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 there,” answered Joe.  “Here’s a coupon that happened to escape destruction.  It was one sold several weeks ago at our ticket wagon, before we noticed this trouble.  I bought the ticket myself, so I know.  I happened to be passing the wagon, and a boy was trying to reach up to buy a fifty cent seat.  He wasn’t quite tall enough, so I reached for him.

“Then, when I looked at him, I saw that fifty cents meant a lot to him.  I gave him back his half dollar out of my own pocket, and passed him in to a reserved seat.  But I forgot to turn the ticket in to the wagon, and it’s been in my pocket ever since.  Now I’m glad I saved it, for it will serve as a tester.”

“Yes,” admitted the chemist, “it will.  It’s a good thing you have this.  But, Mr. Strong, this is going to take some time.  I’ll have to compare all these tickets with the admittedly genuine one, and I’ll have to make some intricate tests.”

“Well, I hoped you might be able to tell me right off the reel which of these coupons were good and which bad,” said Joe.  “But I can appreciate that it isn’t easy.  We certainly have been puzzled.  So I’ll leave them with you, and you can write to me when you have any results.  I’ll leave you a list of the towns where we’ll be showing for the next two weeks.  And now suppose we get at the fire-eating business.”