52 G. PLARR ON THE SOLUTION OF THE EQUATION Vp¢p=0., 
(22) d=a+Bt+y, 
has enabled us to put in evidence the factor 3 in the first term. 
[Suffice it to say, in the following short digression, that it was by trans- 
forming /(¢)=0, in introducing the function 
_ Fg) _ F(a) i 2 
ees a =e ot PF, 
dg 
and forming the operator 
—27 Fio H—o)} =FE=0, 
and finding 
go=F tele GE eer 
and then, from #&=0, deducing : E2sac *a=6P; 
which gives 
6PT = 2SQ(a)O’(a) , 
where 2 represents &+3P€=TEé—*, Q’= &c., and defining 
Nu = LaSeQa, oy4= ZaSBQy 
™m— LaSyQa ; 
and finding by the help of 7a=0: 
hig = 6Py, = 9Qn—4P*6 
o,,=—6Poa, —9Qc 
7,,=6P7,—9Q7, 
I was led to introduce the vector x, defined as above, in order to give to »,, 
the same form as that of o,,, 7,,- 
We will add the remark that the operator #(€)=0, when translated into an 
algebraic operation on x=3h°+P, h being one of the roots of 4(h)=0, pro- 
vides us with a demonstration of the equality between the two expressions (18) 
and (19) of I’, because the roots of #(@)=0 are: 1=Fhi=/M, n=, &e., 
namely : 
=(9,=93)(9s—9i)> (Gn Fine Od, Ga Fae) 
thus far our digression. | 
Let us express 7, and Sy, in function of « and y in the expressions (16), 
(17) of —2P’ and 3Q, before entering these latter quantities into (20). 
: : 2 
The expression (21) gives us 4,=«+5P8, 
squaring this we get 
eh cara: 4 
7, =k +3 PSkd + 5 Pd’. 
As to Sxé, we treat (21) by Sé ( ); this gives : 
