Woodward — Public Schools : Withdrawal Age of Pupils. 189 



made by the city of Chicago in the census of 1890. The 

 growth since 1890 has been all the while rapid, reaching in 

 tfhe year 92 to 93, 9 per cent. 



It is probable that the increase in the school population as 

 shown by the public school report was relatively greater than 

 the increase in the population of the city, for two reasons : 

 (a) the ratio of children to population was greater in sub- 

 urban than in urban districts; and (b) the proportion of 

 children in the public schools was greater in the suburbs than 

 within the old city limits. 



It is evident that both the rate of internal growth and the 

 total rate of growth are affected by the mortality rate of 

 school children, so that element needs no further considera- 

 tion. 



9. Now it is evident that the increase with which we are 

 concerned when we are considering any group of pupils is 

 that which arises from " external " growth alone. No in- 

 crease in the number of births over deaths can add to the 

 number of those who were ten years old last year and who 

 are eleven years old this year; though such increase does 

 help to explain why the number who were ten years old this 

 year is greater than the number who were ten years old last 

 year. Consequently, in order to find the possible increase 

 ( which may be shown as we read down any vertical column) 

 we must, from the total rate at which the school population 

 increases, subtract the rate of internal growth, and then apply 

 the remaining rate to the number enrolled the previous year. 

 For example: I found that in 1890-91 the rate of increase of 

 school attendance in Chicago was 7.6 percent. I had already 

 found that the internal rate of growth was 2.0 per cent; the 

 difference is 5.6 per cent. This is the rate at which the num- 

 ber of pupils of certain ages in 1889-90 would have been 

 increased during the next twelve months had there been no 

 withdrawals. In the year 1889-90 there were 7,029 pupils 

 in the Chicago schools who were between 14 and 15 years 

 old. 5.6 per cent of that number is 394; hence the " pos- 

 sible number " of pupils between 15 and 16 years old at the 

 registration in 1890-1 was 7,423, as given in Table VII. 

 By means of the final rates, which I have in the same way 



