,2,3