M. Greenwood and J. D. C. White 
387 
Professor Bruns, in his work on the Theory of Probability, writes : — 
Es ist niimlich leicht zu iibersehen, dass die von uns zugrunde gelegte erweiterte Begriffs- 
bestimmung der K.-G. die ja auch willklirlich ersonnene Reihe ziilasst, von vornherein eine 
andere analytische Behandluug der Funktioneu S und SB verlaiigt. Denn wenn als Verteilungs- 
kurve ein vorlaufig beliebig gestalteter Linienzug auftreten kann, so ist nicht daran zu denken, 
dass sich solche Gebilde allgemein einer einfacher Formel unterwerfen lassen. Aiis diesem 
Grund sind flir unsere Aufgabe auch die von Pearson angegebenen Formen...unzureichend, 
obgleich sie in mathematischer Beziehung eine grbssere Biegsatnkeit besitzen, als das zweiseitige 
Gesetz (Fechner)*." 
A sufficient answer to Professor Bruns is that the skew curves of Pearson 
describe, and describe well, variation in material frona many different sources ; of 
this nearly all the examples obtained in the present research afford a striking 
illustration. Anyone who takes the trouble to examine the method which 
Professor Bruns holds (erroneously, as we think) to be theoretically superior, will 
not need to be told that the generalised curves of Pearson are easier to work 
within statistical practice. If then they give, as here, admirable results, their 
superiority cannot be questioned. 
Turning to the details, we see that all the S. counts, except III., are examples of 
Type I. with marked skewness. We also notice, as would be expected f, that the 
most extreme skewness occurs in the distribution of least range. 
It may be remarked that the negative start| of the curves (see especially 
Graphs 5 of Strangeways, 11, 13, 14 and 15 of Fleming) may well have some 
biological significance. We believe that those who have studied the mechanism 
by the agency of which foreign particles enter or are brought within amoeboid 
cells, are by no means clear as to its real nature§. 
It is not clear that all the cells containing no bacteria represent tlie same stage 
of phagocytic power. It will perhaps seem that a true interpretation of phagocytic 
counts having a large number of leucocytes with zero frequency of ingested bacilli 
is only possible on the basis of some such analysis as the present. The matter is, 
however, too conjectural for us to consider it here. 
The only exceptional result among the S. data was obtained from III. Here 
the value of the second criterion required, strictly speaking, a curve of Type IV. 
Type IV. constants were calculated, but although the curve was a good graphical 
fit, the value of P was small mainly owing to a want of agreement in the first 
group. In view of the fact that was tolerably close to unity we also tried 
Type v., and, as will be seen, the result is good, and brings this count into line 
* Wahrscheinlichkeitsrechnung und Kollektivmasslehre, von H. Bruns, Leipzig, 1906, p. 111. 
t Pearson and Filon, Phil. Trans. A. Vol. 191, pp. 282, etc. 
+ The start should not of course be before - -5, the large probable error of range gives little 
significance to starts even at - 1. The technique, however, of Sir A. Wright's laboratory appears to 
emphasise the extent of negative range. 
§ For a readable summary with bibliography, see Weiss, Nagel's Handbuch der Physiologie des 
Menschen, Bd. iv. 1908, pp. 629—665. 
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