`You might,' the candid hero admitted; `though such obtuseness would certainly be phenomenal. Still, the event is possible. So I must ask you to grant one more Hypothetical.'

`Very good. I'm quite willing to grant it, as soon as you've written it down. We will call it

(D) If A and B and C are true, Z must be true.

`Have you entered that in your note-book?'

`I have!' Achilles joyfully exclaimed, as he ran the pencil into its sheath. `And at last we've got to the end of this ideal race-course! Now that you accept A and B and C and D, of course you accept Z.'

`Do I?' said the Tortoise innocently. `Let's make that quite clear. I accept A and B and C and D. Suppose I still refuse to accept Z?'

`Then Logic would take you by the throat, and force you to do it!' Achilles triumphantly replied. `Logic would tell you "You ca'n't help yourself. Now that you've accepted A and B and C and D, you must accept Z!" So you've no choice, you see.'

`Whatever Logic is good enough to tell me is worth writing down,' said the Tortoise. `So enter it in your book, please. We will call it

(E) If A and B and C and D are true, Z must be true.

`Until I've granted that, of course, I needn't grant Z. So it's quite a necessary step, you see?'

`I see,' said Achilles; and there was a touch of sadness in his tone.

Here the narrator, having pressing business at the Bank, was obliged to leave the happy pair, and did not again pass the spot until some months afterwards. When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his note-book, which appeared to be nearly full. The Tortoise was saying `Have you got that last step written down? Unless I've lost count, that makes a thousand and one. There are several millions more to come. And would you mind, as a personal favour--considering what a lot of instruction this colloquy of ours will provide for the Logicians of the Nineteenth Century--would you mind adopting a pun that my cousin the Mock-Turtle will then make, and allowing yourself to be re-named Taught-Us?'

`As you please!' replied the weary warrior, in the hollow tones of despair, as he buried his face in his hands. `Provided that you, for your part, will adopt a pun the Mock-Turtle never made, and allow yourself to be renamed A Kill-Ease!'

`WHAT, nothing to do?' said Uncle Jim. `Then come along with me down to Allen's. And you can just take a turn while I get myself shaved.'

`All right,' said Uncle Joe. `And the Cub had better come too, I suppose?'

The `Cub' was me, as the reader will perhaps have guessed for himself. I'm turned fifteen--more than three months ago; but there's no sort of use in mentioning that to Uncle Joe; he'd only say, `Go to your cubbicle, little boy!' or, `Then I suppose you can do cubbic equations?' or some equally vile pun. He asked me yesterday to give him an instance of a Proposition in A. And I said, `All uncles make vile puns.' And I don't think he liked it. However, that's neither here nor there. I was glad enough to go. I do love hearing those uncles of mine `chop logic', as they call it; and they're desperate hands at it, I can tell you!

`That is not a logical inference from my remark,' said Uncle Jim.