Glasgow weekly times. (Glasgow, Mo.) 1848-1861, 1858-03-11
For the "Times."
The Problem Solved.
BrrHrL, Feb. 9th, 1855

/ BrrzEL, Feb. 9th, 1858.
/ Mr.. W. S.: A false problem is one whic
contains fallacy, but the one under con
sideratien does not, even If it were indeter
inmate, as you attempted to show, 1t woul
not be q false one.
You complain of want Of candor In me
but l think that have much the stronge
reason for complaining. I have state,
nothing but facts, which can support; 20,
have taken considerably the advantage, il
refusing to give your meme. and you at
tempt TO get it still farther, by endeavor
ing 10 make ms turn evidence against my
self, BY propounding questions for me t,
answer; which course is not admissible il
any court Of justice. This is certainly, no
fair, but / will crafty you as far as I an
able.
You ask me to take the equations minu,
J equal l, and x plus 2y plus 81 equal IL
and, using the second as common differ.
ence, to add it cOnsecutively to the first
and to answer you candIdly, whether l dc
not obtain all my equations, aad as many
more as I please. Now I cannot conceive
how I, or any one else, can add one thing
consecuiively to another; but il you mean
that | must add the second to the first, and
then add it again to that sum, and so ca,
l answer, can get all my equations and as
many more as I please.
But, can show that the first and second
equations in my problem are all that are ne.
cessary for a solution, and the problem, in
stead Of being indeterminate, is redundant;
and if you objec. 10 solving problems with
fewer equations thea unknown quantities,
l would just refer you 10 Key to Rays Al
zebra, page 96, ex. 20, where Mr.. Ray
has pursued the same course, thus showing,
that, If it is possible to do SO, we are justi-
fable in it. Now never asked you, or
any one else for solution of my problem,
if you did not feel disposed to furnish one.
The sole object which l had in view, in
having it published, was to elicit informa-
ton. l did not expect to get into q dis
cussion over it, am sure did not desire
it. But when you bounced upon me, with
the evident intention Of devouring me,
was compelled to defend my position
Since it appeared in the Times, l have been
enabled TO solve it myself, and as sup.
pose that the community in general, and the
Editor of the Times, in particular, are
weary Of our discussion about nothing, /
will just give my solution.
Substraciing the first equation from the
second, we obtain the equation plus 2y
plus 81 equal II. Now we may make the
values Of the unknown Quantities, in the
given equations, any thing we please, and,
il they are in ArithmeiicaI progression, the
numerical side Of the resulting equation, will
always DO . multiple Of the sum Of the CO.
eficients on the literal side. Hence, we
can always readily ascertain whether the
numbers are in .Ariihmeticsl progression.
In the present case. they are; for divide
IL, which is the numerical side Of the re.
sul,ing equation, by 8, which is the sum Of
the co.efficients Of the letters on the other
aide, and we get remainder Of l, which,
according TO the principle just stated, mus,
be the common difference. Then y must
equal plus /, and Z equal plus 2, and
from the equation itself We obtain, plus 2
K plus 2 plus Ok plus 4 equal IL, and re-
ducng we get 5x equal 8 or equal l, then
y equal 2 and equal 3, which values be-
ing substituted in the given equations satis-
fy the equations; and following the same
rule we can always find the values of K y
and if they are in AriihmeticaI progress
sion. II they are not, we can readily as
certain il, and asked for solution of such
only as are. JEO. G. PRICE.