Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-06-22
THE PUzzLEv,s coLUMN..

disgr.m % correspond 60 is conditions, fnd COM
serve But am not yet ready to give my position
that the square estate was the largest in No g. al
think Il to right
position on No z Is also unchanged. ] win give
A plumbline fropth center of gravity in the load
must cut the axle inside the center between the
IFS circular motion and to preserve the equilibrium
of the car. Will George & Innis maintain there is
ture? Did Re never see a horse upan the trottna
conrse inc inc his bod much to the center to
his center Of grvty inside his base3 He co lid not
maintain that position an instant were he at rest;
loaded upon on the level track 90 that the
gravty would be directly oyer @ the center Of M ,hs
per minute around short curve, the rail- being up
on the same level, and you will fnd the center Of
n sde Ss
This being practical fact in railroading the ou.
S I ran Is elevated at curve ID fTS % speed
of the matter is this: Circular motion of great
ocity creates powerful force which acts upon bod
I Of the mechsncsi powers if brought to beas upon
them. and is the same. whether it is uponfhe
engine. or. .(counterbaanced by attraction) propes
the earth and all the planets, and drives them on
ity of the load should fall sin the center between
than he would Il the Un annns
an air-line track, laid on q e.fect level: gave
an opinion based upon admitted principles in phi
| losophy-he made an assertion which he did not at
that time and has not since attempted maintain
worth the most. = la7s = - T1 LINEsToNE.
| COLUMBUS. O.. June IT, 1867.
| MR. EDIroR: i am glad to be corrected by Bro.
Della on No. se. BE also points out my error when
he rays they must have regarded the semisphere as
thank him for these corrections. They are made as
have been insisting eorrsc ions should be made by
for such corrections. because am made wiser. Bur
am
can conceive Of ne advantage such assertion can
profsss unto Delta lb.lieve him capable of being
g still continue to Minister to the good of the
Limestone Is mistaken is his answer to problem
| I would like 10 know how Bro. Guernsey can say
II agree with Delta" ia his answer to problem No
81. when their answers are both published in the
i ss.ns paper. Query; Do they board at the same
= wsqd also say to Bro Seeds. he is right on No.
etic II problem: but suppose it meant with given
parimeter. which would contain the largest area,
Answer to Problem No. sl@ls miles per hour,
| Answer 70 Prohlsm No sa.s, 4andS Il
Answer to Problem No. 94-The number is 4.
Answer 10 No. s5-l $50 70. correct to two dec
Answert' No es-The mans hight is feet
Answer to Problem No. lOl-Disgona 81 rods:
breadth 80 rods. GEORGE >. INNS.
WAsHINGroN, GUERNSEY Co.. June II, '67.
| Mr.. EDIToR:-In their answers to Problem 5s
Sohr.quet aud Rodehaver give the distancet hoop
will 60, measured. Of course. on the ground. The
which is series of curves, each of which is four
times the diameter of the generstinq circle aa
ceptng the statement il C'sfistance from IN A.
| Answer to Problem os.-55o' 3.s2 yards. Il
ties some relation to the Tower of Babel that was
r
one hundred! 1t is an o~l. Do you c.?
Answ. r to Problem 9,--!f the boy and the man
Problem 100 IS simply problem 'tS' 81 again. again wish
some one would solve it. 90
;, Answer. to, Problem lo1. = Diagonal 81 rods;
Answer to Problem 1o2 -se57s =.
/ Answer to Pfoblen 1G3.-12 Is and 90
ItwSnd give me much pleasure to see the method
with the data Riven. think the answer depends
on the slope of the hill. which is no given. ri
| Mr.. EDIToR: I bow to Delta. He doubtless
lead the pathemateal host lat we k, both as
gun:ter and an expo9nder. His being opposed to
Robin any one of either seeds Roots and his
anxiety to Mniseer the good Innis shows that he
is as firm as Limestone on all our rights. and we
did come from Dixie. i-Fys
My answer, to his Railroad Problem No. 81. is
No. sa-Is an exquisitely fine algebraic Problem.
The numbers are 8. 4, 5. found thus: State three
secondNfactor-a divide and we have sum Of
the three numbers=l2 divided b the difference be-
&C., the second aud third equations eives same
sum=to the same divided by the difference Of third
eq al and the three numbers are evidently in arith-
metical progression. II we now let D--l=:om mon
known numbers. and substitute accordingly, we OBJ
tain the NUM- crs sought This was sweeter to me
Gals Of Billy Root are too hard for - me- would
rather thao $50 could solve such equations as in
vove in the 5th. 4th Sd. I'd and 1st powers. with
4 a
Robin has my thanks tor Nos, II and 10. Worked
% hours thsn
Demonstration, Mr.. Soubriquet.- Teach me how
both q and acaI Be solved csgSo as'cers
grsgation that;i wonder they paid hum at all.
No. Ioi--si BY IS rods-a nice Problem.
| No. s7-What "heighth" for castle; o, er two
| miles highi an dizzy. % ,ae GUERNSEY.
T. sq COLUMBUS. ONO, June 18th, 1867.
Mr.. EDIToR ;-An apoIosy for my carelessness
and myself Ny time has bee 50 Occupied I 4 With AG6
other matters that have only hals written my let
ish myla letter. since the same answers have been
given BY others 9 ,oHgg @S NJ P1be 10 this
what he had at first Then fro nj n the conditions
We hsvs s Pies glu s. RRs e plus
No. 81 is the only probl m have seen in the COL
gmn rs curing aorner's method: thank brother
Dsa fSr tss odng 5 NJ 81 also give him
see it. In No: IS | still believe that the round lady
sns s am % t. that his
these poetic problem.. ! wish Delta would send his
would like to ses his demonstration viii be please
send it? Some of the boys car leave Mat les hoop
The curve is 8 cyeloid.l (See D. omis' Anaiyt Ge-
ometry page los) The ca ire curve formed by one
generating circle. (see Loomis' above page 21g),
hence the mark goes u feet in evolution. aud
j. an easy question taken from one of our standard
Detas question (No. sprequiring the Dferential
Calculus. is a good one. make the train approach
at the rate of Is miles per hour.
No. o. is a difficult one. know what the numbers
are 3, and s. but have trouble ia elimination.
No. ss is a, good bfqusdratic. solved BY simple
No. 81 is cubic equation. solved by Cardan' rule
for cabics, Henke's tentative process or by the
| general rule for finding commensurable roots. The
Answer to No. ss-e feet. sgs-
| Z Answer to No. lOl-Breadth IS rods, diagonal 81
Answer to No. as. l.sso. .ass7 70 inches nearly.
No. 81 is philosophicaIly wrong in the statement.
for less than IS per dsz But any Of Your oorres orr
eSsS Till send ne solution te ths following NO.
rent the numbers from the conditions form form
three equations; Multiply the first by minus y,
minus z then subtract the first from mt the second to
eliminate x3. then combine the equation thus OBJ
tanned with the third derived equation aud eIimi-
nate Y3-z3; then trsnspose the terms containing
to the first member and find the value of in terms
original equatous and get two equations contain
ling two unknown quantities Let x=v and su osti-
tu in these equations and find the values Of z2
in terms of and make the two values equal to each
other, and we have simple quadratic in v. whose
value is 80 6o substitute this ad we get the value
of z2@25 and Is; then substitute and fnd the
value of and easily. - -.
No g. is conditioned correctly. Solve it by Hor
ner 3 Sturne. Second term is '' twice the square
root" DC. -l r -tt...l- d '..-.--- SAMMY.
Il a r.s=- -s.r COLUMBUS GROVE. ONO.
Ne 7 vv;ll sa,d yo,, 81. j