In 1840 he introduced his theory regarding cranial shapes to the Academy of Science at Stockholm, and two years later gave a course of lectures on the same subject. He criticised the results attained by Blumenbach, showing that his group contains varying types of skull form; and he invented the cephalic index, or length-breadth index—_i.e._, the ratio of the breadth of a skull to its length, expressed as a per-centage. The narrower skulls he termed dolichocephalic, the broader ones brachycephalic. By this method Retzius designed rather to arrange the forms of crania than to classify thereby the races of mankind, though he tried to group the European peoples more or less according to their head-form. While thus elaborating the suggestion of Blumenbach, he also recorded the degree of the projection of the jaws, demonstrated by Camper, and he added the measurements of the face, height, and jugular breadth. Thus was Craniology established on its present lines. [Sidenote: =Grattan.=] John Grattan (1800-1871), the Belfast apothecary, has never received the recognition that was his due. Having undertaken to describe the numerous ancient Irish skulls collected by his friend Edmund Getty, he soon became impressed by the absence of that uniformity of method and that numerical precision without which no scientific investigation requiring the co-operation of numerous observers can be successfully prosecuted. The mode of procedure hitherto adopted furnishes to the mind nothing but vague generalities ... until we can record with something approaching towards accuracy the proportional development of the great subdivisions of the brain, as indicated by its bony covering, and by our figures convey to the mind determinate ideas of the relation they bear towards each other, we shall not be in a position to do justice to our materials.... No single cranium can _per se_ be taken to represent the true average characteristics of the variety from which it may be derived. It is only from a large deduction that the ethnologist can venture to pronounce with confidence upon the normal type of any race.[21] Footnote 21: J. Grattan, _Ulster Journal of Arch._, 1858. Grattan devised a series of radial measurements from the _meatus auditorius_, and constructed an ingenious craniometer. As Professor J. Symington points out, “Grattan’s work was almost cotemporaneous with that of Anders Retzius, and nearly all of it was done before the German and French Schools had elaborated their schemes of skull measurements.”[22] He adopted the most useful of the measurements then existing, and added new ones of his own devising. Footnote 22: _Proc. Belfast Nat. Hist. and Phil. Soc._, 1903-4; and _Journ. Anat. and Phys._