( 366 ) 
and taking their sum; in the resulting equation all unknown quan- 
tities g,..-Gm except gi are eliminated. That equation got by sum- 
mation is: 
1 
— Ip (m—t+]) + (m+ l)gi — 19g + 5 i (m—i+1)(m+1) ky = 0 
which yields: 
m—itl i: i i(m—i+l1) ï 
tewel he ene amer 
md as oen Te Md 2 je 
m re : 
lence qd, = = 1 menses ee mk 
ras MA Eilon EL Geeren ij 
1 4 m 7 
anc On ep = 09. = SU 
: ml ep EED 
The quantities g, and g, are still unknown and depend on the 
quantities @Q of the neighbouring intervals; they may be derived 
from them by means of successive approximation. 
1 1 
It gives some advantage to determine ->-(g,--g,) and 5 (Ym +99) 
2 2 
by approximations, because then we shall have to approximate 
only one quantity for each S. The approximation may be made 
— 
1 
in the following way: we put >(g)+9,)=c¢p and >(m+tyg=Co 
then we obtain: 
6 
ki m* +2 (cy ae Ora 2 Qn) 
om dt fa 2m? +1 a rn 
INA ay wl c armenie EN 4 
He A ea m(m?-+2)) * m(m? + 2) Me 
3m m?—1 2m? +1 
= — —__ Q, EN a 1 + ——— ] ¢,. 
Ja m?+-2 Qn + m(m? +2) Te ( 45 er) 4 
For the next interval of 7 units of time between the determinations 
S, and S, we have the following equation : 
2n? +1 n?—1 
nett (te) te 
i n° 4-2 
As gy +4m=2¢, we obtain when finding the summation of the 
two last equations a recurrent equation containing 3 consecutive 
quantities c, so that c‚ can be expressed in c, and c,. This equation 
can also be written thus: 
