A Mathematical Problem in Verse

A Cooper and Vintner sat down for a talk,
Both being so groggy, that neither could walk,
Says Cooper to Vintner, "I'm the first of my trade,
There's no kind of vessel, but what I have made,
And of any shape, Sir, -just what you will,-
And of any size, Sir, -from a ton to a gill!"
"Then," says the Vintner, "you're the man for me,-
Make me a vessel, if we can agree.
The top and the bottom diameter define,
To bear that proportion as fifteen to nine,
Thirty-five inches are just what I crave,
No more and no less, in the depth, will I have;
Just thirty-nine gallons this vessel must hold,-
Then I will reward you with silver or gold,-
Give me your promise, my honest old friend?"
"I'll make it tomorrow, that you may depend!"
So the next day the Cooper his work to discharge,
Soon made the new vessel, but made it too large;-
He took out some staves, which made it too small,
And then cursed the vessel, the Vintner and all.
He beat on his breast, "By the Powers!" - he swore,
He never would work at his trade any more.
Now my worthy friend, find out, if you can,
The vessel's dimensions and comfort the man!