The coefficients of the regression equation, , b^, and b^, depend only on 



the serial correlation coefficients of the slash transects (all three orientations 

 at lag 1 and orientations 1 and 3 at lag 2). The coefficient b^ has an additional 

 dependency on X, the mean bulk depth. 



APPENDIX V: ERROR TERM 



The error term is derived by random access of the cumulative distribution of 

 the bulk depth (.fig. 10). Random access is achieved by entering on the y-axis of 

 the distribution with a random number from to 1 . The mean bulk depth is then 

 subtracted from the accessed bulk depth to obtain the first estimate of the error, 

 e'. The error is further modified by taking into consideration the relation of 

 the variance of the estimate of y, y, given x, to the variance of y (Kendall and 

 Stuart 1967) : 



2 2 2 



s.| = (1 - R )s ^ 

 y|x ^ y - 



where R = multiple correlation coefficient. 



We can write the following expression for the error by recognizing the simi- 

 larity of the variance to the square of the error: 



e = \1 - R^ e'. 



10 



20 



(cm) 

 30 



40 



I ' r 



1 



50 



-I r 



1.0 r 



0.8 



i 0-6 



O- 



< 0.4 



0.2 











20 



60 



-I 1 



-I 150 



120 



90 



60 



>- 

 o 



> 

 1— 



r3 



- 30 



L_ 



24 



4 8 12 16 



BULK DEPTH (in) 



Figure 20. — Cumulative probability distribution of the bulk depth. 



34 



U.S. GOVERNMENT PRINTING OFFICE:! 9 7 9-0-67 7-01 9/3 7 



