76 PROCEEDINGS OF THE NATIONAL MUSEUM vol. lie 



Precaudal vertebral counts are subject to a maximum error of plus 

 or minus two vertebrae. It is not always possible to decide accurately 

 from a radiograph which is the first vertebra because, at the rear of 

 the head, other structures, including the occipital condyles, mask the 

 front of the vertebral column. Occasionally, owing to the angle at 

 which our marking pin had entered, we had some doubt as to the last 

 precaudal vertebra. Most of the counts given here were made by 

 each of us working independently but using the same radiographs. 

 The exceptions to these counts are the counts of the carcharhinid 

 genera on which we are working individually. We never differed by 

 more than one in our precaudal counts and we arbitrarily report the 

 even count, appropriately compensating for the caudal count. 



At the tip of the caudal fin the last few centra of most shark species 

 are frequently too small to give good resolution on radiographs. 

 Sometimes there was a difference of as much as three or four vertebrae 

 in our counts of the caudal section. In such counts one determina- 

 tion or the other has been listed arbitrarily. Because of the range of 

 variation in counts within a single species and because of the high 

 number of vertebrae in most sharks, we believe that such an error 

 is hardly significant. Generally, the precaudal count is more con- 

 sistent than the caudal count. Caudal counts were made under 

 magnification, usually with a low-power binocular microscope. 



The number of precaudal vertebrae is established early in embryos, 

 but the last caudal vertebrae usually are not fully formed until late 

 in embryonic life; hence, only late-stage embryos provide caudal 

 counts comparable to those of adults. In those embryos in which 

 we found calcification incomplete, we give a minimal count for the 

 caudal vertebrae (!>). We doubt that more than 25 additional 

 vertebrae would have been formed in any of the embryos we examined, 

 and we believe that in most of the embryos the number of yet unformed 

 vertebrae would be much fewer. 



Complete calcification of the column is recognizable on radio- 

 graphs by the posterior extent reached by the column (to within a 

 short distance of the tip of the tail) or by uniform density of the 

 images of the last several centra. 



We counted apparent fusions between centra (and also apparent 

 monospondylous intrusions in regions of diplospondyly) as single 

 centra, but we recorded separately the recognizable centra when the 

 fusion was obviously incomplete. 



In most sharks the monospondylous centra gradually increase in 

 length from the cranium posteriorly, so that the centra are usually 

 longest at, or near, the region where diplospondyly begins. The 

 difference in the length of anterior and posterior monospondylous 

 centra may be small or great. The difference in length between the 



