120 MCEWEN AND MICHAEL. 



Substituting the final values, 

 AA = ^ {2d + 5/) = 0.245, AB = '^ {2d + 3/) = 0.263, etc., carried 

 to two decimals, in equations (50) to (55) gives the corrected averages 



A = 12.38 + 0.245 = 12.62 (76) 



B = 12.47 + 0.263 = 12.73 (77) 



C = 8.93 + 0.716 = 9.65 (78) 



D = 9.69 + 1.738 = 11.43 (79) 



E = 11.68 + 1.053 = 12.73 (80) 



F = 12.41 + 0.404 = 12.81 (81) 



and these substituted in equations (56) to (59) give 0.11 for a, 3.08 

 for c, 1.30 for d, and — 0.08 for f, which agree to the nearest hundredth 

 with the final values of these differences entered in table 6. An addi- 

 tional check upon the computations is B = E, which should be the 

 case since each of these two averages correspond to the standard 

 values of temperature and precipitation. 



As stated on page 99, the functional relations found by this method 

 are defined by the series of corresponding averages of dependent and 

 independent variables. Many ways of utilizing these relations will 

 occur to the reaider. The most precise and, perhaps, the most desir- 

 able way would be to plot the averages of w corresponding to Xi, 

 Xo, and X3 and those corresponding to y^, y^, and ye, and so determine 

 the type of equation relating w to x and w to y; and then, by the 

 method of least squares or method of moments, compute the constants 

 from the original data. A more expedient way is to use the relations 

 between the averages directly, and correct for the neglected varia- 

 bility within the group. For this purpose the functional relations 

 may be conveniently expressed as 



w = /i(x) + Uy) = 12.73 -f Fi(x) + F,{y) (82) 



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

 and where Fi (x) and jF2(y) are defined by the series in table 7. 



