Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-08-31
THE rUzzLEa,s CeLUmN.

WAsHIHGToH, o., August 90.
MR. EDITOR: The last STATESMAN informs me
that am Marked absent without leave" This is
"misfortunate." old chum of mine used to say,
but it can't be helped. Ny reasons for absence sre
good but would not likely either entertain or profit
hope that brother Innis wont carry ont the sug.
gestion Of Robip-to, match" the straw man. i is
would he risky way of obtaining it:
t3uernsey's duties have taken him away from
town. and they will hardly bring him back in time
for roll-call this week. but he told me To say his
heart is still in the work.
l have not attempted the solution of last weeks
problems; oily seeing name in connection with
some pears. Hooked to see how many there might
be. BY my measurement there are 8 sex bushels.
For Delta's guess multiplied and Guernsey's divi-
ded by the square root of each gives that numb ber
=. Il is to be hoped that Uhose will not let those
telegraph" problem. and settling the discrepancy
between E. b. and ). x as to their answers to num-
ber 1S4.
Ny thanks to &. b. for his method with number
l3s. drew the figure and followed ont his argu-
ment with an explanatory climax, MAGNIFIoENTl
if you would send the g neral construction of No.
1872 TO my address Delta, box 1875. If its not asking
have tried it, also number 1885, but as yet shave ta
ken nothing" These problems are doubtless very
fine; they appear SO to the eye. but when reach
for them. like the ripe apples suspended over the
head of TanIa they recede. cento n1otd.
Now gentlem, n. | am going to make motion and
let us hear your opinions. L move that the Editor
be requested to limit the problems in any one pa
per to eight as maximum. and that the answers
iication of the problems instead of the rst think
that reflection will show any the reason of these
suggestions in the extension of time it will give to
mature our results to the various problems.
My time is limited and my answers will be few.
ANSWERS.
Number 1927 greatest ellipse" is a circle. and
ii may be, the axes are each 4.Is.
Number 1873 3X years.
Number 194-7-23.
Number 1g6-$250O; ratio As
hO ha liz, -
Number ls5-Provided the bisectiDg line, extend
cd. becomes diameter, the other sides each equals
s73 They are equal because they are lines dra wn
from point within circle. to cepcave arc making
tre." This does not give. however, a general solu-
tion to the problem.
=, Welcome. Amos! Are you recruit. or as Mrs.
once. DELTA.
GREENy1LLE, O.. August %, 1867.
Mr.. EDIToR-I was glad to see the contribution
weeks paper. think he is mistaken mi in i6i. 6i.
answer to No iss: let us see: Construct a right
and stanss Be
structa triangle b ID; make BD=25 feet, and CD
then this AD will be one side of the reaIred rf tri
ANGLE. From A draw AE perpendicular to AD and
make it equal to AID; draw ED and EC; &c will be
40 feet; hence ADE is the required triangle. The
s7e7os feet S. x hss given an snswer to No. s is5
form of rig angIed isoscees triangle the side oi
the largest square that be constructed within it
third Of the hypotenuse One third Of s1s ss5 !,
lO4 652 but the side of this square should be 10;
Sammy thinks Guernsey is worng on No I7e. No
he is not. If the answer referred to is incorrect
ann wrong; for gave the answer. ! will give. my
suppose the ball to be dropped into the cup, ther
half the width Of the cup at the top is to the slant
diatance from the center of the ball the bottom
of the cup; we have the then proportion as g. s.:
from the top Of the bali to the bottom of the cup
Now the cube of the highth of the cup is to the
cube of the from the top Of the ball to The
the capacity of that part, of the cup filed bv the
ball and water. then We haye zig: 46 s5exs s27
462313: hence 4S23x3= the capacity If that part
filled BY the ball and water But zisssxsS the Vol
nme Of the ball. and the amount water in the cur
s54; from which we find x=I.223; therefore the
diameter of the ball must be 2.446 inches
ANSWERS.
No. 1ss-In ~ years. months and 90 days, the
amonnt Of each note will be se.l5s ss.
No. l94-A should Day s1s3H; b. ss3X q, $685.
No. 1866. 500,
feet, and 3967S feet the other two sides T. 1920
feet and s.s745 feet. E. b.
HoPEDALE, OHIo, Aug. q, 1867.
Mr. EDITOR: For some time past l have been
absent from the Puzzling Glass. but have not been
away so long but what know my place in it now.
My place is at the FOOT SO friend Delta will not have
to stand foot this time MIR. Editor; if your
hard problems, think will have 10 switch off
and leave them all for Essex (X), and the rest of
matized or mathematical. Please pardon INV coin
ing. Friend 3. x. thinks some of our contributors
sending plenty of problems. but in retlrn only
few answers. Please do not think so of me- brother
Issent several answers which were not published
ts f %as tSGy Ssor not
time ago stated tnat problem 81 and its solution
are in Greenleafs National Arithmetic on pages $50
ArI Rrnf fhnR InFar hat .Ia1 AOE E11A
luton. and asks if am not mistaken. l will say
no. brother, They are in my copy just as stated
that he and of the rest of the Duzzlers
would like to the solution. will send it just as
find it.
Operations feet four iuches-5 feet inches
and divided inches, by e=2 ipches=the =, O.
beyond the fange on the face of the wheel here
the wheel bears on the rail. The .perpp' dicul :.
that distance the wheel diminishes in diam oc 8
eet-2feet lis ,inches=5 inches. Tn n, a. in.
eter of the wheel at the bearing is feet 25 inches
- feet Ills inches As the radius of the curve OF
. outer rail is to that of the isneI rail SO is the
fset-5 fest1 inchesEiis1 inches feet II IS
of the oameters of the two wheels at the place Of
bearing is 35 rs in n,hes-35. .59l=l5s inches. Then
wheel this difference in diameter will vary the
bearing ass feet-2 feet Ills 1n=5 in. 4 in :: 15s
inches !: 27I inehe,. But this difference must be
applied half to each Wheel viz: 127l inches divided
by2=s3S inches. which brings the place of bearine
.635 inches to the hange on the outer wheel
and 635 inches further from the fange the inner
wheel; and the mi IDLE poiut between the two bear
ing will be 635 inches from the center of the axle
towards the inner curve. and in that place must the
center of gravity of the whole load be placed Ia
make the weight of the load bear equally on each
rail. VIE: e35 inches from tho middle of the axle
towards the inner rail, answer.
For the benefit of the class will now give a rule
for finding the least common multiple of two OF
more fractions or mixed numbers:
Ifthere mixed numbe reduce them to improp-
er fractions; hnd the least common multiple of the
numarators. and the greatest common divser of the
denominators; divide the least common multiple
thus obtained, b, the greatest common divisor aud
the quotient will be the least common multiple Of
the given fractions or mixed plumbers.
After the class have read the above rule they
will please e d the least common multiple of 6G6H
3o3H and 2O2 20. Now if they have found the lea Isl
will please compare it with their to problem
134, Now. if their ans~ ers to problem 134 moi
mixed numbers as found by the above rule. thei
answers are not my answer, nor Rays. nor Pixies
Who will answer problem No. 100
Answer to problem 1873 sons and daughters
Pretty large family. and had good deal Of dodg
ing before got them counted.
I70-Radi eal's age 81.
+ 1910 bushels.
No time for any more at present.
WASHINGTON, Aug. 27th, 1867.
Mr.. EDITOR -Isee most of the boys have beer
playing truant without any 1critsea excuse, anc
hence this weeks column is rather meagre both il
point Of problems and interest.
would beg leave to call the attention of tn,
class 20 problem NO. bl, gwen by Delta. and in
view none have answered it, SO l will give my an
sTer with the other, problems. Thank you. Brother
E; b., am still as far in the dark on 152 was
L hoped when said l had no good solution, that
some one would give one further. E. b. did
say at any time that you were not correct l die
not; was more guarded in my remarks than that
either sent wrong answer to Problem 1S4, or il
does not correspond with my answer in my Scray
Book. My answer is: outside imensions-Lengtf
52 feet breadth 4s5 feet depth IS feet. content
1t appears that Brother Sammy is on his equanirr
ity again. Please stand there, for none desire tt
arouse 20 and much less do desire to spread my
13. as you said in yours of June 22d that your So
luton was not very satisfactory. l presume since
my demonstration that it has grown in Importance
until it has assumed gigantic proportions and No
rule. l am well pleased to find you EXALTED
will inform the class that Bro. Guernsey has beer
away for some time. and Sammy is wrong in sayinl