Karl Pearson and David Heron 
li)7 
nature of the surface of frequency. For surfaces of zero correlation it must always 
take all values from + 1 to — 1 according to the position of the dividing planes. 
We will take one more of these zero correlation tables because it leads up to 
certain new points. Such a table as that given as Table VIII might well occur in 
practice ; worked out by the product-moment method, the regression lines are 
linear and there is zero correlation. Table IX shows how extraordinarily the 
Diagram III. Frequency surface of zero correlation exhibiting every possible variation 
of Q with different dichotomic lines. 
O'O 
coefficient of association varies from point to point of division. It is not only zero 
along the axes, but zero along a contour line in each quadrant. Thus, starting from 
the centre of the surface, we descend in the first and third quadrants to a negative 
association — '45, then crossing the zero contour, we rise to a positive value of 
+ '50 and ultimately reach + "87 ! In the second and fourth quadrants the process 
is reversed ; we rise first to + "45, then sink to zero and descend first to — '50 and 
