1884.] Batrachia of the Permian Period of North America, 31 
forces, the one of growth and the other of change or interruption, 
and they contend, we stili have in the organic being a quite symmet- 
rical result. In the cylinder bending in this way, of course the short- 
est line of curve is at the center of the side of the cylinder, and 
the longest curve is at the summit and base, and the shortest 
curve will be the point of fracture. And I presume it has hap- 
pened in the case of the construction of the segments of the sheath 
of the vertebral column that the lateral motion of the animal 
swimming has been the actual cause of the disposition of the osse- 
ous material in this form. 
A very good illustration of the effect of bending of a more or 
less flexible cylinder may be seen in the folds on the inner con- 
cave side of one’s coat sleeve. In the accompanying figure the 
folds in the cloth represent the lines of flexure, or what would be 
IG, 2,—Sleeve of a coat, showing folds produced by lateral flexure, which leave 
interspaces similar to the segments.of a rachitomous vertebra. Thus č represents 
intercentrum, Ż, pleurocentrum, and #, neurapophysis. : 
in a seat of ossific deposit, of interruption ; while the interspaces 
represent the segments bounded by such lines. The correspond- 
ence with the segments of the vertebrae of the Rhachitomi is 
remarkable. At the base we have the wide lenticular intercen- 
trum (viewed partly from below in the cut); between their Jateral 
apices we have the pleurocentra, and above, another segment, 
which in the vertebra is the base of the neural arch. 
The view that the segmentation of the vertebral column is the 
result of lateral alternating strains, was proposed by Herbert 
Spencer ( Principles of Biology, 11, p. 195). The present re- 
. Searches confirm this hypothesis in general. Mr. Spencer did 
not, however, specify the kind of segmentation to be expected 
from this process, and leaves it to be inferred that the segments 
will be cylinders of greater or less length. Thus he says (p. 205) 
“in a vertebral column of which the axis is beginning to ossify, 
the centrums consist of bony rings inclosing a still continuous 
rod of cartilage.” And it is true that this is the primitive form in 
