CRANIOLOGY OF THE PEOPLE OF SCOTLAND. 605 



taken in twenty-six specimens, twenty-one males and five females ; the mean of the 

 series was 90 : that of the males was 92'3, that of the females 87*8. 



Kollmann divides skulls and heads into two groups according to the relation of the 

 length to the breadth of the face. When the index is 90 '1 or upwards the face, he says, is 

 leptoprosopic, high (long) or narrow faced ; when the index is below 90'1 it is chamse- 

 prosopic, low or broad faced. In the study of the proportions of the face, and in grouping 

 skulls in accordance with their facial indices, it is useful, as in the other relative propor- 

 tions of the skull, to have a group intermediate between the two more extreme forms. 

 We may appropriately speak, therefore, of a third or mesoprosopic group, and include in 

 it those skulls and heads in which the index ranges from 85 to 90, both inclusive. The 

 charnseprosopic group under this arrangement would consequently be limited to those 

 heads in which the index is below 85. In the series of Scottish crania under considera- 

 tion eighteen were leptoprosopic, four were mesoprosopic, and only four were chamse- 

 prosopic in my more limited use of the term. 



To obtain as far as possible an idea of the relation between the length and breadth 

 of the face in skulls where the lower jaw is absent, Kollmann has suggested that the 

 interzygomatic breadth should be compared with the length of the superior maxilla 

 measured from the nasion to the alveolar point between the two central incisors. 

 Seventy-nine crania were measured in these diameters, viz., fifty-six males and twenty- 

 three females. 



The male crania ranged in the maxillary length from 61 mm. to 84, and the mean 

 was 71*6 mm. The female crania ranged from 60 to 74 mm., and the mean was 

 67 mm. An index, which may be appropriately named maxillo -facial, can be computed 

 as follows : 



nasio-alveolar length x 100 

 interzygomatic breadth 



The maxillo-facial index was taken in seventy-nine skulls, fifty-five of which were 

 males and twenty-four females. It ranged from 61 '8 to 46'5, and the mean was 54'6. 



In grouping crania under the maxillo-facial index, Kollmann employs the same 

 terms, leptoprosopic and chamseprosopic, as in the divisions of the complete facial 

 index, but the numerical limits of the two groups, owing to the length representing only 

 a segment of the complete face, are necessarily different. When the maxillo-facial index 

 is 50 "1 and upwards, he regards it as leptoprosopic ; when 50 or less, it is chamseprosopic. 

 In this memoir I have retained the numerical limit of the leptoprosopic group, and find 

 that with seven exceptions all the skulls belonged to it, and that in five leptoprosopic 

 specimens the index ranged from 60*3 to 61 "8. If a division of the chamseprosopic group 

 of Kollmann into mesoprosopic and chamseprosopic were adopted for the maxillo-facial 

 as I have suggested for the complete facial index, and 45 were taken as the lower 

 numerical limit of the mesoprosopic group, the seven exceptional skulls above referred 

 to would fall into that group. No skull, therefore, in its maxillo-facial index was 



