144 
MAJOR P. A. AIACMAHON ON A CERTAIN CLASS OP 
C’xy - 
Cy.r - 
'■xy 
_ _ ^xy 
.r + i Tr + i, ^ + 2 • • ■ '^y-l.y ^*xy 
Clyx 
^ 0 , 2/-1 '" 0 - 1 . y -2 ■ • ■ + "yx 
hj 
where tlie symbols h„j have been introduced, so that now 
in regard to the elements of the matrix of the fundamental form are analogous to 
^xyi /^.ryf '/■>'!/ 
in regard to the undetermined c[uantitie.s. 
It is easy to verify that the two systems of values 
r r 
^\ri/ 9 '^yx 5 
of the quantities y^y, satisfy the whole of the 2“ — 1 — n — equations, but I do 
not stoj:! to prove that these are the only systems of values of 
Substituting in the matrix of Art. 47 we obtain the two representations 
( 
«!! 
AsAi^^is 
1 
A 2 
*^^23 
y^23'^'33^23 
AAh3^34. 
1 
A#43^34. 
As ^13 
As 
Ai 
«24 
1 
<^^44 
Ar ^14 
A 4 
Cl.ytl 
Ct^n 
A« ^in 
«11 
^13^^12 Al 
/^13^13^31 
^14«14Ai 
1 
A 2 
A3A3^33 
^tsi 
1 
*^33 
A4®34^43 
As ^31 
As 
«41 
1 
«'44 
A 4 ^41 
A 4 ^42 
• 
A 4 
CInl 
««;i 
/3i?i Ai 
Ah ^«3 
^4i/ 
I^2n^n2^hn 
a., 
I 
l^2rSkA2 ! 
^3Ah)i^)i3 ' 
I 
a. 
