However, these tickets were not the one-time blue or red pieces of stiff
pasteboard, bearing the name of the circus and the words "ADMIT ONE,"
which were formerly sold at the gilded wagon. These were handed in at
the main entrance, and the tickets were used over and over again.
Sometimes the blue ones sold for fifty cents, and a kind selling for
seventy-five cents entitled the purchaser to a seat with a folding back
to it, though it was not reserved.

But Joe had instituted some changes when he became one of the circus
proprietors, and one was in the matter of the general admission tickets.
He had them printed on a thin but tough quality of paper, and each
ticket was numbered. In this way it needed but a glance at the last
ticket in the rack and a look at the memorandum of the last number
previously sold at the former performance, to tell exactly how many
general admissions had been disposed of.

These numbered tickets were not used over again, but were destroyed
after the day's accounts had been made up. At first Joe and some others
of the officials had had an idea that the man who was charged with the
work of destroying the tickets, instead of doing so, had kept some out
and sold them at a reduced price. But an investigation proved that this
was not the case.

"Some one is ringing in extra tickets on us," stated Joe to the chemist.
"We want to find out who it is and how the trick is worked. So far, we
haven't been able to find this out. As a matter of fact, we don't know
whether there are bogus tickets in our boxes or not. We haven't been
able to detect two kinds. They all seem the same."

"Some numbers must be duplicated," said Mr. Waldon, as he picked up a
handful of the slips Joe had brought. "That's very obvious. The numbers
must be duplicated in some instances."

"Yes, we have discovered that," returned Joe. "But the queer part is,
taking even two tickets with the same number, we don't know which was
sold at our ticket wagon and which is the bogus one. Here's a case in
point."

He picked up two of the coupons. As far as eye or touch could tell they
were identical, and they bore the same red number, one up in the
hundred thousands.

"Now," continued Joe, "can you tell which of these two is the official
circus ticket and which is the bogus one?"

The chemist thought for a moment.

"Have you a ticket--say one issued some time ago--which you are positive
is genuine?" he asked.

"I'm ready for you the