566 
Proceedings of Royal Society of Edinburgh. [sess. 
Jacobi having already pointed out in his long memoir ot* the 
preceding year that the cofactor of a Kk in 
V ± a u a 22 . . . a nn , or N say, 
is 
0N , 
da Kk ’ 
and having now to deal with the case where a Kk = u klc , draws 
attention again to the fact that in solving the equations 
a i\ V\ + a \2 V2 + • * * * + a i n Vn = m \ 5 
a 2 \V\ + a 22 V 2 + • • • • + a 2n y n = m 2 , 
anlVl + a n 2 V 2 +*••• + a nn Vn = ™ n , 
we no longer obtain 
%1 = 
/0N N 
'dN\ 
'SNN 
) m i + ( 
+ • • 
• + ( 
, 
\da n i J 
N2/! = 
/0IS TN 
• • +i( 
r i + u 
)m 0 + • • 
\da 21 J " 
a— K» » 
\oa n i / 
— his explanation being that the differential-quotient of N with 
respect to a Kk , where k and A are unequal, is obtained by first 
viewing a Kk and a klc as being different, adding together the 
differential-quotient with respect to a Kk and the differential- 
quotient with respect to a kK , and then putting a Kk = a klc . His 
own words are — 
“ Si vero a K k = a kt c differentiate partiale secundum a K k 
sumtum, quoties non k = \, obtinetur, si primum a Kk et a kK 
diversse statuuntur, atque differentialia partialia secundum 
a Kk et secundum a kK sumta iunguntur, ac deinde a Kk = a klc 
statuitur : quo facto cum utraque differentialia sequalia fian,t, 
casu quo a Kk = a kK valor duplus emergit eius qui in formulis 
(3) locum habere debet.” 
It may be added that he thereupon obtains the solution of the 
set of equations, as his purpose was, in the form 
n J/r_ 
2"- 1 S ’ JN 
f*n — 1 
x r (m 1 ^ 1 + m 2 x 2 + 
+ m n xf) dx-. dxr 
dx„ 
x n [ %a Kk x K x k ]* (n+2) 
J 
