SEA-FISHERIES LABORATORY. 139 
If our desired result had been some single-valued, natural 
constant, say a molecular weight, we should have expressed 
it as mean + 0°67450 ly We should have assumed that 
there could only be one value for the physical constant, but 
(because of our experimental methods) there were errors in 
our estimation of this value, and that these errors were as 
often in excess of the “real” value as they were in defect of 
it. The most probable value of the constant would have been 
the mean of our multiple estimations, but this could only have 
been the most probable value, and there were other admissible 
ones. By a recognised convention we “commute” these 
other admissible values, restricting them to the very small 
range given by our expression for the probable error of the 
mean. 
But whenever we deal with a number of organisms 
individually, variable in their morphology and functioning, 
every measurable character is a variable: it has many values. 
We cannot examine all the organisms in the “ population,” 
and so we take a sample consisting of only afew. Any sample 
will differ from any other, and so the error of random sampling 
arises. So, likewise, there are 250 one-c.c. samples in our 
measuring flask, and we can only examine (say) 20. The 
micro-organisms are not evenly distributed throughout the 
whole contents of the flask, and so any sample of 20 c.cs. will 
differ from any other sample of 20 c.cs. 
In such a sample of 20 c.cs. the mean is only an abstraction 
and does not represent anything “real.” Hach of the c.cs., 
with its count, is real, and each is a possible and admissible 
value, but some of the counts are more probable than others. 
So we form the function + 0°6745 o, the probable error of 
the series. The mean we take as about 18, o is about 10, so that 
the probable error=PE is about 7. The convention is to say that 
our number of organisms per c.c. is mean + PE, that is, 18 + 7, 
or 11 to 25. It can be shown that (given certain conditions) 
