W. R Macdonell 
201 
Also a = c —f, therefore o-^a = cr-,. + cr^/ — 2<Tc(Xfrcf, 
and substituting we find cr^ = 1'5297, 
and Mean^ = Mean^ — Mean/ = 33'5158. 
Left Foot and Left Cubit. Table XXXIV., p. 227. 
A = - ■10295, ^• = - -06773, 6 = -923660, 
■923660 = 6 + -003486^^ - -002523^-' + -001439^^ - -0009986^' ; 
whence 6 = -9222992 ; r = -79699. 
Height and Left Cubit. Table XXXV., p. 227. 
/i = -01337, A; = --06773, e- -925690, 
-925690 = 0- -000453^'^ - -000794^^ - -000188^^ - -0003I76''' ; 
whence 6 = 9270676 ; r = -7999. 
Here we have adopted the median division. If we work with the skew 
division. Table XXXV.«, p. 227, we have : 
/i = - -38173, A; = --06773, e = -910952, 
•910952 = 9 + -012927^- - -024939^^ + -004901^^ - -009349^' ; 
whence 6 = -9222068 ; r = -7969 ; 
but it will be observed that in the second equation for d the terms converge much 
more slowly than in the first ; we will therefore retain the first value, especially as 
the difference between the two is only -00292. 
Height and Left Foot. Table XXXVI., p. 227. 
= _ -013366, A; = --102952, e = -82577, 
•825770 = 6- -000688^= - -001796^^' - -000285^^ - -0007153^'^; 
whence ^ = ^8276709; r = -7364. 
Here again we have adopted the median division. 
Adopting the skew division. Table XXXVI.", p. 227, we have : 
A = - -38173, A; = --10295, e = -881436, 
•881436 = 6 + -01965^^ - -025795^' + -007422^^ - -009565^^ ; 
whence ^ = ^8845487; r = ^7736. 
It will be noticed that when r is large, the terms involving the higher powers 
of 6 do not always converge as rapidly as we should like in the equations for 6; 
the values of d are therefore not to be relied on beyond the 4th figure or so. To 
go up to the 6th power of 6 would considerably increase the labour of solving the 
equations ; we have therefore not gone beyond the 5th power, the term involving 
which is : 
6^ 
+ [h*t + {k' + k') {3 {li' + k') - Qh'k^ - 8) + 20h'k-] ^ — . 
Biometrika i 18 
