E. Schuster 
473 
seen that the vahies of r vary between 0"45 and 0"62, with a mean value for 
paternal correlation of 0'54, and for maternal of 0'535. 
Now we have two sources of inaccuracy, the tendencies of which are known, in 
arriving at these values. Firstly, the inclusion of persons whose deafness was 
due to causes acting on them from without. Although these are probably 
far less numerous than the whole number entered by Fay as " acquired " or 
" adventitious " cases, yet there are certainly enough of them present to con- 
siderably reduce the value of r in all the tables if, as it is generally supposed, 
this form of deafness is not inherited ; it is however quite possible that the physical 
condition, which renders the owner of it liable to become deaf in this way, is 
inherited. Secondly, the percentage of deaf-mutes given in the census returns 
is in all probability too low. If a higher percentage had been allowed for in 
making the tables the effect would have been to reduce the value of r ; as it 
was not allowed for one must consider that the latter error has to a certain extent 
balanced the former, though exactly to what extent is quite uncertain. 
Another factor to be taken into account in considering the paternal and 
maternal correlation coefficients is that of " Assortative Mating " of the parents. 
The tendency for the deaf to marry the deaf is an exceedingly strong one, and that 
for obvious reasons which need not be dwelt on here. In Table I. a total of 2954 
marriages is recorded, and in 2373 of these both husband and wife were deaf, 
in 344 the husband was deaf and the wife hearing, and in 237 the reverse was 
the case. 
In order to determine exactly the coefficient of assortative mating, that is to 
say the correlation between husband and wife, I constructed two correlation tables 
from these data ; one of these assumed that the distribution of deafness among 
husbands was normal, the other that this was the case for wives. Owing to the 
very large value of ?■ in both cases, it was not found possible to determine it 
exactly, as this would have involved the solution of an equation containing very 
much higher powers of x than x to the twentieth. The tables are therefore not 
included here, but the value of r is certainly considerably higher than '9. 
(2) Fraternal Correlation. 
As has been mentioned previously Fay has endeavoured to give in his tables 
the size of the families in which the 4471 pairs of husband and wife are contained, 
and also the number of deaf-mutes contained in them. In his statement of this, 
brothers are not distinguished from sisters, but all are included and numbered 
together. In several cases the numbers are not known or not stated definitely. 
Excluding these we find that the remaining deaf husbands and wives are included 
in 3837 families, the distribution of which with regard to size is shown in the last 
column of Table XII. It is also shown graphically in Figure I., and is there fitted 
with the skew curve (Prof. Pearson's General Probability Curve of Type I.), which 
seems to represent the observations with fair accuracy. 
Of each of these families every possible pair of deaf and deaf, of deaf and 
hearing, and of hearing and hearing brothers and sisters was made. To take a 
Biometrika iv 60 
