228 A Biometrical Study of Conjugation in Pm-mnecium 
In order to test the approach of the distributions to the normal law the probable 
errors have been determined for the four constants chiefly concerned in such a test, 
viz. V/Si, /So, d (= difference between mean and mode) and the skewness, on the 
assumption that the distributions follow the normal or Gaussian law. These pro- 
bable errors will then define the amount by which the constants will fluctuate, on 
account of the errors of random sampling from their true values for the normal 
TABLE IV. 
Analytical Constants for Variation in Paramecium. 
Series A 
Constant 
Conjugauts 
Non-Conjugants 
Length 
Breadth 
Length 
Breadth 
Number of Individuals . . . 
210 
210 
210 
210 
Unit 
^2 

H-i 
5 microns 
5-0287 
- -9882 
72-6598 
3 microns 
1-9323 
1-1952 
13-5622 
5 microns 
9-6714 
6-2239 
270-7506 
3 microns 
3-8286 
1-9867 
42-6096 
A 
v^0l 
02 
3-02 
'<:2 
•0077 
■0876 
2-8733 
■1267 
- -0209 
-1980 
•4450 
3^6323 
- •6323 
•2330 
-0428 
-2069 
2-8946 
-1054 
- -0958 
•0703 
•2652 
2^9069 
•0931 
- •1353 
Mean 
Mode 
d 
Skewness 
168-1429* 
168-6853* 
-5424 
- -0484 
44-3714* 
43-5997* 
-7717 
•1851 
189-9762* 
188-1581 * 
1-8181 
-1169 
52^8269* 
51^9275* 
•8994 
•1532 
curve. If the observed values of the constants differ from their theoretically true 
values by more than two or three times their probable errors, we shall conclude 
that the distribution does not follow the normal law in one or more particulars. 
The values for the probable errors of the four constants mentioned, on the 
assumption that the distributions are normal are as follows : Probable error of 
V/3i = i"1140 for each distribution; probable error of /32=±'2280 for each dis- 
tribution; probable error of the skewness = + '0570 for each distribution; finally 
the probable errors of d are (a) for length of conjugauts, + -6391, (6) for breadth of 
* It will be understood that the absolute values of mean and mode are given, and not, as in the 
case of the moment-coefficients, the values in terms of the unit at the head of each column. 
