626 
pose with comparatively little trouble. It is possible to develop the 
functions for one region into a series of normal functions of the 
other region. The following development is then obtained: 
r E,(h oo 
= di, 
(sil 
rE 
(25) 
The constants «a, form a twofold infinite system of values that 
a 
r 
do not depend on the variables —, but on the constants y, and y, 
a 
defined by (43) and (21). As we saw before, they depend on the 
dimensions of the tube used, and on the conductivity of the sub- 
stances that play a part in the problem. 
For the determination of «7 both members of (25) are multiplied 
oe. tb) 
by rd, SS 
| dr, and an integration is carried out with respect 
to r from zero to a. When for this purpose use is made of the 
known properties of the Busser functions, and of the equations (14) 
and (20), the following form is found: 
26, 8. (rr) Js 181 
ee : 26 
KT Gey? GON + ys? 6,0), (8,9) Ee 
By substitution of (25) in (23), we get: 
A,(*) = 2 au AGU) TR SL EEN (27) 
il 
If this relation between the coefficients A,% and A, is satisfied, 
(23) holds for all values of 7. 
Also in (24) all the occurring functions of r must be developed 
rie aa Opee . 
with respect to dn — (25) gives this develop- 
ment: we write for the second member of (24): 
= (k) 
ro 
Qe, v, = = BJ, | = 
k=1 a 
Fors 
e 
U 
(28) 
The coefficients 8, are found by multiplication of both members 
ea : 
by rd, = dr, and integration with respect to r from zero 
to a. Then follows from (20) and the properties of the Besser functions: 
2Q 0, v 
Bk Q N 1 1 Ys 5 i t ' ; : (29) 
HH 7,7 (So!) J, (6,%) 
When (25) and (28) are substituted in equation (24), it appears 
that this is identically satisfied when the following relations exist 
between the still unknown coefficients 4, and A,: 
