186 Trans. Acad. Sci. of St. Louis. 



and ten, and so on. These nurnbers are given in every annual 

 report, and I have taken them from the annual reports of 12 

 or 13 consecutive years. I am bound to assume that these 

 reports are accurate, although they exhibit certain anomalous 

 results. By grouping these reports as exhibited in Tables I, 

 II, and III, and then considering the figures in any vertical 

 column, I am able to follow the same group of children 

 through their course in the public schools. I have assumed 

 that no pupils withdraw before the age of eight years. By 

 following down any vertical column we can see how the num- 

 bers increase or diminish from the combined effect of immi- 

 gration, emigration, death, and withdrawals from school, till 

 the class disappears altogether at the age of 20. 



4. To extend my investigations over as much ground as 

 possible I have entered on Tables I, II, III, sufficient data to 

 enable me to make three independent calculations from each 

 table. I have named the columns '* A," " B," " C," in each 

 case so that in all I have applied my analysis to nine sets of 

 pupils, three in each city. I will add that I limited my study 

 to the cities St. Louis, Chicago, and Boston for the reason 

 that all the other large cities failed to furnish me with the 

 requisite data. 



5. It is a source of regret that the data furnished by the 

 three cities are not uniform in character. In the Boston 

 schools the reports give the number *' 16 years old," " 17 

 years old," " 18 years old," " 19 years old and over." In 

 the Chicago reports all pupils " 17 years old and over " are 

 lumped together. In the St. Louis reports all pupils " 16 

 years old and over " are lumped together. It has been nec- 

 essary to distribute the pupils thus lumped together, according 

 to their ages as accurately as possible. 



It was useless to refer to the unpublished records in St. Louis 

 and Chicago for the exact details of such distribution, as they 

 could give no additional information. In this emergency I 

 adopted the following method based upon an examination of 

 the distribution in the Boston schools, and of the ratio which 

 the 16 year old pupils bore to those " 17 and over " in the 

 city of Chicago. I will not give the details of my investiga- 

 tion, but will plainly state that I assumed in the case of 



