1887.] Mr A. H. Anglin on Summation of Alternants. 203 
likewise for the coefficients of the elements involving the indices 
r, s, t, . . . z. Hence we have 
Sju. -~ | 1, 2, 3, . . . fi) /a - 1-2, . . . n — 1 | 
+ | 2, 2, 3, . . . /a -f- 1, [a -f- 3, . . ,7i — 1 | j 
and thus 
2/a = | 1? 2, 3, . . . [i, \a + 2, . . . n — 1 | . . (f)- 
Lastly, the corresponding value of 
:% + l, r+ 1, . . . y + 1, z] or l n _ 3 
is deduced in like manner by the use of equation (n - 4)', when we 
get 
S w _s=| 1, 2, 3, . . . n-3, n-1 \g . . (n- 3). 
The results (1), (2), (3), . . . (n- 3) are the Extensions of equation 
(D), and their right-hand members are formed by deleting suc- 
cessively the second, third, fourth, . . . , (n - 2)th figures from the 
series 1, 2, 3, . . . n — 2, n — 1 ; that is, by deleting these columns 
successively from the corresponding matrix. And we may further 
notice that the coefficients of ^ in these n - 3 identities (correspond- 
ing respectively to an increase by unity in 1, 2, 3, ... n — 3 indices), 
are also formed by increasing by unity the elements of 1, 2, 3, . . . 
7i-3 columns respectively of the determinant | (q - 2), (r - 3), 
(s-4), . . . , (z-n+l) | . 
5. Note on Cobaltic Alums. By Mr Hugh Marshall, B.Sc. 
Erom a peculiar change of colour observed in the electrolysis of a 
solution of copper-cobalt potassium sulphate, the author was recentl} r 
induced to make some experiments on the behaviour of cobalt sul- 
phate solution when electrolysed in such a manner that the reducing 
product of the decomposition could not act on the solution. For 
this purpose a divided cell was used, so that the two electrodes 
were practically in separate vessels. The apparatus will be fully 
described in a future communication. 
It was found that an acid solution of cobalt sulphate alone is 
not changed when submitted to electrolysis in the apparatus. If, 
however, ammonium or potassium sulphate be also present, the 
solution passes through a series of changes of colour, ultimately 
becoming greenish-blue, and this, it was found, is due to oxidation 
