28 6 
Mr. Wilson’s Essay on the 
In the (nth) degree, or generally, 
f A + B + C + D + E&c (» — i ) 
in number 
n 
X 
l 
— A - B — C _ D — E &c. 
n — i x n 
B I Q - - 
— — &c. n — 2 in number 
n — i 
20. The inspection of the table shews us, that in all cases, 
to construct a general simple representation of any number of 
quantities, and consequently to construct a direct resolution of 
their equation, we must first find a certain number of their dif- 
ferences ; but we have no general means of separating particu- 
lar differences from the rest; and the whole number of diffe- 
rences increases in a proportion so much greater than the 
number of quantities, that the former difficulty recurs, the pre- 
vious steps involve higher dimensions than the original equation. 
The original index being (rc), that of the equation of the dif- 
ference of the roots is ( n x n — i). However, from the nature 
of differences, (being taken both affirmatively and negatively,) 
all equations formed from them must (as observed of quantities 
of that sort in Art. n.) be universally deficient in every alter- 
nate term, which brings their equation to the form of equations 
of only half their own index, or [n x — ) : but, in this case, 
their differences are six, and their equation, with that considera- 
tion, is reduced no lower than a cubic form, which is the same 
degree with the proposed equation ; therefore, it does not appear 
