W. F. R. Weldon 
121 
of the computations connected with these Tables. Miss Lee has corrected several 
important arithmetical bhinders of mine, and without her kind help I should 
certainly not have been able to publish this paper for some time. The results 
which follow from a study of this table seem to me of great importance ; and such 
credit as may be due for obtaining them belongs far more to Miss Lee than to 
myself 
TABLE TV. 
Values of Txy, ay, and dy'^l — r^^y for corresponding groups of Peripheral Radii 
in Young and in Adult-shells from Grernsmiihlen. 
Angular Distance 
from Columellar 
''a:!/ 
0 
y 
Eadius in right 
angles 
Adult 
Young 
Adult 
Young 
Adult 
Young 
- 8 to - 10 
J 0-7527 
(±0-0292 
0-7922 
±0-0251 
0-120849 
0-140872 
0-07956 
±0-00379 
0-08597 
±0-00412 
- 6 to - 8 
( 0-8068 
(±0-0235 
0-8374 
±0-0202 
0-133731 
0-153473 
0-07901 
±0-00377 
0-08388 
±0-00402 
- 4 to - 6 
( 0-8534 
(±0-0183 
0-8622 
±00173 
0134119 
0-154627 
0-06991 
± 0-00333 
0-07833 
±0-00375 
-2 to -4 
( 0-8726 
0-8782 
0-146252 
0 168564 
0-07143 
0-08062 
(±0-0161 
±0-0154 
±0-00.341 
±0-00386 
0 to -2 
) 0-9290 
0-8800 
0-1.56270 
0-170469 
0-05784 
0-08096 
(±0-0092 
±0-0159 
±000276 
±0-00388 
0 to 2 
( 0-9415 
0-9367 
0-170046 
0-173881 
005732 
0-06087 
(±0-0077 
±0-0105 
±0-00273 
±0-00292 
From Table IV. we see that the standard deviation of peripheral radii in the 
group from 8 to 10 right-angles from the standard columellar radius is nearly 
the same, both in young and in adult individuals — the small difference actually 
observed being hardly greater than the probable error of the determination. At 
every point, however, the variability of young shells is greater than that of adults ; 
during the six right-angles of revolution immediately above the columellar radius 
the excess of variability in the young is always from about two to more than 
four times as great as the probable error of the determination. 
The chances against an apparent excess of variability in a sample of young 
shells, so large as that recorded in the table, are veiy great, unless we admit that 
there is a real difference in variability between the newly-formed whorls of growing 
shells and the corresponding whorls of adults ; and the necessary consequence 
of such an admission is that the variability of these newly-formed whorls is 
reduced after their formation by a process which destroys individuals with 
abnormal shells more rapidly than others, so that a process of " periodic selec- 
tion " occurs. 
