R. C. PUNNETT 
331 
latiou between total segments and half vertebrae is considerably lower in the 
embryos (of. p. 327)*. 
(3) The position of the pelvic fin (as determined by the 1st g. p. nerve) is in 
either sex fairly highly correlated with the posterior spine, the number of whole 
vertebrae, and the total number of segments. The value of the last correlation 
(average = "46) is however sufficiently low to show that the position of this fin 
cannot be entirely due to any uniform process of reduction or increase in the 
meristic series. It has already been seen that, of the total fin innervation, part — 
the collector — is rostral to the pelvic girdle, and part — the post-girdle nerves — 
is caudal to that structure. On the supposition that the girdle is, so to speak, 
in a state of oscillation (exhibiting either backward or forward honioeosis, but 
especially the former), we should be led to look for evidence of such oscillation 
in the values of the correlations between these two sets of nerves and the position 
of the 1st g. p. nerve. We should expect an oscillation resulting in a more rostral 
position of the girdle to be accompanied by a diminution in the number of the 
collector branches and an increase in the number of the post-girdle nerves. This 
expectation is fully borne out by the correlations. That between the 1st g. p. nerve 
and the post-girdle nerves is high (— '62 for (fs and — "57 for $s) and is negative. 
The smaller the number denoting the 1st g. p. nerve (i.e. the more rostral the 
[* It may be of slight interest to consider the topic of this paragraph from a rather more mathe- 
matical aspect. 
The average correlation between whole vertebrae and total segments is -610 and between half ver- 
tebrae (in whole vertebrae as units) is 'SSi. The mean standard deviation of total segments is l-07'2, 
of whole vertebrae 1-158, and of half vertebrae (iu whole vertebrae as units) is 1-09G. Hence forming 
the regression coefficients : 
S. D. for whole vertebrae , , S. D. for half vertebrae , , 
„ ^ ^ — — — — X correlation -610, and 7 , ^ . — — — x correlation -334, 
S. D. for total segments S. D. for total segments 
we see that on the average an increase of one in the total segments will be accompanied by an increase 
of '66 in the whole vertebrae and an increase of '34 in the half vertebrae (measured in whole vertebrae 
as units). Iu other words one new whole vertebra is as likely to appear as one new half vertebra 
(measured as a half vertebra). But the total number of whole vertebrae is about double (44 -6 to 20-4) 
the number of half vertebrae (in whole vertebra units); in other words the effect of increasing or 
decreasing the total segments is relatively to the whole and half vertebrae sensibly the same as adding 
or subtracting a vertebra anywhere at random, because the total number of whole vertebrae is roughly 
twice as great as the half vertebral series measured in the same unit, the whole vertebra. 
Let !tf = whole vertebrae, 7i = half vertebrae (measured in whole as units), J = total segments, r = corre- 
lation coefficient. Then if the total number of segments were constant, since the standard deviations 
of whole and half vertebrae are approximately equal, we should expect that the expression for partial 
correlation, i.e. 
J{l-r\,)(l-r\,)' 
should be closely equal to minus unity, for when the whole vertebrae lose one the half vertebrae must 
gain one. Equating the above expression to -1, and noting that r„i = -dlO and r;,j='334 nearly, we 
find r,^.,^= --54, the average observed value of r„,ft is --52 — a very close result. In other words the 
correlation of whole and half vertebrae is what we might reasonably expect its value to be, the correla- 
tions for the two parts with the total being as above. In general terms the result is the same as if 50 
per cent, of gain or loss of either whole or half vertebral series came from increase of total segments 
and 50 per cent, from a transfer from one series to the other. K. P.] 
42—2 
