( 923 ) 
ma? 1 
ae sede = Ge") a a Sti. Beh VEL) 
2 5 
ee AAN Lee . 
Noe | UGS fv Mel OP A re rad Crete £ 
a Tas 240 + 100°] (12) 
Substituting the values given by (10), (11) and (12) in the equa- 
m 
tion (7) and afterwards in (4) we find : 
2 a 
Ly SS ram: | 16 —8e + 30°] (r—« 4- 3 ) +. 
ENG Tene EL ison. shel len 13 
20 O° , — — -|lo—24o0 o*|—). : 
rg a TORO RRC date aan 
Now expanding and integrating in the above deseribed manner 
the other terms of the series «, it appears that each term gives a 
contribution to each of the terms figuring in the coéfficients of (13). 
In consequence of the particular regularity of these expansions it 
is easy to determine the laws for the succeeding numerical coéffi- 
cients of the different series. 
In the first term of (15) there appears the series: 
1 1 5 35 
So: al 5 dar dor de + 
8 64 1024 16384 
in the second term 
1 1 5 ao 
Se: po pc Ta aie ye ea lg 
i 8 64 1024 16384 
and in the third term: 
2 Mee nat Gi 
as ean BL pee eae Poe 
From the derivation of the fundamental equation (3), that can be 
found in the German edition of Maxwerr, edited by WeINSTeIN, it 
is evident, that the terms of the series S, are formed by the pro- 
ducts of the equal order terms of four different series. 
It is therefore very difficult to find back the law of succession in 
the above reduced form of these products. 
The law of succession is very simple, viz. 
Uy, (2n—3) (2n—1) 
RT Qn (2n2) 
which gives for the general term of the series: 
(2n—3)/ |? 22n—1 
Ke on 
ni(n—2)! | 24°—4(n-+-1) 
’ 
