110 
Miscellanea 
not see that there is anything more of the nature of " au error of observation " in taking the 
actual sex-ratio of the offspring as a somatic character, than in taking the actual stature or actual 
arm-length of the offspring. Neither represents the actual gametic character, if what is meant 
by that is the mean value for an indefinite number of offspring. What the biometrician is 
concerned with is the relation between the somatic character as actually observed in one 
generation and again in the next, and for the sex-ratio this relationship is practically zero. 
In the case of the sex-ratio the variability ctj;^ noted by Mr Cobb is not a variability due to error 
of observation, but a variability characteristic of the species itself being determined by its 
fertility. According to Mr Cobb it is so great that it renders it impossible to determine for the 
.sex-ratio any relation between the somatic character in parent and offspring. Is this more than 
a biometrician means when he says that there is no inheritance of the sex-ratio l No process, 
for example, of selecting families, giving many sons, would alter the sex-ratio, because the mean 
sex-ratio of families sprung from families with few and families with many sons is sensibly the 
same. I am not certain, however, that the numerical example given by Mr Cobb, i.e. ■^=•028, 
is cori'ect. For, if be really an inherited character it may take all values from 0 to 1, and 
accordingly we shall not get the proper value of this expression by putting ^=?=J, the value 
which gives the maximum value of pq^ but by putting pq its actual observed mean value in man ; 
this reduces Mr Cobb's multiplying factor to about a fifth of the value he assumes for it, and 
such a factor, if it were correct, would not influence the general conclusion. But Mr Heron has 
applied several furthei' tests to liis own data. It will be remembered that for the Whitney data in 
his memoir on sex inheritance Mr Heron took the sex-ratios in two generations of families 
having four or more members, the correlation for 2197 families was found to be "02+ '01. From 
the same data Mr Heron has picked out the 420 f;imilies with eight or more members, the 
correlation is now "01 ± '03. Instead of increasing as it ought to do, on the assumption of 
Mr Cobb, it has got still more insignificant. 
But Mr Cobb's note suggests a point which it seemed well worth while working out. If there 
be no correlation the resulting standai-d deviation of the material ought to be exactly what would 
be obtained on the theory of pure chance, i.e. there would be no variation due to heredity 
superposed on this. Mr Heron has investigated this point for 496 families given by my schedules 
and for 2305 families taken from the Whitney data. Suppose we take all the families of s 
members ; let be the mean immber of males, o-g the standard deviation of this array, then 
m^jiig and o-j/^s will be the mean and standard deviation of the sex-ratios of this array of families 
of s members. Let p be the mean sex-ratio of the whole series of families and o- the standard 
deviation, then 
'-^■^•["■{(-i-T-©}] «■ 
Now o-s/Hs is what Mr Cobb puts o-,,, and he makes this differ from his pq/m, so that he 
obtains a quantity a^, which is the variability of the sex-ratio, if the families were indefinitely 
great, and upon this he tells us the true heredity depends. Accordingly if a-^ be a reality the 
value found for a'^ by putting mgjug=p and a-g/ng=pqi)i ought to be less than the actually 
determined value of a'^ I\Ir Heron finds the following results : 
Value of (T- 
Pearson's Schedules Observed -1944 Calculated '1946 
Whitney Family „ "2079 „ "2086 
In both cases the calculated value is insensibly greater than the observed. In other words a-^ 
must be imaginary, or rather within the limits of the probable error it is zero. Shortly, if any 
individual had an indefinitely large family, the ratio of the sexes would not differ from that of the 
