142 Proceedings of Royal Society of Edinburgh. [sess. 
where, in view of the contents of a subsequent paper (see under 
year 1858), it would seem that A (a ,/3, . . . , l,rj) was used for 
1 cos a 
- cos a 1 cos p 
-cos /3 1 
- cos£ 1 cos g 
- COS Tj 1 
No properties, however, of this determinant are given. 
Ramus (1856, March). 
[Determinanternes Anvendelse til at bestemme hoven for de 
convergerende Broker. Oversigt . . . dansJce Vidensk. SelsJc. 
Forhandlinger . . . (Kjqbenhavn), pp. 106-119.] 
Ramus’ introduction consists in recalling the result of the appli- 
cation of determinants to the solution of a set of linear equations, 
his mode of stating the result being that given by Jacobi in the 
De formatione ... of the year 1841, — that is to say, he takes for 
his set of equations 
a o°Vo + a iVi + a 2°V2 + • • • + afy n = u 0 ' 
V Vo + a \V\ + a 2V<L + • . • + a n hy n = u Y 
a 0 n V0 + a \Vl + KV* + • • * + a nVn = U n j 
and puts the solution in the form 
R n y r = A r °w 0 + A r . 1 % 1 + A r 2 u 2 + . . . +A r n u n (w) 
where 
R„ = 2 ± a a a i a 2 ■ 
. . a n n , 
A ( = 2 ± a 0 V . . 
i— 1 i+1 
• a • i a •. i 
i — 1 t+1 
n n 
• • • u n i 
K= oV- 
i-1 k 
■ • 
J +1 k-1 + 1 
a i+ 1 * • • a n-\ a K.+l • 
. 
• <.* 
* It is in this mode of writing A^, viz., with the negative sign, that Jacobi’s 
peculiarity consists. Not content with removing from R n the row and 
column in which a * occurs and prefixing to the minor thus obtained the sign- 
