M. Greenwood and J. I). 0. White 
397 
uumbei- of bacilli in a leucocyte when the niuiiber is large, and this may well 
account for the irregularity seen at the upper end of the scale where the theoretical 
curve (Graph 12) gives an obviously more probable distribution than the observed 
result. 
It will be noticed that, in the F. material, Type V. occurs as often as Type I. 
and is, in all but one case, associated with a high mean value. The marked fall of 
skewness in this set is also of much importance. 
Having now presented the main results of our frequency analyses, we are in 
a position to scrutinise them nrore closely, toucliing on certain questions to which 
they give rise. 
First, is our material homogeneous, and does it exhibit nomic variation ? 
In view of the size of the counts it is reasonable, even without direct calcula- 
tion, to think that, with the possible exception of N.S.B., the frequency constants 
are statistically significant. This granted, it is clear that the variation is not only 
nomic, but of a definite order. Table VI. contains the constants of importance 
in testing for Gaussian distribution, and it cannot be doubted that random 
sampling of a Gaussian population could not possibl}' 3'ield such values. 
TABLE VI. 
Tests for Normality of Distribution. 
Keference 
Number 
Skewness 
Modal Divei'gence 
S. I (S. C.) 
1-0953 + -0522 
1-0368 + -1045 
-9667 ±-0261 
1-6787 + -0454 
S. II (S. C.) 
1-3356 ± „ 
2-4306+ „ 
-7557 + „ 
1-1250 ±-0389 
S. II (S. & C.) 
1-4757+ „ 
3-1928+ „ 
-7622+ ., 
1-3117 + -04.50 
S. Ill 
1-4271 + „ 
4-6447+ „ 
-4898 + „ 
-8443 + -0450 
S. IV 
1-3818+ „ 
2-7516+ „ 
-8117+ „ 
1-3060+ -0420 
S. VI 
-9776+ „ 
1-0623+ „ 
-6316+ „ 
•9959 + -0420 
S. VII 
1-0485+ „ 
1-0.562+ „ 
•7896+ „ 
1-3199+ -0440 
S. IV (2000) 
1-3408 + -0369 
2-5790+ -0739 
•7093+ -0185 
1-1224 + -0292 
F. N. S. A. 
-7542 + -0603 
-6214+ -1207 
•4385 + -0302 
-9301 + -0571 
F. No. 2 
1-1253 + -0.584 
2-6386 + -1168 
•4345 + ^0292 
-6691 + -04.50 
F. 10 Norin. 
•8732 + -0520 
1-0164 + -1040 
•4708 + ^0260 
-8686 + -0479 
F. Tub. Chor. 
-8876 + -0523 
-8580+ -1045 
-5471 + -0261 
-8973+ -0438 
F. Tub. Arth. 1 
1-0963+ -0498 
2-3331 + -0996 
-4280+ -0249 
1-0194 + -0.393 
It can of course be said that the description of material by a unimodal 
frequency curve does not preclude the possibility of its being heterogeneous. Thus 
a mixture of two or more homogeneous distributions might, if the respective modes 
were close together, be described by a skew frequency curve. 
That, with such totals as one or two thousand, we should under these conditions 
obtain the fits shown, hardly seems sufficiently probable to need investigation 
here*. We have at least established something nrore than a prima facie case 
■"■ It may further be remarked that the rise at a finite angle at the start of the range in nearly 
all the curves in itself precluded any possibility of a heterogeneity compounded of Gaussian distributions. 
