RELATION OF VARIABLES. 



125 



and Rs, and Ry any one of Ri, R5, and Re; and, where Fi{x) and ^2(7) 

 are defined in table 8. 



TABLE 8. 

 Definition of functional relations. 



The value of w corresponding to x = 73.4 and y = 3.6, may be 

 computed, as in the case just considered, by correcting first for the 

 group, which, from equation (115) and table 8 is 



w' = 12.18 - 3.37 + 0.15 = 8.96 (116) 



which corresponds to x = X3 = 69.27 and y = y^ = 4.32. Intro- 

 ducing the regression coefficients to correct for the position within 

 the group; i?3(73.4 — X3) and Ra (3.6 — y^ must be added; whence 



(117) 



w 



= 8.96 - 5.00 - 0.01 = 3.95 



which agrees still better^ with the observed value of 4.0 than that 

 given by equation (83). 



Solution by the slope method is effected, after introducing the cor- 

 rections indicated by equations (88) and (89), by replacing equations 

 (35) to (40) with equations (41) to (48) and substituting Si, S-i, S3, S4, 

 S5, and Se for Ri, R», R3, Ri, Rb, and Re, in equations (29) to (34). 



A = 12.38 + -(2d+ 5/) - I {2m(0.597d + 0.246/) 

 9 9 



+ 0.8(0.179(i - 0.246/) - OA{-0.179d - 0.664/)} (118) 



1 . . . This agreement between computed and observed values is, of 

 course, accidentally close. Considering the observed series as a whole, the 

 greatest deviation between computed and observed values is 7.5 by Blair's 

 method, 6.3 by the first method of successive approximation, and 5.3 by the 

 second method; while the "probable error" of a single computed value in 

 each case lies between 1 and 2 (see page 132). 



