KiRSTiNE Smith 
9 
W2J)-2 
711. 
2p 
.. m 
m 
2P+2 
2p~2 
m 
2P 
m 
ip-2 
771, 
7)1, 
7)1 
223+2 
.(15). 
W2j,_2 
771 
7)1 
2v 
7)1 
2P+2 
m. 
ip 
(7) Before leaving the general case and treating special distributions of 
observations three auxiliary propositions shall be proved. We shall first pro ve thai 
the curve of ^0',, can never he entirely heloiv 
7)1 r 
With that purpose „o-f, will 
be summed over all the places of observation with the weight „ 7-- , i.e. for a 
/(«) 
ih (x) 
continuous distribution of observations, the expression j"^ n^^'udx, where xjj [x) is 
the number of observations, will be integrated over the range of observations. 
Looking first at the numerator of the last term of (11) we find that it can be 
expanded into 
(- l)«+i 
1 
mo 
mj , . , 
... m„_i 
X 
mj 
7)1.2 ■■■ 
... m„ 
x'^ 
... 
... 
a;" 
••• 
^1, n+2, 2, 1 + 
X 
mo 
... 
X"' 
... 7)1 „ 
X^ 
7)%^ 
m 
n+l 
mo 
?»i ... 
... m„_i 
/^n+1 
... m„ 
^ "^1, n+2, 3, 1 + ~^ 
ma 
m^ ... 
... 7n„^i 
X 
3,2,1 
m„ 
m„+i ... 
... m2„_i 
'^1, K+2, n+2, 1 
/"lA fjC) iC*^ 
Now - dx integrated over all the observations is what we have called 
/(^. 
iV . m^ . When integrating the determinants we therefore find that the first 71 of 
them will vanish, two of their columns consisting of proportional elements, whereas 
the integral of the last determinant is 
N 
m„ 
mo 
m^ . , 
... m„_i 
™n+l 
m^ 
... m„ 
^'^n+2 
mg 
ma ... 
... m„+i 
'^2m 
w„ 
m„+i ... 
l)"iVA,,,, 
