124 MCEWEN AND MICHAEL. 



^o:.^. , -0.7244(i+1.8134f-0.1723i?4-2.0639E5+3.3689E6 



10.5400 



(102) 



These equations are solved by successive approximation exactly as 

 indicated in table 4. The final values so obtained are 



A = 12.38 - 0.31 = 12.07 (103) 



B = 12.47 - 0.29 = 12.18 (104) 



C = 8.93 - 0.12 = 8.81 (105) 



D = 9.69 + 2.64 = 12.33 (106) 



E = 11.68 + 0.50 = 12.18 (107) 



F = 12.41 + 0.34 = 12.75 (108) 



Ri = 0.28 + 0.03 = 0.31 (109) 



R,= -0.83 + 0..36 = -0.47. (110) 



^3= -1.21 + 0.00 =-1.21 (111) 



Ri = 2.10 - 2.09 = 0.01 (112) 



i?5= 0.17 - 1.00 =-0.83 (113) 



Re = 1.02 - 0.33 = 0.69 (114) 



Utilizing these values in the most expedient way, the functional 

 relations are conveniently expressed as 



w = /i(x) +/2(2/) = 12.18 + F,{x) + F,(y) + R,{x - x) + Ry{y-y) 



(11.5) 



where x and y signify any one of the three group averages of x and y; 

 where Rx represents any one of the three regression coefficients jRi, R2, 



