Miscellanea 
213 
where the Rs, are minors of 
As before the mean value of comes from the multiple regression equation 
1, r, r, ?• . 
r, 1, r, r 
r, r, 1, r 
r, r, r, 1 
Substituting we get 
S{24.S'(A-i.y2.y3^4)} ^ (w - 2)(w - 3) r S {na,a;,.r3 • ■yl^^^2^3 (■V1+X2 + X3)} 
iVn* -n? ■ l + 2r ^ 2V 
_ (?i-l)(ft- 2)(M-3) r 32 { nx,x.^x^.Xi^XiX^) 
" W ^ " ■ H-2 r" " ^ # 
A 1- /X 3(w-1)(7i-2)(m-3) 9-2 , 
Substituting (ii) ... (vi) in (i) we get 
1/, = + 4 (« - 1 ) + 3 (« - 1 ) [/■V4 + (1 - '•^) /i2'} 
+ 6 - 1) ( « - 2) . r . {r^^ + ( 1 - r) /x./j + 3 - 1 ) (« - 2) (« - 3) . {r^u^ + ( 1 - r) , 
which reduces to the result given above, viz. 
^4 = (T^y - [{1 + (3« - 1 ) r + 3« (•« - 1 ) r^} + 3 (,i - 1 ) (1 - r) ( 1 +«r) 
Using these equations it is possible to find values of /• which would satisfy the conditions for 
the various constants. 
Thus (using Sheppard's corrections for both sets of constants) I find that with the given values 
of and i/2 r=-003, 
of /3i and r=-063, 
of ^2 and B-i r=-033. 
Now clearly if r were fitted by least squares or in any other way from these three values it 
must clearly come closest to the jx-, value owing to the lower prob. error of • As to fit it properly 
is clearly very comjilicated owing to the intercorrelations of the constants I have assumed a 
value r=-01 as a nice round number which gives a value of i/2 higher than that found in the 
sample before us but not at all impossibly so. 
This gives #2= -1101, actual -1074, 
5i= -1397, „ -4756, 
i?3 = 3-2012, „ 3-3185. 
These constants give a type I. curve 
/ ^ \ 24-04 / ^ \ 714-2 
^ = ^"•"0+14) (1-47V2) • 
If we assume no correlation I get a curve 
/ \41-7 / \ 1200-8 
3/=109-0(n-— ) (1-^-^) , 
whence I get the following ' fits 
' The figures given are really mid-ordinates, but for such small numbers the difference between the 
mid-ordinate and the area on the base unit is negligible. 
