New-York tribune. [volume] (New York [N.Y.]) 1866-1924, 1875-10-16
THE DECIMAL SCALE.

MC1rPLEs on NINE AND SUNS OF DIGITs.
To the razor OF me Tri6uHe.
SIR: While waiting few moments IN book
STORE OF Bond-st yesterday happcnedto pick up the
July number Of The GG!Gry magazine which had not
seen before. when my attention drawn to al article
by Richard Grant White. 10 which was appended the
following fcOnOte:
Ihavc remarked fact however which have never
seen recorded. and which mentioning II 10 account
ants and teachers have found to be new 70 them to my
sIirpfisc-that the combinations OF always produce
figures which are either or the sum OF which Is D.
Thus: 8. IL, y. 80, 10 81 50. ~. 81, 3d. 49, loS
H. 126 aud forth The reason OF this remarkable
fact not pretend hope 10 understand; hut is
uOne the less a safe guide.
Mr. White Is not a mathematician, hence 1t is not to be
wondered at that he words faulty in describing
mathematical phenomenon, and talks about "combina-
tons" figures" etc, in ryodd way. Mr. Whites
broad to he trIe for If he will his multples OF
upward from 1926, he VIII certainly got numbers which
los 279. 2ss. 2e7. 1899. Aud indeed regarding the
number 90. which Mr. white gives one cannot truthfnly
say either that II Is g. that the sum OF MS digs II D.
IL Is true, however that nc sum OF inc dlgits OF any
multiple OF 9is ALWAYS dyIsDS pY y ara ~ ,c e" OF
the smaller muitipieS Is generally ltse me OK ala-
ton OF the general fact Is comparatively simple,
and Of the simpler case. which Mr. White has
observed, II If especially so. aud maKcs us up
pearance nj once on simple examination OF inc nature
OF decimal scale To limit ourselves 70 Mr. Whites
proposition so Tar as Is t,ue iet Us '!ae te @ ~
nultipes Of as fer ~ 80: g. IL II 80 40 o. O3 ~
q Supposing however, We start from and nd by
"a ratio of 10. We have 8 49, ~ 80, &C. where VIC no,
being constant increases by one at every step. THIS
arises from the Of decimal scale since every
additional il registered 10y digit higher by one In
the place since ratio in the present case is an
the digit an the units place remains unchanged
hence tine sum the Gs increases SteddB bg one
IL ascend by ratio one less than 10, we
shall register for time a new 10, While thc
units dgit will decrease by one. II, then, We wish
the sum Of the dgits To remain constant, we must as
cend by IN arhmetca ratio OF instead OF 10. when
digit IN the tens place viii increase steadily by one
before but the digit in the units place VIII at the same
time decrease steadily by one leaving the sum always
the This is true up to 90 from which we start out
anew with similar results and similar explanation In
the way also, may obtain Tor tune Other con-
slant sums. Thus <, II, 20, 49, "a, 80, ", H. 80,
where the constant sum Is g. But IL went another
step should stumble Just before we failed TO
get constant AZ 80; but at 1O7 we would re-
cover ourselves again 107 49, 121 etc. Starting with
z, should make three mlssteps before reaching 100;
g. four mssteps etc. Eleven rrpetiOns OF - how
ever enable finish each 100 with only slight trip
ping INCREASING, however, ascend the hundredsl,
and TO begin the next hundred in similar relative posi-
ton. A J.. CHADWICK
Ia6rson, N. j.. Sept. %, 1875.
CHURCH TAXES AND COLD POTATOES.