Miscellanea 
421 
employed. 0 2 is approximately the same as only when cj) is small. If (f> = r=-5, its value is 
•45. Thus in such tables, and for values of r not greater than - 5, those values will not greatly 
differ from the values of C 2 . 
Now in Mendelism we are dealing with discrete entities known as gametes. Referring first 
to the problem of gametic correlation and taking for an example that between parent and 
offspring, each individual in the population considered has a gamete which possesses 0, 1 or 2 
protogenic elements of a particular character. Thus this case falls under the head (c). Taking 
parents with, say, 0 protogenic elements we have an array of offspring some with 0, some with 1, 
and some with 2 protogenic elements, and we can find the mean number of protogenic elements 
in members of the array. Now the parent's gametic character is supposed to be perfectly 
correlated with the number of protogenic elements for the character which he possesses, and 
this is likewise true for the offspring. Assuming then, that if, of four variables u, v, x and y, u 
is perfectly correlated with x and v perfectly correlated with y, then the correlation between 
x and y is the same as that between u and v, we find that the gametic correlation between parent 
and offspring is the same as that between the number of protogenic elements possessed by the 
parent and the number possessed by the offspring. Thus such a table as 
is equivalent to a table between parent and offspring for the particular gametic character. 
Since the observations are concentrated at points within each group, these points in any row or 
column of the above table are equidistant. Thus the legitimate method to employ on this case 
is (iii). A value of C 2 as by (ii) can be found to give a measure of relationship, but as the 
conditions referred to in (ii) are not satisfied it will not be the true value of r. We can determine 
' regression ' lines from a knowledge of the means of the three rows and columns. Here we 
must note the fundamental disagreement between continuous variation and Mendelism. For 
a number of characters regression lines have now been determined of offspring on parent. Many 
of these are perfectly continuous regressions, that is, for any small increase or decrease in 
the value of the parental character we can observe a corresponding small increase or decrease 
in the mean value of the character for the offspring. In other cases, e.g. the petals of a 
flower, the regressions must proceed by steps. But a number of cases which have been shown 
to give perfectly continuous regressions, the Mendelians claim to depend upon a single unit 
character, e.g. piebaldism. All that the term 'regression' can denote in a Mendelian instance 
is that as we jump from 2 to 1 protogenic elements in the parent, the effect on the mean number 
of protogenic elements in the offspring is the same as when we jump from 1 to 0, for we cannot 
split up the protogenic element. Thus although we use the term 'regression' in the Mendelian 
cases we only do so in the signification of the last sentence, viz., that an increase or decrease 
of one protogenic element in the parent is accompanied by an increase or decrease of, say, 
to protogenic elements in the mean value for the offspring. This is fundamentally different from 
the continuous case, in which we can observe an increase or decrease of l°/ 0 of the parent's 
character followed by an increase or decrease of, say, n"j 0 in the mean of the value for the 
offspring. The comparisons throughout this paper are to characters which appear to be con- 
tinuous, but which Mendelians claim to depend upon ' unit characters.' 
If for the columns in the above table, 
Number of Protogenic elements in Gapaete of Parent. 
(2) (1) (0) 
Mean of column (2) — Mean of (l)=Mean of column (1) — Mean of (0), 
