314 
Merism and Sex in " S/nnax Niger 
anatomy, embryology, and palaeontology of the limbs themselves. There is 
however one fundamental difference between them. On the gill-arch theory the 
various positions of the limbs in the meristic series involve the conception of 
limb-migration or homoeosis. On the side-fold theory these positions may be 
supposed to be due to processes of excalation or intercalation of segments, though 
the possibility of homoeosis is not necessarily excluded. Its inclusion however 
cannot but detract from the simplicity of the theory. Consequently, if on 
independent grounds the phenomenon of homoeosis is found to be non-existent, 
the presumption in favour of the side-fold theory is very great. If, on the other 
hand, this phenomenon can be shown to be a reality, the gill-arch theory must 
gain considerable support. For with the balance of evidence equally poised, 
Gegenbaur's theory has the merit of deducing the limbs from a structure already 
in existence. In the present paper a considerable number of one of the most 
primitive of living vertebrates has been examined and the meristic variations 
studied with the aid of biometric methods. The key to the limb qiiestion has 
been sought in the vertebral column, and the evidence there gained in favour of 
homoeosis lends support to the gill-arch as opposed to the side-fold theory of the 
origin of the vertebrate limb. 
Before passing on to a consideration of the evidence I would here express my 
sense of obligation to the Government Grant Committee of the Royal Society for 
opportunities of visiting Norway for material ; to Dr Nordgaard, Director of the 
Marine Biological Station at Bergen, for his most kind assistance in procuring that 
material ; and to Professor Karl Pearson for much generous help in connection 
with the working out of the statistics. 
Material and Methods. 
The material brought together consists in all of 567 specimens of Spinax 
niger, of which 263 are adult (100 (/s and 163 $s), whilst the remaining 304 
are embryos almost ready to be born (145 cfs and 159 $s). In the adults of both 
sexes the following points were noted in connection with the vertebrae, spines, 
and pelvic plexus, though, owing to technical difficulties consequent upon the 
small size of the embryos, the condition of the pelvic plexus in these was not 
examined. The raw data are given in the Appendix, Tables 11 to 47. 
1. WJiole vertebrae. As in all Elasmobranchs the vertebral column is 
composed of whole vertebrae in the trunk region and of half vertebrae in the 
caudal region. The whole vertebrae are therefore delimited rostrally by the 
skull and caudally by the half vertebrae. The junction of the whole vertebrae 
with the skull is rendered fairly simple of determination by the condition of the 
spino-occipital nerves. When the skull is viewed from the inside a small foramen 
is seen just below that for the vagus (Plate I, Figs. 4 and 5). This foramen, which 
is constant in its position, I regard as belonging to the most anterior of the spino- 
occipital nerves (x). Neither this nerve nor y immediately behind it ever possesses 
