104 MCEWEN AND MICHAEL. 



{w, 2/4), and {w, zs) groups, which, for convenience, will be referred 

 to as groups 1, 4, and 8. The correction E — D = c^ (see equations 5) 

 must be added to reduce this particular value of w to that correspond- 

 ing to the standard value ys of y, but no correction need be applied for 

 2, since it is in group 8 which was selected as the standard. If each 

 value of w in group 1 be corrected in this way, the mean of the cor- 

 rected values is, by definition, equal to the required value A. A 

 similar procedure with respect to all the other groups gives the remain- 

 ing required values B, C, D, E, F, G, H, and I. Evidently, this is 

 equivalent to adding to the average of the observed values A^ the 

 average of all the corrections. That is 



2.4* 1 

 A = —^ + -— (?h4 d + ihef-'r nn g + ?(i9 i) 



A' 1 A 1 



= A'' + ~ (71U d + nuf + "17 g + ?h9 i) 



A'l 



where 



(7) 



nu = number of observations common to groups 1 and 4 

 W16 = " " " " " " 1 and 6 



wi7 = " " " " " " 1 and 7 



??i9 = " " " " " " 1 and 9 



In the same manner equations (8) to (15) are obtained. 



B = B' + — (mid + rhef + 7i2ig + 71091) (8) 



A2 



C = C' + — {72zid + "36/ + nsig + ns^i) (9) 



A3 



D = D' + — (w4ia + "43C + Tiiig + 7149?') (10) 



A4 



E = E^ H- — (Wsia + W53C + 7l57g + "59^) (11) 



A 5 



F = F' + — (Tieia + wesc + neTfif + "egt) (12) 



Ae 



G = G^ + — (7ina + nnc + 7iud + ?i76/) (13) 



A 7 



H = H'' + — (nsia + 7?83C + 7isid + nge/) • (14) 



As 



