( 472 ) 
Developing this determinant, and putting 
m* 4b,b,+2b,b, ,  4b,b,°+4b,°b, 
ann. ae ss a ae “tm + b,b,(6,6,—46,),) =P 
we have 
oy.) o =. "ome 2b,m m 
Axau(=)P| 52, Dit OT 1D}. 
If we introduce now the values of the quantities D in the last 
factor, this leads in the four different cases to 
2b 
x = m? + 4byb,m + 2b,(b,b,—40,),) 
2b 
— a m? —- A4bybym En 2b,(b,b,—46,5,) 
25 
as 5 m’ =o 4b, bom <7 2b,(6,b,—45,),) 
26 
— =z! m* + beg + 2B4(046,—48,5,)- 
If we observe that we have by definition 
m*?—6bym 
bb. —4bb, — tae ca 
it is evident that in all cases A = 0. 
The conditions are therefore determined by 5 = 0, and this may 
be written, after a slight reduction 
foie 0 - 0 >. OC eae 
3 
m 
a De ee ee ee 
3 
m 
a, be 2b, 3 0 b, 0 0 
a, 0 b, OW = WB 0 
=— 0 
a, 0 0. sbr 5 2b, b, 
m 
a, 0 VW wee 
3 
>a 
a, 0 0 0 DEES 
| m m m m 
D, z Pe Peak go ale D, D, D, | 
