294 Trans. Acad. Sci. of St. Louis. 
This question — the relation of the growth of the individual 
to the growth of the type —can be determined only by the 
individualizing method. The generalizing method deals solely 
with units, irrespective of their individuality. If for example 
John Smith in the 75 percentile grade and William Harrison 
in the 60 percentile grade at age 6 exchange places at age 7, 
the personal curve of each boy undergoes an important devia- 
tion, but the number of units in the two grades, and conse- 
quently the middle value in each, is unaltered. The generalizing 
method, therefore, furnishes no data by which the future de- 
velopment of individuals can be safely judged. The individ- 
ualizing method, on the contrary, follows the individual from 
year to year throughout his growth and establishes the 
frequency and extent of his deviations from the growth of 
the type. The lack of data collected by the individualizing 
method is regrettable, but this gap in our knowledge does not 
prevent the establishing of physical standards by which the 
probability that the physique of any child is normal or abnor- 
mal can be fixed. 
The facts stated above limit the application of middle values 
to (1) the establishing of physical standards at each age, and 
(2) the using of these standards to determine whether the 
physique of any child is normal: they do not, in the present 
state of knowledge, permit prediction of future growth. 
It has been much disputed whether the median value or the 
average should be taken for the type. Many investigators 
agree with Sir John Herschel, who declares in his celebrated 
review of Quetelet’s Lettres sur la théorie des probabilités 
(page 23) that an average ‘‘ may be convenient, to convey a 
** general notion of the things averaged, but involves no con- 
** ception of a natural and recognizable central magnitude all 
‘* differences from which ought to be regarded as deviations 
‘‘from a standard. The notion of a mean, on the other 
‘** hand, does imply such a conception, standing distinguished 
‘*from an average by this very feature, viz.: the regular 
‘march of the groups, increasing to a maximum, and thence 
‘again diminishing. An average gives us no assurance that 
**the future will be like the past. A mean may be reckoned 
‘‘on with the most implicit confidence. All the phil- 
