ON THE EEROK OF COUNTING WITH 
A HAEMACYTOMETEE. 
By Student. 
When counting yeast cells or blood corpuscles with a ha^macytorneter there 
are two main sources of error: (1) the drop taken may not be representative of 
the bulk of the liquid ; (2) the distribution of the cells or corpuscles over the area 
which is examined is never absolutely uniform, so that there is an " error of 
random sampling." 
With the first source of error we are concerned only to this extent ; that when 
the probable error of random sampling is known we can tell whether the various 
drops taken show significant differences. What follows is concerned with the 
distribution of particles throughout a liquid, as shewn by spreading it in a thin 
layer over a measured surface and counting the particles per unit area. 
Theoretical Consideration. 
Suppose the whole liquid to have been well mixed and spread out in a thin 
layer over N units of area (in the hfemacytometer the usual thickness is "01 mm. 
and the unit of area sq. mm.). 
Let the particles subside and let there be on an average m particles per unit 
area, that is Nin altogetlier. Then assuming the liquid has been pi'operly mixed 
a given particle will have an equal chance of falling on any unit area. 
i.e. the chance of its falling in a given unit area is 1/N and of its not doing so 
1 - 
Consequently considering all the mN particles the chances of 0, 1, 2, 3 ... 
particles falling on a given area are given by the terms of the binomial 
f/ 1\ 11"'^ 
s( 1 — I + li^/- , and if M unit areas be considered the distribution of unit 
N 
areas containing 0, 1, 2, 3... particles is given by M Ul — j^j + jy'f 
Now in practice N is to be measured in millions and may be taken as 
infinite. 
45—2 
