362 MORPHOLOGY OF THE CEREBRAL CONVOLUTIONS. 



Thus we find that even the best treatises on botany and zoology abandon the 

 subject, satisfied with merely contrasting the simple geometrical ground-lcim of 

 crystals with the highly curved and hopelessly complicated lines and surfaces of 

 the organism. 



But there are other considerations which lead up to a mathematical concep- 

 tion of organic form, those namely of symmetry and regularity. These, how- 

 ever, are usually but little developed, botanists since Schleiden contenting them- 

 selves with throwing organisms into three groups : — first, absolute or regular ; 

 second, regular or radiate ; third, symmetrically bi-lateral or zygomorphic — 

 the last being capable of division into two halves only in a single plane, the 

 second in two or more planes, the first in none at all. Burmeister, and more 

 fully Bronn, introduced the fundamental improvement of defining the mathemati- 

 cal forms they sought, not by the surface but by axes and their poles; and Haeckel 

 has developed the subject with an elaborateness of detail and nomenclature which 

 seems unfortunately to have impeded its study and acceptance, but of which the 

 main results may, with slight variations, due to Jaeger, be found in the Lehrbueh 

 der Zoologie, I, 283. The sciences of organic and mineral form would thus, as 

 Haeckel points out, become thoroughly analogous, for as promorphology develops 

 the crystallography of organic form, so mineralogy, in the study of such phenomena 

 as those of pseudomorphism or of mineral development, becomes parallel to mor- 

 phology. The present paper has been an attempt to study the convolutional con- 

 figuration of the cerebral surface from the stand-point of the physical sciences. 

 Promorphology has thus shown that the reigning dogma of the fundamental differ- 

 ence of organic and mineral forms is false, and that a crystallography of organic 

 forms is possible. 



The material on which these investigations were made was prepared, and the 

 figures are from photographs taken, by the author. Except where otherwise stated 

 in the explanation of the plates, the figures are original. 



