142 
MAJOR P. A. MACiMAHOT^ OR A CERTAIN CLASS OF 
or since 
Acy ~ Aiy/Anj 
we may take the undetermined quantities to be 
Ai2) Ai 3; • • • Al, n- 
Each redundant form is thus of the nature 
as was to be shown. 
n — 1 
quantities y can be 
Art. 48. The equations for the determination of the 
:aken from amongst the equations connected witli the co-axial minors of Order 
One such equation is 
which may be written 
, g 
7« 
px qxy - q.v. 
1 Py 
'yxtfiyz 
Jxz 
q’P 
p~~ 
= 
and this is a quadratic equation for yxxlyxxjjyz- 
If X, y, 2 be consecutive integers, this is simply a quadratic equation for y^-.. Hence, 
the n — 2 quantities y^.,^ + 2 are at once determined. The n — 3 quantities yx,x-yz are 
found by the aid of + which is unity, and 7 ,,. + 1 ,^ + 3 . Thence, 7 ^., 3 ; + sis found in 
terms of + + and all the quantities y^y are easily found. 
Assuming the coefficients of Y,, to satisfy the above-mentioned 
2 " — + n 
conditions, we have to find systems of values of the quantities y^y which satisfy the 
2 “ — 1 — n — equations 
in which they appear. 
I find that there are only two such systems, obtained respectively by taking the 
positive and tlie negative signs in the solutions of the quadratic equations. In the 
one solution the signs are all taken positive and in the other all negative. 
