192 Trans. Acad. Sci. af St. Louis. 



number of pupils remains without change, that is, there are 

 no deaths, no removals, no additions, no withdrawals, but 

 every pupil remains in school until the age of 20, and then 

 withdraws. Under such an ideal condition of things, it is 

 evident that the average age at the time of withdrawal would 

 be exactly 20 years ; and yet the average age at the time of 

 registration at the beginning of any one year would be exactly 

 12^ years, which is clearly seen to be a very different thing. 

 This of course is an ideal and an extreme or limiting case 

 toward which results may approximate more and more as the 

 attendance is extended more and more generally throughout 

 the course of the public schools. 



