Karl Pearson 
127 
I think we may conclude that, allowing for the errors of random sampling 
and the errors arising from the resolving process, the deviations observed in the 
variability of our two components do not invalidate the hj^potheses : 
(i) That the widely divergent results obtained from different strains are due 
to the existence in the same individual of two types of trypanosome with very 
varying percentages from individual to individual. 
(ii) That one of these types has a mean length of about 19'8 microns and a 
variability of about 1"8 microns, the other a mean of about 26"0 microns and 
a variability of about 3'0 microns. The means may vary 1 or 2 microns with the 
nature of the host and the variability 0"5 to 1 micron. 
The large type predominates in the Nyasaland human strains*, on the average 
in about the ratio of 3 to 2, but the smaller type predominates in the G. morsitans 
and wild-game strains in about the same ratio ; while in the trypanosomes classed 
as T. rhodesiense, and T. gambiense as well as in the strain from the Mzimba 
donkey the preponderance is still of the smaller type and the ratio approaches 
13 to 7. Whether these ratios are peculiar to the host or due to the infecting fly, 
it is not at present possible to determine. But the hypothesis of the existence of 
these two types, — whether as a dimorphism of T. rhodesiense or as independent 
species seems to bring some order into the apparent chaos of recent trypanosome 
measurements. 
The following paragraphs give the calculated constants of the reductions, and 
the numbers of the diagrams showing the nature of the compound frequencies : 
(i) T. rhodesiense. 
Mean = 23-577, 
fx, = 21-86874, fi, = 1079-10255, 
^3 =: + 4-01986. /i,, = + 1105-74834. 
Reducing nonic : 
24g'^- 298-7232f/- -58175" + 1114-7684g= + 34-76202^ 
- Il79-2495g' + 12-98082^ + -0891^ + -0001 = 0 
where f p.^ = — lOq. 
The root is ^2 = - 12-2578. This leads to the two components in the Table 
p. 125. The histogram of the observations and the two component Gaussian 
curves with their compound are given in Diagram VI. 
The resolution is not a very good one; for 24 groups = 37-48, and P=:-05, or 
once in 20 trials only we should get a worse result. But an examination of either 
the graph or the original frequency shows at once the cause of this divergence. 
In their measurements Drs Stephens and Fantham have had a strange bias in favour 
* The European from Portuguese East Africa had predominance of T. minus. See R. S. Proc. 
Vol. 86, B, p. 288. 
t Notation of the memoir Phil. Trans. Vol. 185, A, p. 84, Eqn. (29). 
