MULTIPLE CASES OF DISEASE IN THE 
SAME HOUSE. 
APPENDIX TO PAPERS IN BIOMETRIKA, Vol. viii. 
• p. 404 and p. 430. 
By KARL PEARSON, F.R.S. 
I regret that a most careless algebraic slip has crept into my work on this 
subject. It stared me in the face when I saw the published number of Biometrika, 
and I cannot understand how it escaped me in MS. or proof. 
After obtaining tbe fundamental equations 
IT" ^ XV1 )> 
^p.=iv(i-^) (xvii), 
where N = n + ^jj (xviii), 
on p. 410, I continued on p. 411 : 
"Now let us write os s = s 2 p s ; then clearly a\ r =s"a 2 p Clearly nothing is 
more false ! a 2 x ^ would then equal sVy and not s 2 cr^ , and thus the value of i.e. 
§ \ f(Ps-p»Y \ 
1 I Ps J 
is erroneous. 
It is not possible I think to obtain the value of in this indirect and brief 
method. We must return to the multiple correlation formulae of my memoir in 
the Phil. Mag., July, 1900, p. 161, and evaluate the determinant R and its minors 
for the special values (xvi) and (xvii). 
Following the lines of that paper let us write : 
p s s"j N = s\n 2 fi s (xix), 
. JVcos a &sin 2 & 
then o~„ = - , 
and a p = VA cos /3 s sin /3 s /s ( xx )- 
