56 BOTANICAL GAZETTE [JANUARY 
sum of the deviations (taken without regard to sign) is needed. In- 
asmuch as the latter method is more convenient, it seemed profitable 
to show the difference in the value of P.E. sing. given by the two 
methods. In table VIII are shown the comparative values found.’ 
It is seen that the difference in the value of P.E. sing. by the two 
methods is at least not more than is shown between two groups of 
even the same lot of fruit. Hence no large error would have been 
introduced by the use of the more convenient Peter’s formula. 
TABLE VIII 
COMPARISON OF STANDARD FORMULA WITH PETER’S FORMULA FOR CALCULATING 
PROBABLE ERROR OF SINGLE OBSERVATION 
P.E. sING. OBSERVATION P.E. SING. OBSERVATION 
No. OF FRUITS IN Solids-acid ratio No. OF FRUITS IN Percentage sugar 
SAMPLE SAMPLE 
Standard Peter’s Standard Peter’s 
formula formula formula formula 
10.0 i oe 1.09 1.08 TGs oi eee oe 39 0.40 
BG Seas eee I.O1 99 TRG ee ese 0.34 0.34 
pL eg ere anereure es I.09 T.10 BO Meares we 0.44 0.42 
ko Eee RSS I.10 1.33 MERE ie Gre case 0.42 0.43 
40.40 ne 1.09 1.02 S85 st 0.40 0.40 
A655 oe t.20 ba 4505. ee 0.40 0.40 
St eee 1.26 1.29 Shia a 0.39 0.38 
Summary 
1. Formulas are given, for use under two different conditions of 
sampling, to determine the number of fruits required in a sample 
in order to give a desired assurance that a certain accuracy has 
been attained. 
2. Approximately 250 fruits of oranges, lemons, and grapefruit 
were analyzed individually, and the probable errors calculated. 
The data so obtained were applied to the formulas, and numerical 
examples worked out to illustrate their use. 
3. It is shown that the values given by the formulas are only 
approximately correct. The sources of error are discussed, and 
formulas given by which the amount of this inaccuracy may be 
estimated under different conditions. 
3 Computations are made much easier by the use of tables given by MELLOR (4). 
