Whilst the words of this poem have been quoted here before, there does not appear to be an associated tune.
I was walking on the Isle of Wight when my wife pointed out to me that I was no longer quite as young as I had been! This poem (learnt in school) then occurred to me, together with a rhythm from our walking. I decided it would fit well with "Rolling Down to old Maui", but with a need to repeat the second four lines of each verse as a chorus.
I decided to use it at the BBC club last night. It was purely coincidence that the Daily Telegraph printed a cartoon of Gordon Brown ("and yet you incessantly stand on your head") on the same day.

As it turned out, I sang it with repeats of the last 4 lines for verses 1 to 3, but an allargando on the second four lines of verse 4 to bring it to a close.

FATHER WILLIAM.

"You are old, Father William," the young man said,
"And your hair has become very white;
And yet you incessantly stand on your head.
Do you think at your age it is right?"

"In my youth," Father William replied to his son,
"I feared it might injure the brain,
But now that I'm perfectly sure I have none,
Why, I do it again and again."

"You are old," said the youth, "as I mentioned before,
And have grown most uncommonly fat;
Yet you turned a back sommersault in at the door.
Pray, what is the reason of that?"

"In my youth," said the sage, as he shook his grey locks,
"I kept all my limbs very supple
By the use of this ointment—one shilling the box.
Allow me to sell you a couple."

"You are old," said the youth, "and your jaws are too weak
For anything tougher than suet,
Yet you finished the goose, with the bones and the beak,
Pray how did you manage to do it?"

"In my youth," said his father, "I took to the law,
And argued each case with my wife,
And the muscular strength which it gave to my jaw
Has lasted the rest of my life."

"You are old," said the youth. "One would hardly suppose
That your eye was as steady as ever,
Yet you balanced an eel on the end of your nose.
What made you so awfully clever?"

"I have answered three questions and that is enough,"
Said his father. "Don't give yourself airs.
Do you think I can listen all day to such stuff?
Be off, or I'll kick you down stairs!"

From Alice's Adventures in Wonderland, by Lewis Carroll.