,3 
By Student 355 
So that if we have counted M unit areas the probable error of our mean (m) is 
If we are working with a hsemacjtometer in which the volume over each square 
is ^^QQ mm. there will be 40,000,001) m particles per c.c. and the probable error 
'ill 
will be 40,000,000 x -67449 ^ m ^• 
Suppose now that we dilute the liquid to q times its bulk, we shall then have 
— particles per square, and if we count M squares as before, our probable eri'or 
for the number of particles per c.c. in the original solution will be 40,000,000 
X -67449 X q X ~ . That is 40,000,000 x '67449 y^'J^- 
That is we shall have to count qM squares in order to be as accurate as before. 
So that the same accuracy is obtained by counting the same number of 
particles whatever the dilution, or, to look at it from a slightly different point of 
view, whatever be the size of the unit of area adopted. 
Hence the most accurate way is to dilute the solution to the point at which 
the particles may be counted most rapidly, and to count as many as time permits: 
then the probable error of the mean is '67449 /^J^'jj- where vi is the mean and M 
is the number of unit areas counted over, squares, columns of squares, microscope 
fields, or whatever unit be selected. 
But owing to the difficulty of obtaining a drop representative of the bulk of 
the liquid the larger errors will probably be due to this cause, and it is usual to 
take several di-ops : if two of these differ in their means by a significant amount 
compared with the probable error (which is '67449 a/ ^ where m-i, are 
the means and M the number of unit areas counted), it is probable that one at 
least of the drops does not represent the bulk of the solution. 
Experimental Wo7'h. 
This theoretical work was tested on four distributions * which had been counted 
over the whole 400 squares of the hsemacytometer. The particles counted were 
yeast cells which were killed by adding a little mercuric chloride to the water in 
which they had been shaken up. A small quantity of this was mixed with a 
10 ° I ^ solution of gelatine, and after being well stirred up drops were put on the 
hsemacytometer. This was then put on a plate of glass kept at a temperature just 
above the setting point of gelatine and allowed to cool slowly till the gelatine had 
set. Four different concentrations were used. 
* One of these is given in Table I. 
