1922] DENNY—FRUITS 49 
This relation may now be expressed in general terms by putting 
“deviation” for +o.17, where it is to be the deviation above 
or below the mean, which we wish to use as a limit for accu- 
racy; then putting “P.E. mean”’ for 0.06, and “coefficient of 
deviation ‘ 
odds” for 2.8, we have: =———=coefficient of odds, but 
: P.E. mean 
P.E. sing. 
P.E. mean= ec (Woop 11), and substituting this value, 
deviation 
P.E. sing. 
the equation becomes = coefficient of odds, from which 
VN 
N= Pa ee of odds PE. sat orl 3. 
deviation 
In illustration of the use of this formula, table VI shows that fifty 
grapefruits from tree no. 1 had an average brix of 13.15 and the 
P.E. sing. was 0.35. What number of fruits are required to give 
odds of 10 to 1 that the brix of that number will be correct to 
+=o.15? Table II shows that for odds of 10 to 1, the coefficient 
of odds is 2.5, therefore N= (28Xe88)’ =thirty-four grapefruits. 
No account is taken of errors in the method of analysis, since in 
the present case analytical errors are small as compared with the 
variability of the individual fruits with respect to the constituent. 
If it is desired to take analytical errors into account also, see 
Waynick (10) and Rosrnson and Lioyp (7). 
Comparison of formulas 
Although formulas 1 and 2 appear to be very similar, the first 
in fact giving values just double those of the second, certain essential 
differences should be pointed out. Formula 1 applies when two 
different lots are being compared, in which case the significance of 
the difference between them is affected by the sampling error of 
each lot. Formula 2 applies to the analytical results of a single 
lot only, its own error being the only one involved. Such a condi- 
tion arises when an analysis is made for the purpose of reporting 
the composition of a product with respect to a certain constituent, 
or when an analysis is made to determine whether a constituent 
has reached a certain required value. 
