42 Nebraska Agricultural Exp. Station, Research Bui. 6. 
In the case of the ratio columns, the average results are obtained 
by finding the ratio of the averages for the other columns, rather 
than by averaging the ratio columns. 
In case of the ratios in the average summaries we have, then, 
the ratio of averages rather than an average of ratios. 
In most cases the differences obtained by the two methods of 
calculating are rather slight and immaterial. Both methods appear 
to be mathematically correct, but the one employed in this bulletin 
appears to be more desirable. From the performance standpoint, 
it is important to know what are the production and the amount 
of water transpired in the aggregate, and then to establish a ratio 
between these average results. Table 4, column 8, illustrates an 
instance where the method of calculating is rather vital. In a 
test to determine the effect of the size of the potometer as a source 
of experimental error, the smallest size limited the plant growth 
to such an extent that ear production was almost impossible, and 
only one plant out of four succeeded in producing a small ear. 
Consequently, for practical purposes, the amount of water tran- 
spired by the four plants must be charged up against the one small 
ear. This can only be done by determining the ratio of averages. 
In all cases where the data of two or more years have been 
averaged together in a summary table, the average of ratios was 
determined rather than the ratio of averages, as was done in the 
case of averaging different individuals within a single year. This 
was done in order to avoid overemphasizing in the average ratio 
the seasonal effects of a given year. For these reasons the sum- 
maries in this bulletin may not appear to be quite mathematically 
correct, but they are in fact merely subject to the well-known 
effects of averages. 
The probable error has not been computed for any of the data 
in this bulletin, altho the potometers have been replicated from 
four to eight times. A calculation of the probable error where the 
frequency is so small would appear to be of little value to establish 
the reliability of the results. Where small numbers are averaged, 
it is entirely probable that the actual error in certain groups of 
duplicates will be consistently and abnormally high above the 
correct mean, while in others it will be below the correct mean. 
The actual error may be large in these cases due to averaging 
either high or low extremes, while the computed probable error 
may be very small, due to consistency of the individuals averaged. 
Again, both high and low extremes may fall within a group to 
be averaged, so that the average result will be correct, altho the 
computed probable error is high. Illustrations of such grouping 
may be seen in Table 12. 
All measurement determinations made in these experiments 
are expressed in the "regular" system, namely inches. Thus, 
