( 86 ) 
Thus it gives rise to the formation of an “assemblant” consisting of 
ge (Um + 1) (lm + 2) 
a3 2 
rows and vj == @, + «z columns, 
where 
(lm —l + 1) (lm — l +2) (Lim — m +- 1) (Um — m + 2) 
= —— and tf, = ; 
2 2 
a) 
The columns of this “assemblant” are in general not independent 
of each other but connected by 
(lm —l—m-+ 1) (lm —1— m + 2) 
Vp == aH = 
= 2 
— 
independent linear relations. 
We now see that between the numbers v, vj and vz the relation 
yy a OM ly ew, py” EN 
exists, as is easily shown by substituting the values. 
We determine the vj undetermined coefficients s in the following 
way: In the function / we make equal to zero the coefficients of 
Lm (lm + 1) 
2 
linear homogeneous equations between the coefficients s which are 
moreover, as was said above, connected by ez linear reiations of 
dependence. 
So the difference between the number of undertermined coefficients 
and that of the mutually independent linear homogeneous equations 
existing between them is: 
all the terms containing the same variable. This produces 
Lin (lm + 1) Lm (lm + 1) 
Dm — nn 
2 2 
(lm + 1) (lm + 2) ban Gant Sa 
PS TTT eee 
which proves that the vj undetermined coefficients s can be deter- 
mined quite unequivocally out of the indicated homogeneous linear 
equations. 
By substitution of the obtained values in the equation “= 0 the 
demanded resultant is arrived at. The given method is rather simple 
to apply. 
