1922] DENNY—FRUITS 53 
value of N by an error in the value of P.E. sing. is as follows: 
coefficient \ 2 ge 
a|a(Seeeee) fee) | 
d(P.E. sing.) 
Deviation in N= X<error in P.E. 
age = 
difference 
To apply this formula to a particular case, we find from 
table III that the P.E. sing. for fifteen fruits was 1.1; the 
error in 1.1 is found by substituting in formula 3 to be 
2 
) <P.E. sing. Xerror in P.E. sing. (formula 4). 
I.I my =0.14. If we wish odds of 22 to 1 for a difference of 
1.0 in ratio, we obtain, by substitution in formula 4: Deviation in 
A 2 
N=4X (32) 1.1 Xo0.14=six fruits, therefore the corresponding 
value, 22, found in table III, is in error by six fruits, and the 
probable number extends from 16 to 28. 
The corresponding formula for applying a correction to for- 
coefficient 
2 
oetncient x P.E. sing. X deviation 
mula 2 is: Deviation in N=2x( 
in P.E. sing. (formula 5). 
Data on other lots of oranges 
The discussion thus far has related to the data from only one 
lot of oranges from a single tree. Fruits from four other trees were 
obtained and analyzed in the same manner. The number of fruits 
used was small, but some idea of the accuracy of the probable 
errors can be obtained by applying formula 3. The data are shown 
in table V, and serve to indicate values of P.E. sing. that may be 
expected in dealing with different lots of oranges. 
Data on grapefruit 
Fifty fruits were taken at random from a grapefruit tree in one 
grove, and a corresponding number from another tree located in 
another grove. The fruits were analyzed individually and the mean 
and P.E. sing. determined. To save space, the complete analyses 
are not given, but the results are summarized in table VI. From 
this table it is seen that P.E. sing. of the fruit from the two lots is 
