DENTAL SYSTEM 25 
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 formule.—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 :— 
- : 1-1 4-4 8-3 11-11 
3_3 canines >—, premolars 1 a ee 
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— 
1$,ct pt m $= 41; total 44. 
incisors molars 
The individual teeth of each group are always enumerated from 
before backwards, and by such a formula as the following— 
; 41,72,73,¢,p1, p 2, p 3, p4, m1, m2, m3 
41,72,73,¢,p1, p2, p38, p4,m1,m2,m3 
or more briefly— 
.1,2,3 1 1, 2, 3,4 1, 2, 3 
ae Ee ea ee 
A special numerical designation is thus given by which each one 
can be indicated. In mentioning any single tooth, such a sign as ™1 
will mean the first upper molar, mi the first lower molar, and so on. 
The use of such signs saves much time and space in description.! 
It was part of the view of the founder of this system of dental 
notation that, at least throughout the group of mammals whose 
dentition is derived from this general type, each tooth has its 
strict homologue in all species, and that in those cases in which 
fewer than the typical number are present (as in all existing 
mammals except the genera Sus, Gymnura, Talpa, and Myogale), the 
teeth that are missing can be accurately defined. According to 
this view, when the number of incisors falls short of three it is 
assumed that the absent ones are missing from the outer and 
posterior end of the series. Thus, when there is but one incisor 
present, it is ¢1; when two, they are 11 and i2. Further- 
more, when the premolars and the molars are below their typical 
number, the absent teeth are missing from the fore part of the 
premolar series, and from the back part of the molar series. If 
this were invariably so, the labours of those who describe teeth 
1 By many writers the letters indicating the different kinds of teeth are 
printed in capitals, as 7, C, P, and M; while very frequently the symbol Pm is 
employed in place of p. 
