, 1883-05-03
I GOO,s EMa lInin.

4 Good E03 gnin.
"FutheT, here is n problem about a
boy who agreed tn work for q farmer for
ayear If the farmer would agree to give
him Il grain Of com the first week, two
grains the second week, four the third,
eight the fourth, and so on, doubling
the amount every week for year. [
wouldn't work for such wages as that.
Only think Of getting a grain Of corn
just one grain for n whole weeks work,
and only two grains for the next week!'
"Well, Henry" said his father, "that
was a good bargain for the boy, but
poor one for tho farmer"
ga poor one for the farmer How
could that be9 A bushel Of corn would
pay the whole years wages
"Hardly, I think. Let's see. This
problem is in rule called 'Geometrical
Progression Have you got that far,
Henry?"
"No, sir, but will be there in a couple
of weeks. 1 was just looking ahead
little and saw this problem"
"Well, let us take lesson in it to-
night, and it will help you when you
get to it in your class. Take your
slate and pencil and begin with /, and
multiply it by 2, and that product by Q,
and SO On until you have doubled it 50
times, as there are 50 weeks in the
year.
Henry went OF it, thinking he would
soon be done, but after working for flf-
teen minutes he said:
81 have filed my slate and have only
got up to SO. Why, it will take good
many grains by the time get through |
But there must be shorter way to do
it. Is there not, father?"
"Not much shorter, but simple arith-
metic. You see is the first term of
the series, Q the second, the third,
the fourth, aud SO on. To find the last
term, or the fifty-second term, you must
keep on multiplying for fifty-one times.
The last product will be the number OF
grains the boy got for the last or fifty
second week., and each product all
through the work is the amount received
for That week. Then, to get how much
he received altogether, you will have to
add these products together"
"Why, that wouId be an awful job,
father. should think they would find
out shorter way"
"And so they have, after you have
found the last term, and to find out the
last term you must go on with your
multiplying. Take some paper and
lead pencil, if your slate is full"
Henry went at it again, and in about
fifteen minutes longer announced that
it was done.
Now, to get the sum, in this case,
all you have to DO is to multiply the last
term by and subtract from the
product"
Henry performed the operation, and
announced the resalb as 1,456, ,593, 257,-
iG3, 8O8 grains.
"Tlat is big SUN, is il not?" asked
his father, with merry twinkle in his
eye.
"Yas, indeed I wonder how many
lpshes il wo2ld make. III go to the
rrio N the morning and shell quart
rnd count the grains; then by multiply
"g ,jnt ty 90 it viii give the grains in
u'!sI4-t, and by dividing that into The
~lolo mglbsr OF grains the boy re-
ue,'"a II win give The bushels"
The next morning Henry won't out to
the crib and brought in enough corn to
I'LL quart measure when shelled. But
counting the grains was a bigger job
than he imagined.
1.-The quickest way, Henry" said his
father, ais to weigh an ounce of corn,
count the grains, multiply that by six
teen to get the number OF grains in O
pound and that by fity-six to get the
number OF grains in bushel."
Henry jumped at the suggestion, and
found that seyenty-fge grains weighed
an ounce, and that there were 67,2O0
grains in bushoI. Then dividing, lie
found that for this years wages the boy
would receive q, l,C75, 494, 902 bushels.
"That is more than has been raised
in the whole United States for iRn voA''