86 
PROFESSOR K. PEARSON AND DR, A. LEE ON 
Hence 
2 ; 
i (W + *,%* - 27 i3 A 1 2„,2 i ,R v ,) 
W | n \ (N — »!> h ; 3 (N — n 3 ) _ 
« 4 N 1 (^Hj) 2 N 2 ^ (A 3 H 3 ) 2 N 3 'foHjKWN* 
Or, Probable error of 17 
•67449 7q7i g [ v s 
= v/N ^ loX) 2 + (7i 3 H 3 ) 2 
v\ 1 3 _ 
AlHj ^ 7« 3 H s 
(xxiv,). 
where u is the range /r> — 7q, and v l and r :J are the proportional frequencies, as before. 
Care must he taken, if the class n 2 cover, as it usually will in our present investiga¬ 
tions, the mean, to put h { negative within the radical. In other words, for a class 
covering the mean we have 
Probable error of rj 
•67449 7i> 3 
At, + 
Vo 
\/N (4, + l h y- 1(4,11,)= ' (4 S H S )= V'hH, 4 s H 
v-j \ 3 H 
Lastly we have 
or, 
Hence 
S£ = 
£ = u /u , 
uhu' — u'Su u' fhvf Su 
u~ 
u \ u 
u 
* 2 = _ 22 XR Utt , 
^ u 2 1 u'~ u~ uu 
R„ u d 
' r 
Thus : Probable error of £ 
fV 2 vs oy v n -ij 
= -67449C \h + ~ \ • • • 
[ u- u z uu 
where we have by (xv.), (xvi.), and (xxiii. Lls ) 
(xxv.). 
(xxvi.), 
where, as before, p’s and vs represent proportional frequencies. 
In the following investigations 011 coat-colour and eye-colour inheritance I have 
not thought it needful to give in every one of the thirty-six relationships dealt with 
the probable errors of the means, ratio of variabilities, and the coefficients of inheri¬ 
tance (q, £, and r). The arithmetical labour would have been too great, for the 
