The normal equations are: 
WOK + Q) K, — w, 
(2) K, + (3) K, = ws 
where: 
gui! EN gun! + gu ust 
(1)= + usu,’ = £g"? u»l uj! ^p gus! us 
+ usu,’ = gay! d 2°3us'us! 
+. 
1a 
guit! ^ gustus! + gonna! + 
(2) - — g?!uz?ui! - g??uz?u3! Ar guet ug! A 
Tg us c g?usa*u»! + 2°3us"u3! 
ga a te a en WS US + 
(3) = 4 gu? A gu u” —- gus us? + 
+ ge? + 252 us us” c gus? us? 
in which: 
gi, g°2, 293 are weight numbers; 
g'?, g° etc. are correlation numbers; 
Ki, K2 are correlates. 
The correlate equations are: 
el L (gu! a gu n gust) Ki B (gui? d g"? uy 4 gus?) K 
e? zm (gu! c g^?» c gus.) Ki 4 (gu? b g?u? 4 g?us?) Ko 
es — (2541! 4 gy + gua.) Ki + (giu? E ggg? c g?us?) K 
2 
Appendix V. Lists of the quantities B, C and F. 
The following lists give for some quantities B and C respectively two expres- 
sions; the first one is the direct result of the derivations, whereas the second 
expression is to be used for the actual computation. 
B = Q zz dr Q' Zi Zi 
B 2 7 Q' x La ia + Q xix: 
B, = p* (2 A, + B,) +4 (4 + 1) (A7 — As) = Ba + 2 Ban 
B, — —2pA, - 2(qg 4-1) (4, — A) 3- B, = B, — 2 B4, + Bao 
B, — p (24,24; t Bi) = 2Bı +8 
B, =p A, — 2 (@ + 1) (A: — A) = By, — B, 
B; o pA, + q (4; — As) = Bu + Bi 
B, = pA.— gq (4 — As) = B, — B, 
By = PA. (A Ar) 7 — By X Die 
Bu — pA AH B) + (A; — A) = Bis + Bis + By 
Bi, — pA, 
Bi, — pA; 
Bir p(A + A) = B., + B,, 
Ba > PP 12 A, + 81) + 24 + 3) (y=) Bec Bio ct Bag 
Bu= p* (2 A; + As + Bi) + 2 (@ + 1) (A; — As) = Ba Bo + Bin 
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