R. C. PUNNETT 
339 
These are manifestly inconsistent with the observed vahies. For adult (/s 
I find: 
a; = 15-979, <t^= -670, C. of V. for = 4-194, 
^ = 24-561, <xy= ■785, „ „ 2/ = 3-198, 
3 = 24-500, = -794, „ „ 3-240, 
« = 65040, o-t= 1-048, „ „ « = 1C11, 
which are far from satisfying the above relations. 
Clearly : (i) judged either by the standard deviations or by the coefficients of 
variation the median and posterior series are equally variable, (ii) the anterior 
series is absolutely less variable than the median oi- posterior series, but relatively 
more variable, and (iii) absolutely the whole series is more variable than any 
subseries only in the ratio 4 to 8, and relatively it is far less variable. 
The existing correlation and variation values are not given by any distribution 
of insertions and withdrawals in which the ratio of the changes in the subgroups 
to the total change remains constant. 
Next suppose the segments inserted at random, there being no relation whatever 
between the numbers inserted in any of the subseries. We should then have 
1'x + y,t = 0-x + yl<^U 1'x,x+ij=(^:r/o-x + y 
But (Tx+y = 'S88. Hence we should expect, with the observed values of the 
variabilities : 
r^.j=:-6393, *v = -7494, r,( = -7573, r^+j,,f = -847, and r^, = -7550. 
Actually we have : 
ry,= + -067l, ?-^( = -1544, r^.+y, , = + -6753, 
r,^ = _-3797, ryt = -6318, rx,x + y = + -5216, 
rx,j= - -2633, r^t = '5648, 
which differ very sensibly from the above values. 
Clearly additional segments are inserted in the three subseries in a correlated 
manner, and the existing series could not result from a mere random insertion 
of segments, or a proportioned insertion (nor of course by like withdrawals). 
Whether the original variation was of one of these kinds and the result was then 
modified by selection, it does not seem possible to assert on the basis of a statistical 
examination of one race at one epoch. 
43—2 
