Karl Pearson 
541 
slips (see footnote, p. 521) in the values of /Sj and /Sa. These are not sufficient to 
account for the divergence of their results from mine, and from the trend of their 
samples of 25 and 100. I am inclined to think the divergence is due to the 
presence of the outlying index 2'16 in their chance drawings — a result my curve 
shows to be exceedingly improbable not once in 3000 drawings, and the like of 
which does not occur in their samples of 50 (drawings replaced) (see p. 525). It 
would clearly be possible from their experimental method of drawing samples 
of 800, 400 and 200 indices to closely approach the corresponding theoretical 
distributions of 640,000, 160,000 and 40,000 represented in our curves. Our 
results then are in every way confirmatory of theirs, but place on a rather more 
satisfactory theoretical instead of experimental footing their deduction of index 
distributions. The general conclusion seems to be that except in the case of 
an extremely low or extremely high value of the opsonic index, little if any 
weight whatever ought to be placed on a single determination of this index. 
Hence the method would not be valid when applied to cases in which, owing 
to the evolution of a morbid process or the action of some drug, very few observa- 
tions can be made under the same conditions, i.e. it must be of doubtful application 
in treatment. Further the concentration obtained by basing the index on a count 
of 100, rather than one of 50 or even 25, while sensible is not very rapid. It 
would require very large numbers — much beyond every-day practice — to reduce 
in a marked manner this variation of the opsonic index from unity, when an 
individual even is tested against himself. Generally the diagrams indicate that 
an extreme variation in excess is more likely to occur than an extreme variation in 
defect, but that the most probable index, when the individual is tested against 
himself, will be one somewhat less than unity. 
Biometrika vii 
69 
