re are only forty-eight places in
those four columns."

"That works by the permutation of numbers," was the reply. "You can
arrange two numbers in only two ways, but you can arrange three figures
in six ways, four in twenty-four ways, five in one hundred and twenty
ways, six in seven hundred and twenty, seven in over five thousand ways;
ten would give you over three and a half million ways of changing them
around--and you can see for yourself where forty-eight would land you.
The actual address, street, and house number, and everything else we get
by reference to the schedule."

"That's enough!" cried Hamilton. "I can see now. It would take a sheet
of paper a city block long merely to write down the figures."

"If you wrote down end to end all the possible relations that
forty-eight figures could be put into you'd need a lifetime to write
them down. Why, just with an alphabet of twenty-four letters, Leibnitz
the great mathematician, calculated that over six hundred septillions of
easily pronounceable words, none over three syllables long, could be
arranged. We have room enough to arrange any trifling little matter
like seventy or eighty million addresses, although, in truth, the
gang-punch merely provides the district and section of district, and the
schedule would give the rest if we had any need to refer to it."

"I see," said Hamilton, "and I suppose a number is put on the card which
corresponds with every district number on the schedule. Then I come in
on all the rest of the card."

"Yes, every other hole is punched by the clerk."

"But this machine doesn't seem to punch," the boy objected; "I put in a
canceled card just now and tried it, but when I put the key down,
nothing happened, the key just stayed down."

"It's not supposed to punch until the whole card is ready," the other
explained. "You depress into position the various keys you want until
all the records needed for this one card are ready. Then you can glance
over your keyboard, comparing what might be called your map of depressed
keys with the line of the schedule you are copying. If one is wrong, you
can release that one and put down the correct one in its place, the card
being as yet untouched. You see, each field or division of the card
corresponds with a differently colored section of the keyboard, and this
makes it easy to insure accuracy in reading from the schedule."

"But how is the punching done, then?" queried Hamilton.

"You press th