bo4 
bers in the series and treat these departures according to the following 
formula: 
Index of variability of the plats equals 
40.864. / Sum of all the (Departures)? 
Number of departures less 1, 
which formula may be interpreted as meaning that from the squares 
of the departures added together and divided by the number of plats 
less 1 we derive an index called the “ probable uncertainty of 1 meas- 
ure,” or “the probable variability of 1 plat as compared with all the 
plats of the series.” Again, knowing this uncertainty of any one 
measure, we find the “ probable uncertainty of the average of n meas- 
ures” by the following formula: 
Probable uncertainty of the average = + mee 
This latter formula is to be interpreted as meaning that there is 
an even chance that the computed average is too large or too small 
by this probable uncertainty. Applying these principles to the meas- 
ures of plats C and E, I obtain the figures 34.3 and 22.9 as the indices 
of variability and 8.33 and 5.26 as the probable errors of the two 
averages. That is to say, so far as any internal evidence is given 
by the discrepancies between the measurements of the plats them- 
selves, there is an even chance that the crop from a plat in series C is 
between the lhmits 212.9 and 196.3 or outside of these limits; simi- 
larly, for series E there is an even chance that the crop from any 
plat is within the hmits 188.9 and 177.4 or outside of these limits. 
But the numbers within each of these two series overlap each other so 
much that it is perfectly possible that if we could increase the number 
of plats in each series sufficiently, all other conditions remaining the 
same, we should eventually arrive at very nearly the same average 
value for each. In other words, the mere difference of the two aver- 
ages 204.6 and 182.7 is no evidence that in this particular case there 
was any important constant difference between the plats of series C 
and those of series E, but that, on the contrary, unknown sources of 
influence are at work in each series and in all the plats that are more 
important than any that were thought of when the experimenter 
endeavored to make these 36 plats perfect duplicates of each other. 
Professor Plumb shows that this difference did not depend upon the 
previous crops or treatment of the plats during the previous five 
years. It certainly did not depend on the meteorological climate, 
the mechanical condition of the soil, nor on the seeds, nor on injury 
by insects and animals. We may possibly find a partial explanation 
in the irregular distribution of microbie life in the soil, but it is 
more likely that it depended upon the inherent variability of the 
