330 
Merism and Sex in " Spinax Niger" 
number of whole vertebrae, the meristic units characteristic of the trunk region, 
is largely governed by the total number of segments (average correlation = -61), 
the number of the more variable half vertebrae constituting the caudal region 
is far less dependent upon this factor (average correlation = 'SS). From this 
difference* it must be inferred that the influence of any factor leading to an 
increase or decrease in the total meristic series will not be equally exhibited in 
the change in number of the whole and of the half vertebrae. Thus, reduction 
of the total segments will be accompanied by a marked reduction in the 
number of whole vertebrae, and by a much smaller one in the number of half 
vertebrae. Hence, the result of increasing reduction of the total number of 
segments, and consequently of the whole vertebrae, must be to increase the ratio 
number of half vertebrae mi , i • , n ,i • , -i • i i i , 
:j — — j — , . i hat such IS actually the case is strikmgly brought 
number of whole vertebrae o ^ o 
out on correlating the numbers of the half and whole vertebrae. The correlation 
value (Table 5 h) is fairly high (average = "52) and is negative. In other words, 
the greater the number of whole vertebrae the relatively smaller is the number 
of half vertebrae associated with them. Elsewhere (p. 334) reasons are given for 
supposing that a gradual reduction in the number of segments is in process 
phylogenetically. The above facts would lead one to suppose that this is being 
brought about by reduction of the whole vertebrae, owing to their transformation 
into half vertebrae, and the variations already observed (p. 315) at the point of 
junction lend colour to this view. At the same time the number of half vertebrae 
is being reduced caudally but recruited, though to a somewhat less extent, 
rostrally from the whole vertebrae. Were the reduction in the number of whole 
vertebrae to keep pace with the reduction in the total number of segments, 
the coirelation between these two characters would be unity. The number of 
half vertebrae would however be recruited by an increased amount, and its 
correlation with the total number of segments correspondingly reduced. Hence, 
on this view we should be led to expect that the higher is the correlation between 
the whole vertebrae and total segments, the lower will it be between the total 
segments and half vertebrae. If we consider the sexes separately this expectation 
is borne out by the actual numbers. Table 5 h shows that the correlation 
between whole vertebrae and total segments is slightly higher in the embryos 
of each sex than in the corresponding adults, whilst at the same time the corre- 
* The extent to which the whole and half vertebrae respectively would be affected by a change in the 
total number of segments is more correctly given by the coefficient of regression of either of these two 
characters on the total number of segments. Thus the value of the regression of whole vertebrae, on 
the total segments is given by the expression ^""^ whole veitebrae ^ correlation between whole 
fl- for total segments 
1-147 
vertebrae and total segments. In the case of adult s s this is ^.^^^ x '553 = •602. Similarly the value of 
the regression of half vertebrae on total segments is x •375 = -SSS. These two values show 
clearly that any change in the number of the total segments affects the whole vertebrae much more 
than the half vertebrae. (The value of <x for half vertebrae is 1^901 (Table 2) but this must be first 
translated into terms of total segments (cf. App. Table 27) which gives the above value 1^002.) 
