KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58. NIO 3- 27 



and further 



co oo oo 



) I n F 2 {ij)dr t = f ff<F(£. r))d§drj = 0; 



— Xi — OO — OO 



(36*) 



00 00 00 



• » n 



00 — oo 00 



Multiplying (34*) by F 2 (t^)dt l and }]F 2 (rfjd^ respectively and integrating we find 



I. O = r 03 — r 03 + terms of order neglected, 



r = r — 3r 01 + 3r 04 + terms of order neglected; 



II. O = fo3 — r 3 + terms of order neglected, 



r = r— 3r 04 + 12^ 03 > 03 + 6,? 03 r 03 + 3r 04 — 18^ 03 ' u;t + terms of order neglected. 



(8) The curves of scedasticity or regression of the characteristics of the second order. 

 The moments of the second order of the i-':s in an ?/-array are given by 



oo oo 



The moment about the mean f, ; of the array will then be 



''2(5)1/ = v 2(5)»/ Sv 

 We clearly have 



J(2 + ■> /(2) , a J{2) 1 j jm + a /(2) + 1 7(2) 1 a/ 7(2) i 



(37) •,(£), 



This gives for our two cases according to systems I, III p. 14 



(37*) T •,(£)„ = [1 + r i B 2 (rj)+p Q3 (R 3 (r ] ) + r*B 5 ( v )) + fi^B^) + r^R^)) + 2p t3 rB M ( v ) + 

 + 2p u rB t ( V ) + 2/»„Ä l (i ? ) + 2p 22 B 2 (rj)] : [1 + Ä„£.(i?) + ,^^(',11; 



(37*) II »/,(£)„ = [1 + 1*8,(1?) + /U&fa) + r-R-AO) + /W*«0?) + r*B 6 ( V )) + 2/?„ rÄ,(, ; ) + 



+ 2p lz rB i ( V ) + 2& 1 iJ 1 (i?) + 2/?,,Ä 2 (i?) + ^* 8 (Ä 6 (i?) + r 8 Ä 8 (i?)) + 2p 03 p i2 rB a ( v ) + 



+ 2(A,Ä, + l /tÄ,)^(i?)]:[l + /»„Ä,(i?)+A 4 B < (i ? ) + |ä.B.(i7)]. 



