The theory of determinants in the historical order of development, by Sir Thomas Muir.

LESS COMMON SPECIAL FORMS (GUNTHER, 1874) 487
Glaisher, profiting by Ginther's initiative and skilfully economizing
labour, pushes the investigation forward and finds the numbers
4, 40, 92
for the cases where n is 6, 7, 8, his result in the last of these cases
agreeing with that which Gauss had finally reached after two or
three trials.*
Serdobinsky in his procedure does not really use determinants.
GUNTHER, S. (1875).
[Aufoisung eines besonderen Systemes linearer Gleichungen. Archiv
d. Math. u. Phys., lvii. pp. 240-254.]
The system in question is that in which the determinant of the
2n unknowns is of the form
a b b a
c d -d -c
e f f e
g h -h -g
-that is to say, has a,.,S = (-)-l'1a',,-s+i. So far as our subject
is concerned, all that is effected is the resolution of the determinant
into two of the nth order: for example, the four-line determinant
just given is equal to
22. a b. c d
e f gh.
In the application to the axisymmetric case where
=. r.'s.7r
ar,. 2n+1'
the stage reached falls short of Hunyady's of 1872 (p. 104 above).
SPOTTISWOODE, W. (1872).
[On determinants of alternate numbers. Proceed. London Math.
Soc., vii. pp. 100-112.]
What is here meant by a determinant of alternate or alternating
* See Bellavitis in Atti del R. Istituto veneto, (5) iii. (1876-77), pp. 186-187.