( 534 ) 
general course by which at the same time the application in special 
cases is rendered possible. 
The equations (4) can be written as follows: 
kp = A, + B, A + ka, 
kg =A, + B, À ky, 
kr = A, + Ba + ka 
Let us multiply each of the equations (2) by # and replace the 
values kp, kg, kr; we then obtain: 
(411 zie db) (A, af B, d dr ka) si (41, ae Ab.) (A, IE Bà al ky) TE \ 
(4,,; + 40,;) (Ast B,A + kz) + ka, =F kb, A0; 
or: 
(A, + BAe + (a, + O11 (A, + B, 4) + (Gas + 4,24) (A, + BH 
(a,, + 6,,4)(A, + B, 4)= 0. 
We likewise find: ‚© 
(A, + B, ak + (1g Hbo DA, HBD) + (yy + Baad) (A, + Baa) + 
(a, a= bys A) (A, tr B, 4) = 0, 
and finally : 
(A, slp B, Ak + (ds ar bis a) (A, == Ab) + (4,5 aa bd (A, ain B,A) ae 
(ass br ANA, + B,a)=09.- / 
If we reduce these equations and if we regard / and 2 as variables, 
we shall get as result three quadratic equations, out of which % and 4 can 
be eliminated. As however these equations are linear in 4, the elimi- 
nation of / can take place without any difficulty. By putting the 
values of / in the first and second equations equal to those in the 
third and the fourth we deduce from (5): 
(ae bs) (Ay BB, a)\(ALS- BY) -f (a-0,, 4 (4, Beas 
(a;,+5,, 2) (A, LB, 2) (A, 4B, D=(,,42,,4) (4, +B, Pe 
(@,--1-b,, 2) (4, 4B, 2) (4, 4B) a) (atb 2) (4, 4B, NEEN) 
and (6) 
(an BED (AEB INA EBD Ela DD (A.B, (A, BREE 
(asbl) (A, HB (ars Hb (A HBD (A HBD 
(aasb NA BE (apd, Ay BI) (A. 4+ B.A). 
When reduced these equations prove to be of order three in 2; we 
? 
can write them in an abridged form: 
