John Blakeman 
341 
for 1r the vahie found from the usual approximate formula S,- = — . Thus 
values for S^, S^, 2^, were found which are certainly true values excepting in so 
far as the formula for 2/ is only approximate. 
Writing E^^, E^, E^ for the probable errors thence deduced we have 
^^ = •674492^, ^f=-G74492f, ^^ = -674492^. 
The standard deviations and probable errors were now found from the simple 
formulae (xxiii), (xxvii) and (xxix) and the resulting values denoted by 2'^-. ^'f > 
E'^,E'^,E'y. Finally the ratios w,— , , 7=?^ Avere calculated and the significance 
or non-significance of the deviations from linearity judged by the values of these 
ratios. 
Exhibiting the values of the constants thus deduced; we have 
Illustration A. On the Skew Correlation between Number of Branches to 
the Whorl and Position of the Whorl on the Spray in the case of Asperula 
odorata. 
The position of the whorl is the .^-character and the number of branches to 
the whorl is the ?/-character. Taking the values of n^^, y^-^, cr,,^ as given by 
Pearson, we have 
■■'■1 
150 
0-7800 
■8553 
X2 
150 
6-8133 
-8437 
X3 
150 
G -8 1.33 
-9047 
142 
G-4859 
•8780 
■^5 
87 
6-1724 
•8605 
We find, the quantities being determined without the use of Sheppard's 
corrections, 
i\^= 679, 
2^8027, 
y 
= 6^6554, 
1-3369, 
ay 
= ■8978, 
Vi = 
1-7873, 
= -8001. 
V4 = 
5-8417, 
■0503, 
Pu 
= -2492, 
K = 
•0075, 
Pn 
= ■8964, 
■0342, 
= 1-4906. 
X,o. - 
•1678, 
(7M= -2244, 
7j = -2499, 
Xi = -9909, 
%3 
. = •9771. 
