188 Trans. Acad. Sci. of St. Louis. 



7. The Rate of Internal Growth. As the number of 

 children of school age in a city bears a very nearly fixed ratio 

 to the total population, the increase in the number of school 

 children from year to year is the same as the rate at which 

 the total population increases. This is true of both the " ex- 

 ternal " and the " internal " growth. Now the internal growth 

 of a city is exactly measured by the increase of births over 

 deaths. Hence I calculate the rate from the official reports 

 of births and deaths. All cities give accurate reports of 

 deaths; the reports of births are incomplete. In Boston they 

 are more nearly complete than in Chicago, and in Chicago 

 they appear to be better than in St. Louis. In Boston, as 

 would be expected, the internal growth is least, viz.: 7-1000 

 or 0.7 per cent. In St. Louis it is, as nearly as I can learn, 

 16-1000 or 1.6 per cent. In Chicago it is greatest, viz. : 

 20-1000 or 2 per cent. While these rates are not uniform 

 they are approximately so. In fact these results are averages 

 of several years. In a former discussion of this problem in 

 May, 1879, I did not distinguish the two kinds of growth, 

 but allowed for the death rate of school children directly. 



8. The Total Rate of Growth in School Population. 

 This rate is readily found by comparing the enrollment any one 

 year by the enrollment for the same ages for the preceding 

 year. For example : take the two years 1889-90 and 1890- 

 91 in the table of the Chicago schools. The attendance of 

 children above 7 years of age in 1889-90 was 115,366. The 

 next year the enrollment was 124,144, a growth of 7.6 per 

 cent. This approximately represents the growth of the city. 

 In the last column but one on Tables I, II, and III, represent- 

 ing the attendance in St. Louis, Chicao-o and Boston, this total 

 rate of growth of school population for each year is given. 

 It will be seen that in some cases it is small, in others very 

 large. Thus in Chicago schools the increase from 82 to 83 

 was 5.7 per cent; from 83 to 84, 4.5 per cent; from 84 to 

 85, 5.8 per cent ; from 86 to 87, 2.5 per cent, and so on. In 

 the year 88 to 89 I find the enormous increase of 41.5 per 

 cent; this signalizes, of course, an immense accession of ter- 

 ritory with a school population two-fifths as large as that of 

 the former city itself. This explains the unexpected showing 



