28 
PEOFESSOR K. PEARSON ON THE INFLUENCE OF NATURAL 
^23 = Pi; let Pi' Ije tlie true value of r^o, corresponding to the values /Xj + S/Xj, 7’^, "h 
7 ’j 3 + Sr^g, ?’o 3 + S^’no. Thus we have, as far as first differences : 
Pd = Pi -P 10 (A^Pl) Spi + 4 {(A,-j„Pl) 87’g2 + (A;.^Pl) S7 ’i3 + (A;.^E) S7’23]. 
In our case /Xj = 3 %, 7 ’i 3 = ‘5, 7-53 = '5, 7 23 =: ‘75, = '05, S 7’33 = S 7’;^3 = ' 1 , 
S^’og = '05. Further, we look uj) Table IV. (a), and the nearest case is (j) under P 25 
which gives P = ’67105, We then see that (A,.j^Pi) + (A^-^^Pi) = difference between 
(j) and (/w) cases = — '21455 ; (A,.^R) = difference between result in IV. (a) and 
Ah (a) = '32895 ; and lastly (A^^R) = difference between Eg and E 2 columns of (j) 
row of Table lAh (a) = '00535, Thus we find : 
E' = '671050 + '002675 - '04291 + '06578 = '6966. 
The value by straightforward calculation of formula (Ivi.) is *6981, the two results 
giving substantially the same value '7. Thus we see that such a selection would 
reduce the correlation of tibia and femur by 12'5 per cent. 
Illustration {1I-). —Suppose the correlation of humerus and femur to he '5, and of 
those with stature to '7 and '8 respectively. How would the correlation of humerus 
and femur he modified by a selection of stature given by Si/cti = '5 ? 
In this case, /lX] = ‘5, 7*13 = *5, 7’]3 = '75, 7*23 = '5, S/Xj = 0, 87*^2 = * 2 , 87*33 — 
87-23 = 0 . AVe turn to Table III. (a) and take out {h) under Eg, which gives us 
Pi = '3192. We have A;.j^R = — '1841 and A;.j^R = — '04185, whence we find 
IT = *1636, but the differences of the table are too great at this point for the 
result to be very trustworthy."^' Suppose we take /x^ and 7*33 as before, but 7*32 = '75, 
7-|3 = '75, and therefore R, to he found from {m), — '1351 ; then 87*33 = — 
S 7'33 = *05 and A^^^E = — *1841 as before, A^-^^R = — *2995. Hence we deduce 
Pi'= * 1120 . The mean of these two values of E' is '1377, and the true value 
calculated from (Ivi.) is E' = '1395. Taking '14 for the practical value, we see that 
tlie correlation of humerus and femur has been reduced by this comparatively 
moderate selection of stature upwards of 70 per cent.! 
Illustration {HI). —Suppose a case in which humerus and femur were not correlated, 
l)ut that lioth were correlated '7 with stature. What would be the effect of 
selecting stature with the same intensity, i.e., sJcti — '51 
Our best results from the tables will he to take Eg {m) from Table I. («■), which 
gives E = — '7297. We have then 7*33 = 7*33 = '75, hence 87 *^ 3 = — '05, 87 * 53 = ~ T5. 
A,.j,Pi is to he found from {m) and {h) and = — '3193 = A, 3 ^R, and 
E' = - '7297 + (A .3 E) 87*52 + (A^g^E) 87 * 53 , 
= - '7297 + -1277 == - ' 6 . 020 . 
The actual value by formula is — '5810. 
* Second differences onglit to be used, and the process indicated is practically equivalent to using 
them, 
