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 vertebne, 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 (gi'oup 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 

 tectums 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°sufficieut 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 

 supernumerarv 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 



