W. F. Harvey and A. M^Kendrick 
67 
law of some kind governs the degree of phagocytosis. If we appreciate the point 
that a deficiency in the number of leucocytes containing any given number of 
bacteria is balanced by an equal excess distributed amongst the numbers of 
leucocytes containing different numbers of bacteria and assiime that all ordinates 
representing these magnitudes are interdependent owing to their being governed 
by some law, we can see how the help of the mathematician becomes indispensable : 
he will determine, if supplied with sufficiently large numbers to avoid gross error, 
the smooth curve which will most closely fit the totality of observations. We may 
then be willing to concede that such a curve will give us a near approach to 
the condition of things as they ought to be, but which are not so owing to experi- 
mental error and to smallness of data. 
It is necessary in the first instance to afford the mathematician sufficient data 
by which to construct his curve but once constructed it may become of the utmost 
utility as a test of the degree in which we are approximating to the ideal by the 
method which considerations of convenience lead us to adopt. The same sort of 
standard of comparison might be set up by the bacteriologist himself if he took 
the pains to collect very large data. The larger the number of leucocytes counted 
for example, the fewer would be the irregularities, and finally, when the numbers 
were very large indeed, we may imagine that our frequency polygon would be 
identical with the mathematician's curve. But the labour of such a task would be 
very great, and if it had to be done in many cases would take up too much of the 
observer's already too short life. It would be folly then to refuse the shorthand 
expressions of the mathematician in the shape of curve or formula, or his state- 
ments as to degree of error, simply because he has deduced these from the data 
supplied to him on the supposition of the operation of a law governing the varying 
magnitudes of the observations. In many cases it is quite unnecessary to under- 
take the labour of fitting a curve, since a single measure like the Arithmetic Mean 
serves to give all the information which is really necessary. But we must at least 
know what are the limits of error of our average, and this is almost totally neglected 
by medical observers. 
To return to the example given, we should naturally, in seeking to give ex- 
pression briefly to what is exhibited here in a somewhat lengthy form, take the 
Arithmetic Mean of the whole distribution. This is 3"11. In words the average 
number of bacteria taken up per leucocyte is 3"11. Obviously no leucocytes take 
up this number of bacteria, but long familiarity with such a measure has made all 
men acquainted with what is meant by the expression. No leucocyte contains 
this number nor ever will contain this number; nor can even the majority of the 
leucocytes be said to contain approximately this number. The Arithmetic Mean 
then in this case does not correspond to the character possessed by the majority. 
This is due in reality to the want of symmetry of the distribution. This asym- 
metry or skewness is typical of all phagocytic distributions which have been as 
yet investigated from this standpoint, and is itself characteristic of the particular 
law which governs these distributions. It has an important bearing on the claim 
9—2 
