266 FolJcmar—The Duration of School Attendance . 
too larom and next too small have neutralized each other. But, 
since this is after all only an approximation and not a perfect 
demonstration, the second great aim must be to determine the 
outside limits between which the truth must lie. The maximum 
limit will be reached under the inductive method. The mini¬ 
mum limit may be got at once by reducing percentages. 
Minimum Limit of Error. — As was shown on page 264, if we 
reduce the percentages (the totals for the second and other 
grades in Table IX) without reducing the base (the one and one- 
half million grand total), or at least without reducing it in so 
great a ratio as the percentages, we shall reduce the rate per 
cents. But we know that the base is at least three times too 
large. (See p. 264). The question is how much to deduct 
from the apparent enrollments, especially in the first four grades, 
to make the numbers stand in the same relation to each other 
as do the true enrollments. That all the other grades are within 
from one to ten per cent, of the actual enrollment will probably 
be granted after the following discussion. 
Correction for Double Enrollment. — The apparent or printed 
enrollment in each of these grades is too large, because many 
pupils are not only enrolled in them on entering the grade but 
also on coming back to it the next year — those pupils, namely, 
who failed of promotion. The determination of the number en¬ 
rolled twice in each grade, is the most incomplete part of the 
present paper. It would seem to be impossible to get accurate 
results from the material at hand in Chicago and Milwaukee. 
The question is, therefore, turned over to the future investi¬ 
gator in this subject with the following imperfect data and in¬ 
ferences. 
Since we are seeking only a limit of error, perhaps so large 
a reduction of the grades may be made that anything greater 
would be clearly unreasonable. The next table of promotions 1 
is of prime importance. It can not be inferred, however, that 
all who fail of promotion were enrolled in the same grade 
for the following year. How many of these dropped out of 
1 Table VIII. Number of Pupils Promoted (Chicago), p. 289. This 
table is compiled from the Superintendent’s Reports in the Annual Reports 
of the Board (e. g., report for 1897, p. 30.) 
