98 The Correlation Ooeficieut of a Polyclioric Table 
the argument ^* ^^^^ . It will be convenient to refer to this tabled integral as ®, 
V 1 — 
so that 
Wl — r'^ 
It is convenient to note that with this notation 
(IB (- a:) = 1 - ® ("^O- 
N f^^ 
Further since vk. = -y?^ / e~i^^ dx. 
and dh, = f.!"^' . 
Hence ^ cZ/i, = NA.tH,. = ^^tf^^^-s (15). 
df 
Similarly ~ dl't = B^tdm .f (16), 
Lastly ar afl I z (x, ij, r) dxdy 
-CO . — -y 
d 
^ z (x, r) dxdy 
00 . —00 
= iV2(^„ A:,, r) 
= X.. ■ (18), 
which is the length of the ordinate at the point (s, t.). We may now write 
dm,t = A,tdni,. + B.tdui.t + Xstdr (19), 
and - Xstdr = A.tdm,. + B.fdm.t - dm,t (20). 
Considerable use will be made of this formula later and the following abbreviated 
notation will be used: 
Astdm,. + B.tdm.f - dm,t = SP^t = - Xst^^' (21). 
and A,tm,. + B.tVi.t - vi,t = Pst (22). 
The reader must be careful to note that SP^t is not dPst but only a part of it, 
and this symbol is used here as at once a conventional abbreviation and a memoria 
tecJinica. 
Since W.22 = '"^c ~ "ha ~ "^21 + "hi > 
— A.^xdm^. — B^^dm.^ — x^dr + A-^^dm^. + B-^^-^^dm.^ + Xn^^^' (23), 
