R. C. PUNNETT 
320 
the two spines — the fact that the average correlation with the total number of 
segments is nearly three times as great for the posterior as for the anterior would 
seem to point conclusively to dissimilarity in the factors determining their 
position*. Certainly they cannot owe their various positions to some uniform 
process of shortening or lengthening of the vertebral column alone f. Probably one 
must regard the spines as structures showing oscillations from a mean position 
backwards and forwards along the vertebral column. These oscillations are 
relatively greater in the anterior spine (where the CV. is about 4), and are more 
independent of the total number of segments because there are no specialized 
structures in close proximity tending to fix its position. Consequently the 
correlation with the total number of segments is small. The posterior spine on 
the other hand occurs in the region of the pelvic fins and of the junction of the 
whole with the half vertebrae. With the number of the whole vertebrae, and 
with the position of the pelvics as estimated by the 1st g. p. nerve, it is highly 
correlated (the average values of these correlations being about '72 and '55 
respectively). The coefficient of variability for the posterior spine is smaller than 
that for the anterior, which is probably to be explained by the fact that the high 
correlations alluded to tend to limit the oscillations of the former structure- 
These high correlation values force us to conclude that the three structures 
concerned vary very much in sympathy with one another. The fact that the 
position of the posterior spine is largely dependent on the number of whole 
vertebrae and on the position of the pelvic fins must lead us to suppose that its 
independent oscillations are to a great extent checked, a view that is borne out 
by the relatively low variability (average C.v. = 2"19) of this spine as compared 
with that of the anterior. Moreover, the intimate relation of the posterior spine 
with the whole vertebrae serves to explain its high correlation with the total 
number of segments. For the number of the whole vertebrae is largely dependent 
on the total number of segments, as the average correlation value '61 shows. To 
sum up, the position of the spines was probably in the first place largely inde- 
pendent of the total number of segments, and, where no further complications are 
introduced, remains so, as in the case of the anterior spine. When, however, the 
spine enters into close relation with other structures whose position is largely 
dependent on the total number of segments, its variability becomes checked and 
the value of its correlation with the last-named feature increased. 
(2) As the vertebral column is composed partly of whole and partly of half 
vertebrae, one would expect any change in the total number of meristic units to 
affect both of these regions. This is the case, though not to an equal extent in 
each. A high correlation exists between total segments and whole vertebrae — 
a considerably lower one between total segments and half vertebrae. Whilst the 
* On the hypothesis of random interpolation the ratio of these correlations should be the ratio of 
the standard deviation of the posterior spine to anterior spine, or on the average '892 to '636, i.e. rather 
as 3 to 2, than the observed 3 to 1. 
t Nor to random interpolation. 
Biometrika in 42 
