Karl Pearson 
97 
Stephens and Fantham, who term their work a " biometric study," speak of 
" the general resemblance between the curves representing the measurements of 
these three trypanosomes {T. ganibiense, T. rhodesiense, T. briicei)." They con- 
tinue : " We do not consider, however, that identity of measurement would 
necessarily imply identity of species. We still believe that the difference in 
internal morphology, namely the presence of the posterior nucleus, is sufficient to 
separate T. rhodesiense both from T. ganibiense and T. brucei*." As a matter of 
fact the " biometric study " of the data does not indicate identity in the measure- 
ments, but confirms the result of internal morphology by proclaiming wide 
differentiation f. 
(d) We can now compare T. brucei and T. gambiense. Of these Sir David 
Bruce writes ; " Whether these slight differences are fundamental or only acci- 
dental it is impossible at present to say, but enough has been written to show 
that Trypanosoma gambiense and Trypanosoma brucei approach each other very 
closely in size and shapej." The biometric commentary on this is that for length 
of the two series = 126"52, giving P< •000,000,1 and that as far as size is 
concerned the samples differ immeasurably, i.e. far beyond the limits of the 
calculated tables of P. 
We should thus conclude, merely from the statistical evidence, for close same- 
ness in T. brucei and T. rhodesiense but for marked divergence of both from 
T. gambiense. 
* li. S. Pror. Vol. 85, B, p. 233. 
+ In a later section of this memoir I show that Stephens and Fantham have been markedly biased 
in their judgment of even and odd units of measurement (p. 129 below), and that the recognition of 
this makes a wide difference in the goodness of tit of my resolution into components to their data for 
T. rhodesiense. It seems desirable therefore to inquire whether this bias affects the test of "sameness" 
of T. rhodesiense with T. gambiense, T. brucei, and the Human strains (6) and (c), see the Tables 
pp. 95 — 6. The data were accordingly classified into groups of two microns, starting with 12 and 13, 
14 and 15, etc. , so as to get rid of the even bias as far as possible, and we find : 
Strains compared 
Old Unit Ranges 
New Two Unit Ranges 
n 
P 
n 
x' 
P 
T. rhodesiense and T. (jambiense 
28 
140-27 
< -000,000,1 
14 
118-73 
< -000,000,1 
T. rhodesiense and T. brucei ... 
28 
46-83 
•019 
14 
25-76 
-018 
T. rhodesiense and Human 
strain (6) 
28 
69-95 
•000,01 
14 
45-92 
•000,06 
T. rhodesiense and Human 
strain (c) 
28 
325-47 
< -000,000,01 
14 
253-37 
< -000,000,01 
The bias towards even numbers of Stephens and Fantham has thus not substantially influenced our 
results, which still show the relative likeness of T. rhodesiense and T. brucei, and the marked divergence 
of the former from T. gambiense and the human strains. 
t R. S. Proc. Vol. 84, B, p. 832. 
Biometrika x 13 
