304 Note on a Race of Claudlia Itala {Von Martens) 
III order to determine this, the first step was to find the correlations between 
the dimensions measured, taken in pairs : the correlation coefficients obtained are 
given in Table III. They were determined for each group corresponding to half a 
TABLE III. 
Correlatiom between the Dimensions measured for every Half-Revolution of the 
Shell-Spiral. 
r 
> 
r 
p 
Limits of C 
Young 
Adult 
Young 
Adult 
Young 
Adult 
2-00— 2-49 
0-9281 
0-9412 
0-5296 
0-6727 
0-5950 
0-6624 
+ 0-0094 
+ 0-0077 
+ 0-0485 
+ 0-0436 
+ 0-0379 
2-50_3-09 
0-9451 
0-9528 
0-5932 
~ 0-7048 
0-6317 
0-7285 
+ 0-0072 
±0-0062 
+ 0-0437 
+ 0-0339 
+ 0-0405 
+ 0-0317 
3-10-3-79 
0-9351 
0-9439 
0-6340 
0-6589 
0-6552 
0-6090 
+ 0-0085 
+ 0-0074 
+ 0-0403 
+ 0-0382 
+ 0-0385 
+ 0-0424 
3-80— 4-54 
0-9647 
0-9449 
0-6575 
0-5510 
0-6770 
0-5874 
+ 0-0047 
+ 0-0072 
±0-0383 
+ 0-0470 
+ 0-0365 
+ 0-0442 
4-55— 5-49 
0-9412 
0-9691 
0-6591 
0-6551 
0-6623 
0-6678 
+ 0-0077 
+ 0-0041 
+ 0-0381 
+ 0-0385 
+ 0-0379 
+ 0-0374 
5-50— 6-54 
0-9450 
0-9491 
0-5980 
0-6205 
0-6448 
0-6412 
+ 0-0074 
+ 0-0067 
+ 0-0433 
±0-0415 
+ 0-0394 
+ 0-0397 
6-55— 7-64 
0-9609 
0-9048 
0-5737 
0-4509 
0-6281 
0-5362 
+ 0-0052 
+ 0-0122 
+ 0-0452 
±0-0537 
+ 0-0408 
+ 0-0481 
revolution of the shell-spiral, because within these limits the lines of regression 
were seen to be sensibly straight, and the ordinary measure of the standard devia- 
tion of an array could therefore be used with confidence. The high values obtained 
for correlation between the columellar radius and the peripheral radius seem to 
show that the measurements were fairly trustworthy, but at the same time the 
differences between values obtained for corresponding sets of measures in young 
and in adults are so great and so irregular that it is difficult to see how they can 
be due to any other cause than error of measurement. In series of only about 100 
measures, a single small error of measurement could easily change the second 
decimal of a correlation coefficient so high as 0-95. 
From the correlation coefficients, and the standard deviations of the various 
groups, the standard deviations of arrays were calculated in the usual way, the 
i-esults being given in Table IV. In this table P means peripheral radius, C 
columellar radius, and p the perpendicular from the peripheral spiral on the 
columella. The standard deviation of an array of peripheral radii, associated with 
a fixed length of columellar radius, is given by the value of o-jj Vl - j-^^jp ; and 
similarly in other cases. It will be seen from Table IV. that there is no case in 
which the standard deviations of the arrays of measures from young shells are 
