The evening times. [volume] (Grand Forks, N.D.) 1906-1914, 1912-01-10
FACTS ABOUT A PACK OF CARDS
CHANCE OF HOLDING SAME HAND TWICE Is NOT VERY LARGE
WHEN WORKED OUT IN HIGHER MATHEMATICS

may seem. to obtain a volume Of wa
ter containing a sufficient number of
drops IT is necessary to imagine a
globe of water with a diameter equal
to $1,000 900 of miles.
If the center of such a globe is TAX
en- at the center Of the SUM-, then
Neptune the remotest planet in the
solar system. would he immersed
therein to a depth no less than 7OO.-
100000 of miles. In other words,
such a ball Of water would have a
diameter about 25 per cent greater
than that of the whole solar system as
at present known. In addition t.
which, remember, the solar system is
practically included in = flat disc, with
i'll one plane only, where
as the ball to which We ave been so
unexpectedly led would extend not on
~ In that plane. but also. and to an
equal extent. upward and downward
from 1t. The relation. in fact. would
be that of a cricket ball to a biscuit.
After the evidence m the sum-
ming up. Thus, firstly, we take one
drop OF water to represent the whole
result of sustained energy Of the hu-
mar race Cor, indeed. more than the
present number thereof), directed at
breakneck speed to only one object
throughout an interval of time EXTEND
ing not into the dawn of history, but
beyond 1t into a period when man had
probably not established his mastery
over the animal creation.
And. secondly, we find that, though
this one drop of water represents a
result so enormous that 1t can hard
" be Srasped. vet the total result to
he obtained is still SO far off that to
represent it on the same scale re-
quireS what is almost described as a
Watery universe.
The result obtained is so surprising
that it will be useful to set out the
calculations by which it is reached, so
as to show that 1t is really correct. In
the first place, the method by which
nc total number of arrangements of
the ffty-two cards is calculated can
be readily explained. For any one Of
the fifty-two may be chosen as the top
card, and when some card has been
chosen. the any one of the fifty-one
remaining cards can be chosen as Sec
n card. so hat the two first cards
may be chosen in order in fifty-two
times ffty-one, Oh 1859 ways.
There then remain fifty cards any
n of which may be selected as third
card. from which it results that the
three first cards can be chosen in or
der In fifty times 1862, or 1S2.6O0
ways. Proceeding thus, it is evident
that the total number of arrange
ments of the f1fty-two cards can he
calculated by multiplying together all
the numbers SO, 81, so etc., down to
!.
Such a calculation presents no diff
ficulty but its length and tediousness;
the result is a number of sixty-eight
figures. the last twelve of which are
show that. on the scale adopted, a
globe of water with a diameter larger
than that Of the orbit Of Neptune
would be needed to represent the to-
tai number of arrangements as given
below. 1t should be mentioned that
the drop" used as the unit in this IL
lustratior is the chemists drop, or
'minim.' of which $50 go to the
ounce, or 76,s00 to the gallon.
Drops vary in size. according to the
conditions under which they are pro-
duced: in an actual experiment in fill
ing a one-ounce measure from a drop
ping-bottle. Three hundred and nine
ty-nine drops We're needed; thus these
drops We're twenty per cent larger
than minims. and with such a drop
as the basis the volume of the inn
mense globe of water we are consider
ing would be correspondingly greater.
The calculations are. of course. dona
by Of logarithms, correct to
that some quantity is more than the
number given. the meaning is that
such a number is correct as far as 1t
goes. but that further figures would
have to be added at the end in order
to set it Out in full. AS the words
billion "trillion.' ETC.. are used with
different meanings in England and in
the United States. it should be men,
toned that the English usage is here
employed. According to this each
billion" is one million times its pre-
decessor. and would be written down
as a / followed by a number of zeros
to six times the number indicated in
name of the 'illion.' Thus one sep
tillion would he written 1 followed
six times seven, or forty-two zeroes.