180 SECTIONAL ADDRESSES. 
Compare next young children with those that are older. Here I may 
quote from the admirable work of Prof. Burt. Applying his test of 
reasoning to numerous children of different ages, he obtained the following 
correlations with the estimates of the teachers : 
pedi Hila Earp agua 11-12 12-13 13-14 
Correlations .. 78 81 64 59 
No less marked is this tendency on comparing children with adults. 
As examples may be taken the correlations obtained by Otis and Carothers 
respectively for what appear to have been similar tests in each case. 
Test Correlations with g 
Otis, grades IV-VIII. Carothers, students. 
Analogies $s 2 84 71 
Completion .. ats are 88 -53 
Directions .. oe 33 -86 : 45 
Digits, memory .. : 41 22 
Now these changes obviously follow a general rule. The correlations 
always become smaller—showing the influence of g to grow less—in just the 
classes of person which on the whole possess this g more abundantly. 
The rule is then that, the more energy available already, the less 
advantage accrues from further increments of it. And this is a well-known 
property of engines in general. Suppose that a ship at moderate expenditure 
of coal goes 15 knots an hour. By additional coal the rate can readily be 
increased another 5 knots. By doubling the addition of coal, however, 
the additional knots will certainly not be anything like doubled. This 
relation is observed not only in engines, but also widely elsewhere. In the 
science of economics, for instance, it comes to expression in the well-known 
law of diminishing returns. A moderate amount of capital spent on a given 
piece of land will produce a certain return ; but on adding further doses of 
capital the returns will not go increasing proportionately. 
In our psychological case of different classes of persons there enter no 
doubt various complications which render the theoretical interpretation 
more dubious. Above all, there is the fact that the classes better endowed 
with g have usually undergone more or less selection. For instance, the 
university students of Carothers had been cleared of the weaklings who 
could not matriculate. And this in itself would tend to lower all correlations 
due to g. However, such facts would seem capable of accounting for only 
part of the phenomenon, not for the whole. There remains enough over 
to suggest a genuine law of diminishing returns for mental as for material 
processes. 
IV. Corollary of Independence. 
The next and final point to be raised here is a corollary of what has been 
said. Since a great many abilities depend almost entirely upon the 
efficiency of the engines involved and this efficiency varies independently 
from individual to individual, we may conclude that these abilities them- 
selves vary almost independently from individual to individual. 
This theorem has, indeed, been called into question. Some authorities 
have asserted the existence of a general ‘ sensory level’ of ability, so that 
the persons who are successful at one kind of sensory performance will 
tend to be so at others also. Other writers have adopted a similar position 
as regards what they call ‘ practical’ ability; persons are taken to be 
either endowed or not endowed with this all round. But no such position 
