( 468 ) 
This takes a simpler form if we eliminate all the powers of m 
except the first. The definition of mm gives 
m* — (36b,? — 3b,5, — 12b,b,) m + 18b,b3b, — 72b,bob 
1 8by — Big 
m 3(45,5, — bb) 
hence 
3b,7b,? — 12b,b,b,b, 
m 
— — bob, (6b, — m). 
With these values, and putting 
i, = b,bob, + ‚bob, — ba — b,b,? — b,°b, 
we obtain finally 
Aig rion, @ 4 4 
N= = m — = GH) = 5 HV BiA, = | (4/3i—9%,). (18) 
Introducing now the values of u, and u, in function of uw, in the 
numerator, we may reduce this to Au,’ + Bu, + C, where the 
coefficients are to be determined still. 
If we put u, == 0, C is immediately found 
1 0 oS De 
6b, 
—' l 25, . 6, 
m 
3 
tr den yl a 
mem 3 
3b, m 
0 — 0 — 
| m 3 
If we divide further the second and third columns by u, and substi- 
tute afterwards w=, the equation is reducible to 
(3b | 
— Le 0 ee B Aa DD 
m 
6 6b 6d 
eer SR fell (a Wa 
m m m m 3 
AE b, 6b > RNN 
Tes abe he Eee SS 
| m m 3 om m 
| 3b, m 3b, m 
| 0 Un (Sees ao == 
m 3 | | m 3 | 
Differentiating the numerator with respect to u, and putting u, = 0 
afterwards, we find the value of B. This value consists of two 
determinants; the first of these is identically zero, therefore 
