The Scranton chronicle., 1901-01-19
GENIUS IN MATHEMATICS.
A Missouri Professor Has Discovered
New Principle In
Equations.

When William g. Horner. OF Bath,
England. an obscure school-1eacher. in
1919 made known TO the world his
method of solving numerical equations
OF any degree the discovery was viewed
with suspicion by nearly all the ssev-
braists of Great Britain. The Royal
society of Great Britain had the luck,
so Prof. Augustus De Morgan says In
his Budget of Paradoxes,' 10 acNept
Horner's celebrated paper containing
the method which is far on the way 10
become universal. but they refused the
paper in which Horner developed his
views of this and other subjects. II
took more than 90 years for Horners
method to get a foothold in the Uni
versity of Cambridge. The professors
and tutors in that stronghold of mathe-
matical learning never used II till stu
dents coming in from the most pro-
gressive preparatory schools employed
il in their solutions of cubic equations,
and at first they were criticised because
1t was out of the usual line of work
although Il was ten times as simple as
the methods of approximation then In
vogue. SAYS the Kansas City Star.
All attempts to solve general equa
tion of the fifth degree have proved
Intellectual and one noted analyst, Abel
has demonstrated to his own satisfac
tion, at least. that the solution is i'm
possible. Equations are divided into
two classes. numerical and literal. an6
a general equation of whatever degree
is an equation whose coefficients as well
as the absolute term are literal.
In the history of mathematics II
took long time to obtain a general
solution of an equation of the third
degree. and after repeated efforts and
many failures the general solution OF
an equation of the fourth degree was
effected by several different mathema.
ticians, and here general solutions have
been at standstill more than 200 years
Horner's method was such an improve.
ment over all former methods that as
soon as it became known il took high
rank and is the simplest yet discov-
cred.
Recently a new discoyerer has ap
peared and he handles numerical equa
tions with an ease and precision that
relegate Horner's method to the de
partment of ancient history. This au
thor is Prof. NJ. A. McGinnis, of Neosho
Mo. In book of 1875 pages Prof. Me
Ginnis presents his system. The key tC
the discovery consists of certain def
mite relations that the coefficients o
the unknown quantity bear to the root
of the equation. Analysts had discov
cred certain laws governing the co
efficients when the coefficient power o
the unknown quantity is unity. b,
working with the sum of the square
of the roots Prof. McGinnis shows tha
certain relations subsist when the sun
of the squares of the products of tn
roots are taken two and two, and so ol
for higher degrees. The author lay
down five fundamental theorems whicl
he has discovered and by the applica
tion of these and some other principle
he has succeeded in solving numerica
equations in the briefest manner eve
presented. Abel demonstrated that tn,
general solution of an equation of tn,
fifth degree, according to the methods
employed in the solution of lower equa
tiors, was impossible, which mean,
that the modes OF attack hitherto re
sorted to would not work. The compli
cations were so great that they coulc
not be unraveled Prof. McGinnis does
not work at equations according TO the
usual methods presented by mathema
ticians, but he goes at the subject from
another point of attack altogether. By
discovering new laws, not hitherto sus
pected, that enter into the structure Of
equations, and that the coefficients bear
constant relation to all the roots oi
the equation. he deduces the principles
that were unknown. These being ad
mitted, he then proceeds to solve gen
eral equations both of the fifth and
sixth degrees, and the beauty of the
method is that IL solves all numerical
equations by processes almost arith-
metical.