86 
A Studjj of Trifpanosome Strains 
The distributions in appearance are wholly dependent on the choice of scales 
and the eye alone cannot possibly make any measure of the degree of accordance, 
which will have scientific value. 
In the accompanying Diagram I. for example, we have the frequency distri- 
butions permille of two strains of trypanosomes, (oa) from a Donkey and (W) from 
a Hartebeeste. These we are told are identical. Below (cc) and (cZtZ) are given the 
frequency distributions of head-breadths for two races, Egyptian and English women, 
separated by 7000 years interval. These strains we know to be different, but the 
eye that judges {cm) and ihh) to be the "same"* might well suppose (cc) and {dd) to be 
also the same. Actually when we come to the quantitative measure of divergence, 
the probability that {aa) and (hh) are samples of the same thing is P < -000,000,1, 
while the probability that (cc) and (dd) are the same is P = '001. In other words it 
is 10,000 times as likely that Egyptians of 6000 B.C. and the English of 1G80 A.D. 
are the same strain as that the trypanosomes from the Hartebeeste and those 
from the Mzimba Donkey are of the same strain. Both may indeed be of the "same 
strain " if a sufficiently wide meaning be given to the term. But is such a racial 
resemblance as we find between the Prehistoric Egyptian woman and the English 
woman diluted 10,000 irmes what we understand in ordinary language by the "same 
strain"? All the mathematician can understand by "sameness of strain" is the 
identity which corresponds to random samples of the same population. If the identity 
has been modified by a long evolutionary process, by markedly differential environ- 
ment or treatment, is it not better to have some measure of a scientific nature of 
the extent of the difference or of the sameness ? The eye can never provide aa}^ 
judgment of value on such a point. Especially is this the case if the graphs 
represent percentages, as the degree of divergence is of course a function of the 
number employed to determine the percentages. A deviation of frequency by per- 
centages based upon samples of 200 might look to the eye absolutely like the 
deviation of frequency due to samples of 2000, but the scientific measure of the 
probability of sameness would be widely modified. 
That the reader should have evidence how excellent is the test, I have taken 
the cranial lengths (Flower's measurement) of 67 female skulls dug up in Liverpool 
Street and compared them with the like lengths of 142 female skulls dug up in 
Church Lane, Whitechapel. It is possible that both these sets of crania formed 
part of the contents of plague pits, or there may be an interval in date of a century 
between themf. Diagram Ibis shows the data arranged as percentage frequency 
curves. The %- for 17 groups proceeding by 2 ram. ranges = 19'38, giving P= "250, 
or once in four trials, if the material drawn from were the same, we should obtain 
pairs of samples more divergent than the pair recorded. In other words we can 
be confident that the Liverpool Street and Whitechapel crania represent persons 
* An attempt to define the word "sameness" as used by writers on trypanosome strains would 
doubtless serve a useful purpose, and emphasise the fact that we can only define "sameness" by appeal 
to the theory of sampUng, or by the adoption of some quantitative measure of the grade of likeness. 
t See Biomctrika, Vol. m. p. 191 and Vol. v. p. 80. 
