170 Trans. Acad. Sci. of St. Louis. 
This table shows that the statements in the preceding 
pages are supported by averages as well as means, andon 
this double foundation the law of the relation between pre- 
cocity and physical development may well rest secure. 
It is not enough to know that the mean and the average 
child follow this law. We must also know whether small pre- 
cocious children are heavier than small dull children and on 
the other hand, whether large precocious children are heavier 
than large dull children. 
To determine this we will have recourse to Galton’s schemes 
of distribution.* If a thousand children at the same age were 
placed in line according to stature, the height of the middle 
or 500th child would bethe mean (Galton’s nomenclature) 
of the heights of the entire number. The larger children 
would be at one end of the line and the smaller children at 
the other. If we took the 300th child, counting from the 
middle of the line in both directions, we should have one large 
and one small child at an equal distance from the mean, and 
the weights of these children might be safely compared with 
the weights of children similarly selected from a series of 
1,000 at another age. 
A process analogous to this has been followed with the 
children’s weights in the present instance. I have taken at each 
school grade and age 20 and 80 percent of the total observa- 
tions. The figures in the pound column opposite which these 
percentages fallrepresent respectively the weights of a small 
and a large child, and these weights may be compared with 
those obtained in a similar manner from other school grades 
and ages. Table No. 6 is made from the 20 * percentile ,’’ a8 
Galton would call it, and thus contrasts the weight of small 
children in different school grades, and Table No. 7 is made 
from the 80 ‘ percentile,’’ representing the large children. 
In both tables, boys’ weights are printed in DOUBLE-FACED 
type. The mean weights of small children (20 «percentile ”’ )> 
irrespective of school grades, are placed in. the column 
on the left in Table No. 6 and the mean weights of large 
children (80 ** percentile’), irrespective of school grade, 
- occupy a similar position in Table No. 7. 
___ *Fally explained iv Galton’s Natural Inheritance, London. 1889. Chap. 1V- 
