KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58. N:0 3. 15 



(18) ig>— ^y;> ~^ di irM =-[3Ä^) + 3r^ +2 ( J? )] 9 > ( li .) ) 



(19) 7 "r 6r ^j^ -«^+i(i?)9.ft?). 



(20) 7JJ- -6^;!' j =-6/^(07,(0 



V (21) IJJ-i^ ^ 6r-^^ + r*^^-[8^(,) + 6f-^ + ,(,) + 



(22) /<*> = 12/^j + 4r»^gi r <> I 12/ ■*,>,(,;) + 4»-»Ä i + 3 (», )l./. g (, ), 



(23) /y- l2' /y J;;' ) I l2r»^^ -[12Äffo) : ]2r^ + ,(,)] 7 „(,J. 



(24) ig = ttf ^^ 1 - 24rRs +1 (r))(p ( V ) t 



(25) /W = 24^^ -24Ä i (,;)f/> (, / ). 



These are the systems of formulae that will enable us presently to find our 

 equations for the regression of the characteristics. 



Systems I, II are required to obtain the curve of regression of the means of 

 the » ( -arrays. 



Systems I. Ill are required to obtain the curve of regression of the second 

 moments in the »,-arrays. From these curves we find the scedastic curves. 



Systems I, IV are required to obtain the curve of regression of the moments 

 of the third order in the ??-arrays. Hence we derive the clitic curves. 



System I, V are required to obtain the curve of regression of the moments of 

 the fourth order in the >;-arrays. Hence we derive the synagic curves. 



All these curves will be — mutatis mutandis - - the same for the regression 

 of the characteristics in the £-arrays. 



Finally, remem bering that 



x — m, . y — m. 



we find the curves of regression of the characteristics in the x- and ?/-arrays. 



(6) The order of magnitvde oj the different coefficients in the expression for the 

 correlation function. Before proceeding to the development of the regression for- 

 mulae it will be necessary to pay some attention to the order of magnitude of the 

 characteristics of higher order. When that has been done we shall find exactly where 

 the ^-series for the correlation function (and with it the regression formulae) are 



