Ci 
By eliminating A, Aj, K, and K, we derive from them the 
following equation: 
1 (ar, 9) 
Ce ee 60r, 
Bay pia 2r, 2 +2r, Tart, —3r,° 2. t,’t,(4t, —3r,) NS 
ie 60r, 720 DN NE 
*(2r, = bt.) 
Eg Eek eho /\ ea. 
( ‘a zin Gor, 1 
can (Bette tiant ain! nnn), 
er 60r, 720 ey) 
For shortness I replace the expressions which only depend on the 
intervals of time by single letters, putting 
i __ ty (2r, or) des _ Ts (2t,—9r,) 
Alas Nee Ser Ag 
a 60r, 601, 
ore ~2r,” oT —2r, st, +37," —2r,° —2r,* *7,—27,7,°+3t 
Bog pn Ce = berek Se B39 nn ia 
60r, 607, 
(Gi TT, (ár, —ôr,) bing = TT, (ár, = 3r,) 
Soe 720 i 720 
then the equation, solved with respect to ”,, yields for this relation 
the following expression : 
7, 14 Aso 21 + Bao 23 + C32 21 23 
— x OAN RE Jf 
a eee en z9 ie 4 00) 
The ees R, contains the quantities #,, 7;, #, and /,; 
these I set, in order to form the value of R, in the 5 order 
with respect to the intervals of time, 7, = K,t,°, /, = Kr 
Va 30K, rj andersO 59 then find: 
eh KON (ee a Tee AU Cae UN 
As the root of the 42 power equation 1— #— «? —2*+a*=0 
lies between zero and 1, viz. « =0,5806, ae terms of the 5‘ order 
will vanish from the residual, if rt, = 0.5806 r,. 
We obtain the corresponding approximation for 7, when we derive 
an expression from that for #, by interchanging everywhere the 
indices 1 and 3, hence 
wt, ,1+ Aiozs + Buoer + Cis 2s 21 
<= bed tock (VAL 
k T, s 1 + Aoi zs + Boi z2 4+ Cai 23 22 ey 
The meaning of the new letters agrees with the rules tor the 
interchange of the indices Ll and 3. 
