K. Pearson and A. W. Young 
89 
cx,3,,=''^-'{ioop'G,2-p\ir (-^i)- 
, = ?8, 2 - 5^4, 1 + 1 622, 0 q\ 1 + go, 2 g'a, 0 
+ Sgi.i^s.iga.o - 8g5,i!?3,i - 2^4, 2 '74,0 
= a,«cr,/ {lOOOyj'g, 2 + 1 6p%, 1 + 9 + 24r7>'3, ^ - SOp',, ^ v'z, 1 " GO;/,, J, 
= ^llOOOp's,^ + 16?/\i + 9 + 24r?/3,i - m^'^.iV'z,i - 002/4,2}^ 
(xii). 
We require accordingly to determine the following j/s: 2/2,2^ l^'3,i» 'P'i,2^ 
p's, 2 and j/g, 2 by aid of our table with second differences or direct calculation from 
the algebraic values in terms of r. We have 
p'2 2 = 1-173,0226, 2/3,1 = -782,3840, 2/4,2 = -403,8135. 
p'5,i= -441,1920, 2^'6, 2 = -227,8602, 25'8,2 = -177,6695. 
Also •6744898/ViV = -014,1505. 
Substituting we find the following probable errors : 
P.E. of r = -012,926, 
P.E. ofg2,i= -720,631, 
P.E. of ^3,1 = 6-625,903, 
P.E. of ^4,1 = 51-267,688 
We can now sum up our results for these data: 
r = -2941 ± -0129, 
g^,! = 0 ± -7206, 
= 87-7600 ± 6-6259, 
= 0± 51-2677. 
The probable errors would have been to some extent modified had we been able 
to calculate them on the true and not the observed r. We have 
A92,i/P-E. of = - 2-716, 
A93,i/P-E. of 93,1 = - 2-009, 
Ar/4,j/P.E. of (74,1 = - 2-120. 
Thus none of the deviations are excessive in terms of their probable errors. 
The system accordingly does not diverge very widely from the normal. At the 
same time the deviations are all in one sense, i.e. in defect of the normal value, and 
are all greater than twice the probable error. It appears therefore probable that 
there is some significant if slight deviation from normal correlation in the growth 
of the auricular height. 
Illustration II. For the correlation of the contemporaneous barometric heights 
at Laudale and Southampton the following values have been found : 
Southampton (x) = 3-250,067) r = -780,225, 
Laudale (y) ay = 3-932,290j iV = 2922. 
