o 
PROFESSOR K. PEARSON ON MATHEMATICAL CONTRIBUTIONS 
§ 3. Proof of the General Convergency of the Series for the Correlation. 10 
§ 4. On the Probable Error of the Correlation thus Determined. 10 
§ 5. To Determine a Physical Meaning for the Series and on Divers Measures of Association ... 14 
§ 6. On the “Excess” and its Relation to Correlation and Relative Variability. 18 
§7. On a Generalisation of the Fundamental Theorem of the present Memoir. Special Formulae 
for Triple and Quadruple Correlation.23 
§ 8. Illustrations of the Methods of the Memoir. 35 
Illustration I. Inheritance of Coat-colour in Thoroughbred Horses. Sire and Filly.35 
,, II. Chance that an Exceptional Man is born of an Exceptional Father ... . . 37 
„ III. Inheritance of Coat-colour in Dogs, Half-“ Siblings ” 38 
,, IV. Inheritance of Eye-colour between Maternal Grandmother and Granddaughter . . 39 
„ V. Inheritance of Stature between Father and Son for different groupings.40 
,, VI. Correlation between Strength to resist Small-pox and Degree of Effective Vaccination 43 
,, VII. Effect of Antitoxin on Diphtheria Mortality.44 
„ VIII. Chance of Stock above the Average giving Produce above the Average as compared 
with the chance of such Produce from Stock below the Average.45 
,, IX. Chance of an Exceptional Man being born of Exceptional Parents.46 
(1.) On a General Theorem in Normal Correlation. 
Let the frequency surface 
2 = 
N 
i 1 / t 2 . y 2 _ 2rxy \ 
' “1 — V 2 \<Ti 2 (To 2 clog/ 5 
where 
2tt v /(1 — r 2 )cr 1 cr 3 “ 
N = total number of observations, 
oq, (t o = standard deviations of organs x and y, 
r = correlation of x and y, 
be divided into four parts by two planes at right angles to the axes of x and y at 
distances h' and k' from the origin. The total volumes or frequencies in these parts 
will be represented by a, b, c, and d in the manner indicated in the accompanying 
Then clearly 
d = 
N 
— If e-»r M^-Wdxdy 
j 2 ® /i * Jc 
if 
27T V /(1 — ?’ 2 )cr 
2 q/ a -W) L l e " ir ^ w+ dx dy 
h = h'/o q and k = /f/<x 2 . 
