DENTAL SYSTEM 25 



other hand (as in Cotylops,axi extinct Ungulate from North America) 

 the tooth that would thus he determined as the first premolar has 

 the form of a canine ; hut it should not he 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. 



lh iit<tl formula'. — 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 : — 



. . 3-3 • 1-1 , 4-4 , 3-3 11-11 



incisors — , canines - — -, premolars - — 7 . molars r — - = — — — : 



3-3 1 - 1 L 4-4 3-3 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 — 



* f » c h P b m f = tt J 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, in 3 



or more briefly — 



. 1, 2, 3 1_ 1, 2, 3, 4 1, 2, 3 

 1 1, 2, 3' C 1' P 1, 2, 3, 4' m 1, 2, 3' 



A special numerical designation is thus given by which each one 

 can be indicated. In mentioning any single tooth, such a sign as Hi 

 will mean the first upper molar, ^n the first lower molar, and so on. 

 The use of such signs saves much time and space in description. 1 



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 i 1 ; when two, they are i 1 and i 2. 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 /, C, P, and M ; while very frequently the symbol Pin is 

 employed in place of p. 



