R. C. PUNNETT 
335 
structural peculiarities become as it were the fixed attribute of certain particular 
segments. Thus in Spinax the vertebra that carries the anterior spine is to be 
regarded as strictly homologous in different specimens. The serial position of 
such a segment may vary in different individuals— in one it may be the nth, in 
another the (n + l)th, &c. On the hypothesis of excalation it is supposed that 
creatures such as Spinax have been derived from forms with a larger number of 
segments and that the various positions of the segments with a marked individuality 
are due to a uniform process of shortening up owing to the vertebral column 
splitting into a lessened number of parts. The amount of change in position in 
the specialized segment depends partly on the amount of redaction or excalation 
in the meristic series of which it is a member, and partly on its original position 
in that series. As a simple illustration we may take the case of a series consisting 
of 40 segments, the 10th and 20th of which are specialized, let us say by bearing 
spines. If we suppose the series to be reduced to 36 segments by a uniform 
process it is obvious that the spine-bearing segments will now be the 9th and 18th. 
Reduction of the whole series to the extent of four segments implies a change in 
position of the anterior spine to the extent of one segment, and in the posterior 
spine of two segments. In other words, the nearer to the middle of the series the 
specialized segment lies the greater is the change in its position involved by 
reduction in the number of the whole series. On the excalation hypothesis we 
are led to expect (1) a positive correlation between each specialized segment and 
the total number of the meristic series, and (2) approximate equality in the value 
of these correlations. Reference to Table 5 b, p. 327, shows that the former of these 
expectations is fulfilled. The value of the correlation between posterior spine and 
total segments is however very much greater than that between total segments 
and anterior spine, whilst the value of the correlation between another specialized 
segment, that of the 1st g. p. nerve, and the total number of segments is intermediate. 
Such facts throw considerable doubt on the possibility of symbolizing the facts by 
the excalation theory and the following considerations serve to emphasize that 
doubt. 
TABLE 6 a. 
A. Posterior Spine. . . . .: . 
, Number of segments ... 62 63 64 65 66 67 68 
.3^ Number of specimens ... 2 26 91 158 81 33 5 - 
Calculated values for position 1 3g.g 39.^ ^^.^ ^^.g ^^.^ ^^-l 42-8. 
of posterior spine J 
The mean calculated position of posterior spine is 40'8 and is associated with 65 segments, 
which is the mean of the total number of segments. The standard deviation for the posterior 
spine (calculated position) works out to ± BIS. 
Observed values for position of postei'ior spine : 
38 39 40 41 42 43 44 
Number of specimens ... 1 21 124 156 81 11 2 
Mean position = 40-8, o-=± :942. 
