x's and y's are interchangeable (see p. 13) as we move through array filling cells. 

 Thus 



X. - X. = X 



J j+a 



and 



X . X . 



The following diagram is used to determine orientation and lag of the correlation. 



As examples, it can be seen that the correlation of cells x^ and x^ have orienta- 

 tion 1 and lag 1. The correlation of cells x^ and A have orientation 3 and lag 2. 



Cells A and B are included to help in evaluating x^.x,.. The correlation, x, .x_., 



^ * li 3i li 3i 



is estimated by averaging the correlations of lag 2 illustrated by cells A and B 



in relation to cell X^^ , because a direct estimate from the linear transect does not 



exist . 



x^.x_. as 

 li 3i 



_S_ince cells A and B are adjacent and directly above and below X^, we define 



Xt .x_. 

 li 3i 



Also, we can make the following observation; 



X-,. ~ X^. ~ X— - — X 

 li 2i 3i 



and 



2 2 

 x^ . - x_ . 

 li 2i 



2 2 

 x_. - x , 

 3i 



We can now transform the coefficients of the b's of the normal set of equations 

 with information gained from serial correlations along the three principle axes. 



32 



