30 Multiple Cases of Disease in the Same House 
To evaluate these we note that 
jt-i 
S (=— ^ — ) = 8 (sin»&) = -8 
but S(p )S s' ! ) = iV" as shewn on p. 411 of my Biometrika memoir. Hence: 
i 
U -r} ( 1 \ 1 
Thus we have : J"=(- 1)»X^ 
iV" ' 
1+ Vs \M N J' 
T (-lV'^x 
O St 
(l + Vx )(l+ Vt ) 
Next as in the Phil. Mag. paper (p. 161) : 
R = (-iyj/\, 
Xst = (- 1 Jh cot ft cot ft/\. 
Thus : J2 = p u u?/N, 
R ss = cos 2 ft (&s 2 + p w u°-)/N, 
R st = cos ft sin ft cos ft sin ft . 
Finally we have : 
R ss _ cos* @g(p s S* + p u v?) 1 
and 
Ra 2 Ps p u a 2 cos- ftj9 s 
»- Vp u p g / p u u 2 p, 
R sf _ cos ft sin ft cos ft sin ft st 
Ra a p w u°jN N cos ft sin ft cos ft sin ft 
J. S« 
Thus finally ^ 2 is given by 
*f 7% - W + 2S S^r <?.-ft) to " ft) 
-'8'<p--w + ±r a '.( P ,-p, ) \'. 
1 £>s i*'i>u ( 1 J 
But S"*(l).-p.) = 0 J 
i 
«-i 
therefore S s (p s - p s ) = - u (p u - p u ). 
i 
