R. C. PUNNETT 
341 
taken, we do not find all the subgroups either constant or again independent, but 
since the variabilities of the three are not widely different, the loss of a segment 
by one is roughly on the average an equally divided gain to the other two. For 
example if the anterior series lose a segment, this is not added wholly to the 
median series, but rather more than the half goes on the average to the posterior 
series. In other words for fish of the same total number^ of segments a forward 
movement of the anterior spine will on the average be associated with a forward 
movement of the posterior spine through somewhat more than half the number of 
segments through which the anterior spine moves. 
It would thus appear that the existing system of variations and correlations is 
not consistent with any definite position of the two spines for fish of a constant 
number of segments ; it is not consistent with any system of independent shifting 
of the spines about their mean positions in the same fish. It is only consistent 
with an associated motion of the two spines in the same direction, their average 
motions having a simple ratio. Thus, while the division between whole and half 
vertebrae (see ftn. p. 331) appears to vary in a manner not inconsistent with 
random interpolation into the total series, the relation between the three groups 
determined by the two spines appears to be of a wholly different character.] 
III. Heredity of Meristic Characters, 
Shortly after the collection of the present data was begun the idea suggested 
itself that, owing to the viviparous nature of Spinax, such data might be used for 
the determination of fraternal and parental correlations. For purposes of fraternal 
correlation, 230 embryos belonging to 27 families (110 (/s and 120 $s, cf. Appendix, 
Table 13, Nos. 75 — 304) are available. As the $ parent was not determined in 
Nos. 163 — 168 the number of embryos of which use can be made for calculating 
parental correlations is 224, belonging to 25 families. The actual calculation of 
the correlation coefficients, involving correction for the selection of both parents, 
was very kindly undertaken by Dr A. Lee in Prof. Karl Pearson's Laboratory, and the 
results are given in Table 8. The parents are of course unknown, but their 
influence has been deduced from the data given for adults on the assumption 
that the selection of </ parents from the ad alt ^ population is equal to that 
of ^ parents from adult $s. 
Fraternal Correlations. 
A glance at Table 8 at once brings out two points of interest, viz. (i) the 
diversity of the correlation values for the five characters treated, and (ii) the 
lowness of the average value even after parental selection has been corrected for. 
(a) The diversity of the correlation values is very considerable, being as high as 
•447 for the whole vertebrae, and as low as "254 for the half vertebrae. Moreover 
