Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1868-03-28

2 The question. How many revolutions on its own
axis will . wheel make in rolling once around q
hxed wheel of the size Z" though explicit and
plain is abstract and seems to have bothered
Some of our correspondents considerably. They
seem to have been entirely unable to dissociate
from the term axis some distinct body separate
from the moving Wheel 1t is only necessary to se-
cure one wheel on table. lay down the other and
roll it once around the fixed one and the result will
be seen in the number of times point near the
circumference of the movable wheel points in one
direction, not relatively to the fixed wheel. but
relatively to its own center. This is tpice. In
other words the nsass of the movable wheel moves
through space Just equal to twice it's circumference
{ How can it roll this distance without revolving
twice The circle described by the center Of the
moving msss. gives the distance travelled by the
mass in making the circuit Of the fixed wheel. N.
W. seems to catch the idea advanced by US on this
RI subject, -..5 i IL =. f.esI ~ .-i, ssl5ig-
ls In answer to the inquiry from Washington C. q.
Ohio we say the Puzzler's Column is as free as all
to those who choose to enter the lists. 81.
We must AGAIN insist that our correspondents
write on one side of the paper only. A failure to
do this in the future will forfeit the offenders place
in the column.
PETERSBURG. VA, March II. .
Mr.. EDIToR-Dear SIR: Sickness and business
kept me from writing to you before. will imme-
to solution
ss hs point rasTs hs angle Gf
hypoth,sysss AB equals 80, BG n ssgas 80 and the
DAE. Let DxE equal x. then bBE equals TX.
and pcE equals sx , HeT from box lst grop e.
* equals * Plus Bee BED equals eaa.s % AEB
* see sGS e..
From book 4. props u and ls, We have GI BEs
SD f1Sas Be- " 3 pins % plus %uipisd
by CD. Substituting the value OF the known guam
in S ss S the sqas As IS socT ed
s 500 minus CEai 90 60 1soAp @ equals leo q qlo
paf p%ae saass sAEa
%nSs sasSs HSw %1lsly ssu.t0n 90 By g.
and IS @ saEa plus sGEs eeaas
Multiply equation ts) by 5. Qo) sAE2 plus "a CE2
equals aso4oo. Square eeuation first . and subtrset
Il GE equals & ome
and every angle san be found The rest Of the work
is SO simple. do not give it. Ny answer to the
I onl. h.vs time to send few snswer,:
No. 52-64H miles DOWN. or i2s1I together. J's
No. 34--Son's age Is. Fathers 36. IN a. So.
No No. ss-sSl ss-Sd, tons. 0ns eaHai5i sa.esaE
No. 37-s2 1s square rods. oty ...ia ,,- .ss-a.
No. 38-Can but takes TOO much time. ,lh
~ No. 3D. years months days. tt-5--.r
No. 4o-Don't exactly understand it, -,
No sngle, ,,s st % base 81 and es
ular ll4l6. Bisecting line 1l4S
No $50 five rails high. $50 six rails high.
week. Dec rotsnts. 3 & 25fTa JACK.
-,-----I - March "A. 1868.
Mr.. EpIToR: My spare evenings. which I was
of late consecrated to q new use-instead of attend
ing mat 1ematicsl school. have attended a sing
TO- n.x11 DroF Wall Df N.rw loDI La.
eass o about rs pus Il TSs
pl ins my mistakes in il last weeks paper:
and it appears to me, very becoming. concerning
the town Wsshington Come. because Robin. of
ton. slthonsh did start fiom her. D : -s''--
No: 43.Let AbCp be auadrilatera, circum-
scribing the circle whose center is o. Me are to
the rsd oE snd to points & Contact Of tbs
dSs sids b aSd @ &C. Then the Igst apgIed srisnges
Prove ssss s$as IL sgass Al; SF cS and 81
% have BIZ pius G &C esusis BF plus plus CF as b anu "'
Add DIG to the first number, and DH to the sec
have .AE .pla. De equal All plus III (a). BY the
addition Of ( and G2y We find that BE plus E plus
PLUS ns cD s s Sc m ss Oh
No. 4s.aO4 feet of boards inch thick by 20 inches
No. 40 The numbers are 8. 5:7.s. sles -
No. 47-X equal 80. Y equal 10. A equal 90. q
/ 1 received. last week. very interesting letter
lutions, for which am very thankful. OTIosE.
= = WILsEYvILLE, OHIO. March 90, 1868.
/ ED. .SrATEsMAN-Dear Sir: Presumng that all
is quiet the Potomac. and that military govern
me1t is not yet extended over US. hays resumed
its friends for the it gives me while confined
think that Washington got the cart befo Q the
horse in the wheel puzzle. have been rotating
two apples. The movable one in passing round tn 9
the other appe but if both apples rotate.
each one revolves on l. own axis once In the hrst
case it may Justly said that it makes I Two REVOLT %
sas ANSWERS.
No. s7-Each side Of oetagon. 2,ss chains; diam
:etsr S IS chsl1s; area Of ane & o;f Sos7e acres
else to do. 1t can just take its time.
No. 39-4 years. months and days.
No. 4o-I wish to introduce another bird to answer
below saf feet The seeoad bird the
moment of the first. and fly the rate of % Sc
to Gupsnseys % feet @ each bird would aisht at the
same time; On the hypothenu;e from gate to pin.
gate to Guernsey feet would be sl6.ls feet
No 4l.Anse at base 80 degrees angle at It, inter s
0 od ana e saSses HynoS
ennse - feet. bisectng line ss5 feet perpendicular
No. 42-l44 of rails and 4s of rails. "A rails;
SOLUTION OF PROBLEM NO. 43.
If we join the vertex CAD of of the four angles
of the quadrilaera with the center Of the circle co
by straight line (AC) and draw radii (BC and DC)
to the adjoining points of tangeney % and D:we get
two right augled triangles which have the hypothe
muse (AC) in common and the sides BE- and DC
mutually equal. Hence the sides AB and AD q. O..
the distance from the vertex to the points OF tam
Reney) are also equal. By applying the same pro
to ca n Of the remaining three angles of the
quadrilateral and. then, adding equals to equals,
we find the sum Of two of the opposite sides to be
equal to the sum of the other two. II.
Divide the number 332 into six parts, 20 that if
we add to the first part. take from the second,
multiply the fourth by q divide the third by 2, ex-
tract the square root of the fifth and square the
f,xth part the sun, difference, product, quotient,