86 BULLETIN: MUSEUM OF COMPARATIVE ZOOLOGY. 
variation of the serial position of the sacrum by assuming that the 
appendage has a locus fixed at a point whose linear distance from the cra- 
nium is a definite and constant proportion of the entire length of the 
animal. The change in serial position of the girdle is then effected by 
compressing the presacral vertebra, making each shorter and diminish- 
ing their combined length, thus bringing a vertebra caudad to the nor- 
mal, opposite the stationary appendage locus. While such a view may 
be made to account also for asymmetrically placed sacra, it is difficult 
to see how it will adapt itself to the occurrence of supernumerary 
sacral ribs, and especially those asymmetrically placed (see Plate 2, 
Fig. 8). 
What seems most probable is that in different individuals the girdle 
may develop at primarily different distances (measured in segments) 
from the cranium. In Necturus we find a pair of sacral ribs on verte- 
bra 19 (group A), or on 20 (group B). The explanation by intercala- 
tion implies that vertebra 20 in group B is the same vertebra as 19 
in group A. That of slipping of the girdle — literally taken — implies 
that a girdle beginning to form in the 19th segment later (in ontogeny) 
is transferred to the 20th segment. Both explanations, as already 
stated, seem unsatisfactory. It is more logical to consider that the 
new position of the girdle is due to a stimulus to girdle formation 
having been applied at a new point, i. e. in a segment other than the 
normal, and hence that a sacral rib may arise in any one (or more, as 
shown in supernumerary ribs) of several points in this region. In 
Necturns these points are at least three, located in the 18th, 19th, and 
20th segments. 
Such a view explains the variation as to place of origin in different 
segments of sacra placed symmetrically, and also the condition of un- 
symmetrical sacra, such as have been described in group C, — since the 
stimulus to girdle formation is not single but paired, i. e. from the future 
appendages, and so need not necessarily be symmetrical ; and above 
all it is sufficient to explain the occurrence of supernumerary sacral 
ribs. These latter may be on one side only (Plate 2, Fig. 8, Howes, 
86, p. 279, Lucas, ’86, p. 562, and others); or a symmetrical pair of 
supernumerary ribs may appear (Case, ’96, p. 232; Lucas, ’86, p. 562), 
From the foregoing discussion I conclude that neither intercalation or 
excalation, nor slipping, are involved, but that the abnormal position of 
the girdle represents development of a new girdle at a new point. 
This new position is usually caudad to the normal, though in a few 
recorded cases in Urodela (Davidoff, ’84, p. 412, and others) it is 
