X , x' , ... 
, KU. 
£ 
, 7) 
Ap+Ba+..., A'p+B'a +..., 
Aa+AV+... 
, Ba B a -P..., 
so that finally 
F{K(U + U). UU-KU.V(U+ U)} = V [K (U+ U) FU — KU. F(U+U)} (63). 
■;r.PJ:rx 
x , x 
Ap-\-Bcr-\-..., A p-\-B <r-\-..., 
I > V 
A a 4* A 'a' -f-..., Ba-f-B'o! -t*..., 
The second side of this may be written under the forms 
'K(U+ U)' n ~* 
KU 
AX+A'x’ + ... , Ba; + BV + ... , 
A (Ap+Ba..) + a'(A'p + B'a..)+..., B (Ap + Ba..)+B' (A'p + B'a..)+..., 
multiplied into 
R£ + Sr] + ... , R'i; + S'r) + ... , 
R(.Aa + A'a!..) + S(Ba + B'a'..) + ... , R' (Aa + A'a'..) + S'(Ba + B'a'..) +..., 
... (64). 
And 
'K(U + U)\ n ~ 2 
V KU J 
Rx + R'x' + ... , Sx + S'x' + ... , 
R(Ap+Ba..)+R'(A'p+R'a..)+..., S(Ap + Ba..)+S' (A'p + B'a..)+ ..., 
multiplied into 
A£+B v +... , A'£+B' v + ... 
A (Aa + A'a'..) + B(Ba + B'a'..) + ..., A'(Aa + A'a'..) + B' (Ba+B'a'..) + ..., 
And again, by the equations (52), (53), in the new forms 
(K(U+U)\ n 
... (65). 
KU 
fK(U+U)' 
F.X{[(A P + Ba ...)(a£ + b v ...) + (A'p + B'ct...)(a'£ + b' v ...)...] 
x [(Aa +A'a'...) (bx + b.'x' ...) + (Ba + B'a' ...)(sa; + sV...)...]} (66), 
(RU y-j V .2 {[(Ap + Ba ...)(ȣ + &* ...) + (A'p' + B'a...)(R'f + sV..)...] 
x [(Aa + A'a'...) (Aa; + a'x' ...) + (Ba + B'a' ...) (Ba; + bV ...)...]} ... (67).