NUMBER- WORK IN NA TURE-STUD Y 69 



meaningless. With the discipHnary idea out of it, the ancient 

 method of teaching number that still so largely prevails has not a 

 single foot left upon which to stand. 



The lessons given here are submitted as illustrations only. 

 They are worthless to any except those pupils who actually made 

 and recorded their observations. The work was done with great 

 deliberation and covered many weeks, because great nature-images 

 grow slowly with children. The lessons in this connection, are only 

 intended to illustrate what has been said as to the function of num- 

 ber in defining an image. 



I. THE DISPERSAL OF SEEDS. 



An attempt is made to form some idea of the rate at which 

 plants might multiply, as indicated by the seed-production. 



1. Near the schoolhouse a vacant city block rather thickly cov- 

 ered with wild verbenas was selected for study. 



2. By measurement and calculations this area was found to 

 contain approximately one-fourth of an acre. 



3. Areas of one square yard each were measured in various 

 places and the average number of plants was calculated. 



4. An average of thirty plants per square yard gave approxi- 

 mately 36,000 to the quarter acre. 



5. Each seed pod contained four seeds, one of which, on the 

 average, it was found, failed to mature. The number of pods on 

 a spike was counted, which, when multiplied by the number of 

 spikes, gave 2,300 seeds as the average number produced by each 

 plant. Since only three-fourths of the total number matured, each 

 plant furnished, therefore, (approximately) 1,700 good seeds avail- 

 able for growth. 



6. If these good seeds were properly distributed, and if each were 

 to produce a plant, the one-fourth of an acre the second season could 

 populate 425 acres — approximately two-thirds of a square mile; 

 i. e., equal to an area bounded by Cottage Grove Avenue and State 

 street on the east and west, and Sixty-third and Fifty-fifth streets 

 on the north and south. 



The third season, under the same suppositions, enough seeds 

 would be furnished to populate 1,122 square miles; i. e., more than 

 six times the area of Chicago. 



The fourth season, under the same suppositions, the area popu- 



