ON A MATHEMATICAL THEORY OF DETERMINANTAL 
INHERITANCE, FROM SUGGESTIONS AND NOTES OF 
THE LATE W. F. R. WELDON. 
By KARL PEARSON. 
(1) Inti^oductory. In the memoir of Weldou's life published in the last 
volume of this Journal* occurs the following paragraph referring to the year 1905 : 
" In the summer the present writer was at East Ilsley, some seventeen miles 
from Oxford, and there was cycling out several times a week ; the writer's chief 
work was on other than biometric lines and broken by other claims on his time, 
but there was steady joint work on the determinantal theory of inheritance as 
outlined by Weldon, and it is hoped that it is sufficiently advanced to be completed 
and published." 
That hope is not wholly fulfilled. My mathematical draft of the theory was finally 
taken by Weldon from Ilsley to Oxford to be rewritten with proper biological 
terminology, and to have erroneous developments marked for reworking; this 
revision never appears to have been accomplished, and beyond my attempt at 
mathematical interpretation of Weldon's ideas, which I knew to be inapplicable 
at certain points, and his letters and a notebook full of numerical illustrations due 
to an earlier period of the same year, I have practically nothing to guide me in 
reconstructing Weldon's theory. The possibilities before me were threefold, to 
allow the matter to drop, to wait till I could find a cytologist with an interest in 
and a knowledge of the theory of chance at all comparable with Weldon's before 
going further, or lastly to publish what I could put together on my own responsibility. 
I have adopted the latter course, not because I am unconscious that I am likely to 
blunder, but because the material may at some time prove sufficiently suggestive 
to a reader with competent knowledge to cause him to take up the subject on 
broader and more effective lines, than I can pretend to do. 
Accordingly for all that is suggestive or valuable in the present discussion 
Weldon is responsible. My contribution is solely the mathematical analysis, and 
even here dii-ectly, and by force of numerical illustration, he had gone a con- 
siderable way independently. Any defects in terminology and misstatements of 
cytological facts are mine alone. 
* Vol. V. p. 46. 
