210 Expectation of Moments of Frequency Distributions 
Substituting in (43) we find, after suitable transformations : 
, . 1 . 3 . 5 ... (2{— 1) 
E {vr - v^Y = — '-^i [^2r-/^/ + ^""/^>-i/^2-2r/x,,+i;w^_i]' + ... (47). 
Noting that ^-^^ ~p tends with increasing iV'to the limit 1.3.5 ... (2i — 1), 
and the ratio ^ ; tends with increasing iV to the limit zero, we see 
that the law of distribution of the values of F/ tends with increasing A'' to the 
Gauss-Laplace law. 
Comparing (47) with (14) of Chapter II, we see that -prr^^ tends with 
increasing N to the limit 1. 
In the case in which the law of distribution of the values of the vai'iable X 
follows the Gauss-Laplace law and /Xo^+i = 0, for r = 0, 1, 2, 3, ... oo , — --^4^- 
tends with increasing N to the limit 1, for every positive integer r. But 
. . tends even for a Gaussian distributi(jn of the values of X to 
E {fJ- 2r+l ~ /^2r+i)"' 
the limit different from unity : 
1.3.5 ... (2r+l) 
1 - 
(2r-f 3)(27- + 5)...(4r + l) 
Corrigenda to Part I, Biometrika, xii, pp. 140 — 169. 
p. 142, Eqn (2) for ai-jNl-^'^ read a^^iJVl-'l 
p. 142, Eqn (4) for A^O* read A'O*'. 
p. 147, 1. 19 for ^j.+i read g^_y. 
p. 151, last line Eqn (11) /or (a^) read w^jy)- 
p. 156, Eqn (27) for read' fir-i- 
IN IN 
p. 157,1. 6 for -r^ 2 {Xi-nii) read ^ 2 (A'j)-mi. 
p. 157, footnote, for Proc. Imp. Acad, read Mem. Acad, and under ChebyshefF refer to t. ii, 
p. 478, especially of Knssian edition of his works, 
p. 160, 1. 8/0?- v^!^l^.^ read vlll^y 
p. 160, last Eqn of (11) for Z)™"^, read D^'"'X-r 
p. 162, throughout this section of authoi-^s MS. has been printed X. 
p. 163, last line of Eqn (15) insert m^~'^^ after ''^"^ ~ ^ - , and in 6th line of Eqn (15) for ml''^'^ 
after '"^^ read mV'''^^. 
bO 
p. 167, 8th line from bottom of page/o?- E^-u) read E(2i) dfx. 
p. 167, 2nd line from bottom of page /or K,^''A'''f-r -'r-'t-ii-j) read /r'^^'^^'J^' ''^'-'(-•A-i'. 
p. 168i 2nd line from bottom of page for A'/'-'i ' read agaiii A'^''^ 
