EVOLUTION OF THE SKULL AND TEETH OF EOCENE TITANOTHERES 



255 



8. Molar length and width, anteroposterior measurement of 

 first superior molar (m') and transverse measurement of the 

 same (least width, near center of crown). 



Indices of skull (expressed as per cent) 



- „ , . , ,. ■ J breadth across zygomata 



9. Zygomatic-cephalio mdex=r — n , .. ^ — —nr 



■^ ° basilar or cephalic length 



length of six superior 



r, 1 1 1, 1- • J grinding teeth, p^-m' 

 Premolar-molar cephahc index=^ iT't — j — <£ 



iiiujc^i ^^ij^ia.j^ iiiiic^v cephalic length 



I, ,, , u 1- ■ J length of upper true grinders, m'-3 



II. Molar-cephalic index =■ — ^, -,.-, -,-, 



'^ cephalic length 



, „ - , , . , breadth of a molar, mi or m^ 



12. Molar index= -. rr — c i 



length of a molar 



lensth of face ^' 



13. Faciocephalic index= ^r^. — , — -r;— 



'^ cephalic length 



length of cranium -' 

 cephalic length 



14. Craniocephalic index =- 



Flexures of skull 



15. Palatooranial flexure = angle that the palate, from the 

 posterior to the incisive border, makes with the basal line of the 

 cranium. (Not used in the study of titanotheres.) 



16. Faciocranial flexure = angle that the preorbital part of the 

 skuU, determined from the optic foramen (see figs. 213, 214) to 

 the incisive alveolus, makes with the line from the optic foramen 

 to the middle of the occipital condyle. 



SUMMARY AS TO CRANIOMETRY 



1. Direct measurement. — Since the fossil skulls and 

 dental series are rarely complete or perfect, the paleon- 

 tologist requires an additional series of direct detailed 

 measurements of parts of the skull and teeth that are 

 not needed by the zoologist. 



2. Significance. — Every one of these direct measure- 

 ments, indices, and angles is significant, because all 

 skulls are in a continuous process of movement, or 

 evolution. The indices are even more significant than 

 the direct measurements, because every genus and 

 probably every species has its distinctive indices in 

 adult specimens, and the direct measurements vary 

 greatly with the age, sex, and individual variation of 

 the specimen. 



3. Imperfection. — In fossil skulls the indices are 

 often difficult to determine; a slight crushing or dis- 

 tortion seriously disturbs the index, for a skull that is 

 crushed on its side is narrowed and lengthened at the 

 same time. Nevertheless, the indices and ratios 

 should be used wherever obtainable. 



4. Age. — The proportions between the several parts 

 are largely altered with the age of the animal; this 

 statement is especially true of progressive allometrons, 

 such as the proportion between the face and the 

 cranium. Thus the faciocephalic or craniocephaHc 

 index may alter rapidly as the titanothere advances 

 from youth to maturity; similarly the flexure (cyp- 

 tocephaly) becomes extreme only in mature skulls. 

 The age of the animal measured is thus to be con- 

 sidered in all the indices and ratios of the skull, teeth, 

 and skeleton. 



'* As projected on basilar line. 



5. Sexual correlations. — Certain proportions and indi- 

 ces are correlated sexual characters — that is, in brachy- 

 cephalic phyla the males have relatively broader heads 

 than the females. For example, we observe in the 

 genus Brontops the following proportions : 



Males of Brontops validus (braohycephalio), indices 73-87. 

 Females of Brontops validus (mesaticephalic), indices 

 60-70. 



FiGUBE 211. — Standard measurements of Eocene 

 titanothere skulls 



Palatal view of a skull of a middle Eocene titanothere, Mesatirhinus 

 petersoni, showing (by arrows) how the basilar or cephalic length, 

 the zygomatic width, and the length and width of the upper pre- 

 molars and molars are measured. 



6. Effects of crushing. — The indices of fossil skulls 

 are profoundly modified by vertical or lateral crush- 

 ing: vertical crushing tends to give brachycephalic 

 indices; lateral crushing tends to give dolichocephalic 

 indices. To these facts are due in part the wide 

 variations in the tables of indices, especially in the 

 chapter on the Oligocene titanotheres. 



