â6 c. V. L. Charlier. 



^0 = \>'0^ 



c = b — v^, 



and it is 



|4 5, = p.o (v^ _ 3v| - 6V3 + 5v,), 



where it is supposed that 



lic^ xyF{c-\- x) = lx'F{x) = \).:. 



3:o. We determine X, w and c in such a manner that B^ = B^ = B^=: 0. 

 Multiplying (13) by 1, x, x} and a;^ we then obtain the equations 



X= — 00 



(18) lxF{x(ü~\-c) =Bf,lx<!^{x) =Bq\ 



S x'F(x(ü + c) = B^ I x^ {x) = (X2 4- X), 



X ic»F(;r(o + c) = 5, ^ x^']; (ir) = (^^' + + X). 



These equations may be regarded as exact ones. For solving them in respect 

 to Bq, (0, b, X we must have recourse to approximations. Defining the moments 

 [J./ of the frequency curve about a provisional origin by the equation (12*), we 

 suppose that 



+ 00 



(19) \l; = I.{xM ^ cyioF{xM -\- c) 



X= CO 



and hence — using this value of [i.J — we have 

 0) S F{xui -f c) = [J-o', 



co^ S xF{xM -f c) = Ü) I {mx c — c) F{x(ü -f c) 



= [J-i' — ciJ-o', 

 (1)^ s x^F(x(ü + c) = « S {(tàx -\- c — cyF{x(ü -\- c) 



= — 2c[i.i' 4- c'jXo', 

 to* X x^F{xiü -]- c) = — Scjig' -f 3c^[x^' — c^[j.q'. 



The above equations (16) then assume the form 



iV-2c^.; + c^tV = ''>«i?,(x^ + x), 



J,; - 3qj.; + 3c^ix/ - - co*5o(X« + 3X^ + X). 



or, putting 



