I hastily disclaimed any intention of obtruding my foolish dollars, and he went on: 

“Your letter surprised me not a little.  I thought you would be the last person in the world to presume to an alliance here.  But having a regard for you personally”—­and again I saw malice twinkle in his small eyes—­“and still more regard for Abscissa’s happiness, I have decided that you shall have her—­upon conditions.  Upon conditions,” he repeated, with a half-smothered sneer.

“What are they?” cried I, eagerly enough.  “Only name them.”

“Well, sir,” he continued, and the deliberation of his speech seemed the very refinement of cruelty, “you have only to prove yourself worthy an alliance with a mathematical family.  You have only to accomplish a task which I shall presently give you.  Your eyes ask me what it is.  I will tell you.  Distinguish yourself in that noble branch of abstract science in which, you cannot but acknowledge, you are at present sadly deficient.  I will place Abscissa’s hand in yours whenever you shall come before me and square the circle to my satisfaction.  No!  That is too easy a condition.  I should cheat myself.  Say perpetual motion.  How do you like that?  Do you think it lies within the range of your mental capabilities?  You don’t smile.  Perhaps your talents don’t run in the way of perpetual motion.  Several people have found that theirs didn’t.  I’ll give you another chance.  We were speaking of the Problem of the Couriers, and I think you expressed a desire to know more of that ingenious question.  You shall have the opportunity.  Sit down some day, when you have nothing else to do, and discover the principle of infinite speed.  I mean the law of motion which shall accomplish an infinitely great distance in an infinitely short time.  You may mix in a little practical mechanics, if you choose.  Invent some method of taking the tardy Courier over his road at the rate of sixty miles a minute.  Demonstrate me this discovery (when you have made it!) mathematically, and approximate it practically, and Abscissa is yours.  Until you can, I will thank you to trouble neither myself nor her.”

I could stand his mocking no longer.  I stumbled mechanically out of the room, and out of the house.  I even forgot my hat and gloves.  For an hour I walked in the moonlight.  Gradually I succeeded to a more hopeful frame of mind.  This was due to my ignorance of mathematics.  Had I understood the real meaning of what he asked, I should have been utterly despondent.

Perhaps this problem of sixty miles a minute was not so impossible after all.  At any rate I could attempt, though I might not succeed.  And Rivarol came to my mind.  I would ask him.  I would enlist his knowledge to accompany my own devoted perseverance.  I sought his lodgings at once.

The man of science lived in the fourth story, back.  I had never been in his room before.  When I entered, he was in the act of filling a beer mug from a carboy labelled Aqua fortis.