a, a, a, a, —dnti? On on 1.8 SEG) 
It is apparent from those series that the removal of the 0 from 
left to right causes a regular change of the signs. 
Now we have n+ 2 reaction-equations, so that we can easily 
find the type of the P,7-diagram. It is evident that this type shall 
depend on the signs of a,a,... (a, is viz. positive); we could think 
now that those signs can be quite arbitrary, we can show however, 
that this is not the case for the sake of (2) and (3). 
Let us imagine that the signs of a, a, ... are represented by the series: 
ee i eet pe ene aia reo ((C.) 
This means that «,a, «4, are positive, a, and a, negative, a, 
and a, positive, etc. We shall call a group of » equal signs following 
one another: an „-group; as case of limit 2 can also be =1. 
Jonsequently we find in (9) firstly a positive 3-group, afterwards a 
negative 2 group ete. As a, is taken positive, the first group 
therefore must always be positive. 
Now we can show: “each series consists of three groups, at least”. 
It is apparent, without more, that the occurrence of one single 
group only is not possible. The impossibility of two groups occurring 
appears in the following way. 
When we put in (3) 6,:a,=4,, 6,:a,=, ete. then it follows 
from (1) and (2): 
Arias alert Bp ap Opel fo sten f= Arlen Ot (ton) 
and 
UA + UA Hee + Up Gp Up Ap +--+ + Une Ane — 0 (12) 
in which 
DN OAN EEE oe (IE) 
We take herein a,...a, positive and a)41...Q,42 negative; as 
regards the signs of u, u,, we take u, ...u, positive and uti... Ute 
negative ; in this q may change from 1 towards „+ 2. 
Let us take g=n-+2; this means that all values in (13) are 
positive. As apy1...djp2 are negative, we replace them by — a, 
—a,42 ete. Now (11) and (12) pass into: 
a, a, es Oy = yt Sowa reo ea on 6. | ((125) 
and 
Ur A Hg Gy Hes Up Ap — Up Op Heee + lint ante « (15) 
The first side of (15) is smaller than uw, (a, + a, +... + ay) and 
larger than u, (a, +a, +... + 4) ; consequently we may write for this: 
a(a, +a, 4... Hap) in which p, > a >u,. 
We write for the second part of (15): 
B (apa H.H ante) in which wa > B > nge: 
