110 MCEWEN AND MICHAEL. 



words 2(yl' — A) (x — Xi) = 2(^1^ — AO (x — Xi). Introducing 

 these equivalents into equations (16) to (21) and (24) to (28), equa- 

 tions (29) to (40) are obtained 



A = A^ + -^ {nud + Mie/} - ^ {R^Pai + R,P,i + R^Pei] (29) 



B = B^ + -^ {n2d + 7i2ef} - ^ {R^P^ + R^Pt2 + ReP,2} (30) 



A 2 •A'2 



C = C^ + -^ {/;34f/ + 7^36/} - ^ {i?4P4, + RoP,^ + i^fiPes} (31) 



iV3 iVs 



D = D^ + -^ l/^4ia + m^c} - -i- {i?iil/i4 + i?.3f24 + i?3il/34} (32) 

 E = E' + ^ {;?5ia + 7^530} - -^ {Piil/i5 + ^2^/25 + ^31/35} (33) 



A B A' 5 



F = F^ + -^ {naa + ngsc} - -^ {RJU, + i?2il/26 + P3M36} (34) 

 A 6 As 



Ri = Rl H p (35) 



M 24^ + ^26/ - ^4^4 - R5K2, - RelUe 



u 



R, = i?i + --^24C. ^ --^26J - .U.V24 - ..5.V25 - .>5.V26 ^3^^ 



^2 



M34f/ + 3/36/ - ^4^4 - i?5A^35 " R,K,, 



LI 



■n _ T>i \ ^^34" -P -t>-t36J ~ Jt4-tV34 ~ -tt5J^-35 ~ -'l'6-tV36 /qy\ 



^3 



P4ia + P43C - P1/I14 - P2/V24 - P3A" 



P4 = R\ + ^"^ ' ^'^^ -^"^^^ ^""^^ ^^^^* (38) 



Psia + P53C — Pl/Vi5 — P2/V25 — P3/V35 /onN 



P5 = P5 H -' 7^ (39) 



_ „. PeiCt + P63C — R1K16 — R2K26 — PsA'se ,,„s 



Pe = Pe H 7^ (40) 



where P{, P,, P3, etc., are coefficients of regression of the dependent 

 on the independent variable for groups 1, 2, 3, etc., respectively, com- 

 puted from the original uncorrected values. The part added to this 

 coefficient in each case is the correction which must be added to the 



