678 
Proceedings of Royal Society of Edinburgh. [sess. 
Scott, R. F. (1878, Dec.). 
[On some symmetrical forms of determinants. Messenger of 
Math., viii. pp. 131-138.] 
The first of the forms referred to is 
c a 
b c a ... . 
b c .... 
which by means of its difference-equation is once more found to be 
equal to 
\c 2 + Jc 2 - kab J ~ \c 2 - Jc 2 - 4 ab } 
2“ +1 7,2 - 4 ab 
Five special cases, more or less known, are mentioned, the last 
being that in which c 2 = 4 ah and the value of the determinant 
n 
(ab)\n +1). 
Sylvester, J. J. (1879, March). 
[Notes on continuants. Messenger of Math., viii. pp. 187-189.] 
Here the main point of interest is the use of the old “ rule ” 
referred to in his paper of May 1853 to provide a proof that the 
number of terms in the simple continuant (a 1 , a 2 , . . . , a n ) is 
1 + („_!) + (”- 2 )(”-3) + («-3)(n-*)(»-S ) + . _ _ > 
1-2 1*2*3 
the various parts of this expression being shown to correspond 
with the various kinds of terms obtained in following the “rule,” 
viz., 1 term containing all the elements, n - 1 terms containing 
n - 2 elements, %(n - 2) (?i - 3) terms containing n - 4 elements, 
and so on. 
In stating some related results he uses the word “pro-con- 
tinuant ” for a determinant of the form 
a 1 
1 b l ... . 
1 c . . . . 
that is to say, for the continuant 
( -i . -i . -i . 
, c , 
,) 
