5° BOTANICAL GAZETTE [JANUARY 
Accuracy of formulas 
In the preceding paragraphs it was found that the use of formulas 
1 and 2 gave forty-nine fruits as the required number in one illustra- 
tive case, and thirty-four as the required number under the other 
set of conditions. We should not be justified, however, in conclud- 
ing from this test that forty-seven would be too few in the first 
case, and thirty-six would be more than enough in the second. 
With either formula it is seen that the number N depends for its 
value upon the value of the probable error of a single sample, and 
therefore it becomes necessary to inquire how variable this value is, 
and what effect changes in its value have upon N. 
TABLE III 
DIFFERENT VALUES OBTAINABLE FROM SAME LOT OF FRUIT 
TAKEN IN ORDER REARRANGED BY LOT 
TAKEN IN ORDER OF 
ANALYSIS 
ULA AFTER ; 
one Secure NUMBER First rearrangement Second rearrangement 
OF FRUITS ANALYZED 
P.E. sing. |No. of fruits} P.E. sing. |No. of fruits} P.E. sing. |No. of fruits 
found required found required found required 
MOG 7 22 1.4 36 1.0 18 
£50 Gia here t.% 22 ta 36 1.2 26 
oe i A pe 1.0 18 4 36 i.2 26 
ce MO a are ea rs 22 14 36 1.2 26 
Cre Pes Papin i re ON org 1 bees 22 1.4 36 1.4 36 
Bee es ee <1 22 1.4 36 a 36 
Me Oe eee Me 22 I.4 36 1.3 31 
Pe RE ee OE r2 26 13 31 1.5 31 
Slo £.3 31 ris 31 t.3 31 
It is instructive to note what values would have been obtained 
if the value of P.E. sing. had been taken, not after fifty-one fruits 
had been analyzed, but after the analysis of say ten fruits, or after 
fifteen, or twenty-five. The different values for P.E. sing. and N 
that were obtainable in this manner calculated from formula 1 are 
shown in table III. It is thus found the P.E. sing. varied from 1.0 
to 1.3, which values, substituted in the formula, caused the value 
of N to vary from 18 to 31. Formula 2 would likewise have given 
variable values, but the actual figures would have been one-half 
as large. 
The fruits in table I were analyzed in the order of size, number 
_one being the largest. It may be urged that therefore we do not 
