190 Trans. Acad. Sci. of St. Louis. 



calculated for each and every year in the series, T have cal- 

 culated the possible attendance for each year. 



10. Now turn to Tables IV-XII. I have here in every 

 case in the third column one of the columns from Tables I, 

 II and III. In the fourth column I have the rates of external 

 increase alreadv obtained. The next column o-ives the theo- 

 retical ''external" increase in numbers, and in the sixth 

 column, the " possible " or ideal number for each age, ob- 

 tained by adding the increase to the enrollment of the previous 

 year. Now subtract the actual attendance from the " possi- 

 ble " attendance and we have of course the number who 

 during the year withdrew. 



11. It is evident that the average asre of those withdrawing 

 during any one year is one year greater than their age when 

 they were last enrolled. For example: At enrollment the 

 pupils in their fifteenth year are enrolled as 14, and it is 

 evident that their average age is 14^. Then those who with- 

 draw before the next enrollment are on the average half a 

 year older, so that those 14-year-old pupils who do not 

 reappear withdraw on the average when just 15 years old. 

 Hence it makes no difference at what date during the year the 

 ages are registered provided the date is always the same. 



12. The average age of withdrawal is, of course, found by 

 adding all the products found by multiplying the number of 

 pupils withdrawing each year by their age, and dividing the 

 sum by the total number of withdrawals. 



13. It will be noticed in certain tables that not only is the 

 rate of external gain minus, showing loss of school popula- 

 tion, but in some cases they show a negative withdrawal, or 

 an abnormal entrance of new pupils. This involves of course 

 an unusual withdrawal during the same year from other 

 groups or columns, as the rate of increase is calculated from 

 all ages. I have carried out all such negative results, sub- 

 tracting such amounts as have prefixed a minus sign. 



14. Results. Table XIII gives the results of the nine cal- 

 culations. I submit them without comment. 



15. The Average Age of Withdrawal versus The 

 Average Age of Children in School. I was originally led 

 to this discussion by what I regard as erroneous statements 



