238 
Consider the determinant consisting of the elements of the first 
five rows and columns. This can be conceived to be the result of 
the elimination of y; from the linear equations 
p ZjFip 4; 8 y= rde) 
where Hi; is the element of the 7 row and the j column. 
The new unknowns y; are connected with the original unknowns 
ce’; and c"; of the equations (27) by the relations: 
Ge Vi EU (HL A) 
¢," =Ys + SY + dy, 
c = Ye + 2 
Cn 
VE 
To each of the five roots 6*, corresponds a set y;, (2 — Î...5). 
Then y,, y,; and y, are determined by 
aj Fijyj B yi= 0. Gn Al Oe 
We now determine 2; from 
F'55 = Fos + 2; tj F'5;, 
G,j—=1...4) 
Fis + 2; 0; bij — wi F's5 = 9, 
and we put 
| ee I el Gi =a) 
and 
Yi = 2i + Bi Ys. (@= 1... 4) 
Then z and #? are determined by the equations 
(a) Zj F525 — B29, (Cs) eet) 
and y, is given by 
Zj Faj aj + (F's5 — 8’) ys = 0. (j= 1...4) 
This determines four roots 8. The fifth is given by 
p= Bin 
and the corresponding values of z; and y, are 
iti 1 ’ ie |S Ek 4) 
To solve the equations («) we take z,,= 1. Since the coefficients 
of the diagonal #';; are much larger than the others, we can take 
Then the quantities € and n;, are small, and we easily find a 
set of equations from which they can be conveniently determined. 
