126 
MAJOR P. A. MACMAHOR ON A CERTAIN CLASS OF 
Art. 24. The relation 
n- — (2" ~ 1 — a,) = n — 1 
will be established, and this leads to the conclusion that the redundant form, when 
possible, is always of a 
{n - 
infinite character. 
Art. 25. The fact, subject to the above-mentioned conditions, that there is an 
infinite flexibility in the redundant forms is of great importance in the Theory of 
Numbers, because the potentiality of arithmetical interpretation would appear to 
have no finite limit. 
Art. 26. Observe that 
denotes the number of identical relations or syzygies connecting the coaxial minors of 
a general determinant of order n. 
Art. 27. The discussion of the theory of the first few orders forms a convenient 
method of approaching the general theory. 
I take the general form of V„ as 
1 ‘ • • • H” H” • • • ~h ( ~..m^l'^2 ' ■ • 
Art. 28. The case n = 1 . 
This case is trivial because the perfect form 
1 
1 
coincides with the redundant form 
— (2” — 1 
0-1 = 0 ; 
o-i) = 0. 
Art. 29. The case n = 2. 
In order that 
_ 1 _ 
{1 "t ^12*^2)} ^^^22^)1 
may be a redundant form of 
