CORRELATION 105 
of the corresponding classes of fathers being read off 
on the horizontal scale. It will be seen that this series 
of dots lies nearly in a straight line which is inclined 
at a certain angle to the horizontal. 
Now if there were perfect correlation between the 
heights of fathers and sons, and no tendency existed 
for sons to be more like the general mode of the popula- 
tion than their fathers are, the inclination of the line 
obtained in the above manner would be one of 45 
degrees, as in the case of the line CD which passes 
through the points at which the values as read off 
in the vertical and horizontal scales are identical. If, 
on the other hand, there were no correlation the line 
would be horizontal, as EF. 
The value taken to represent the amount of correla- 
tion is the degree of slope of the line AB. This is 
expressed mathematically as tan a, a being the angle 
which the line in question makes with the horizontal. 
When there is positive correlation this angle falls 
between o and 45 degrees, and tan a between 0 and I. 
In the present instance tan a is 0°5. This value is 
known as the coefficient of correlation, and affords 
the basis of a numerical comparison with other similar 
coefficients obtained for other characters besides 
stature, and in the case of other pairs of relatives 
besides fathers and sons. 
It ought now to be clearly understood that a com- 
plete resemblance between each class of fathers of a 
particular stature and the average stature of the 
corresponding array of sons would be indicated by 
the close approximation of our plotted points to a 
