From Jim Smith, I have received the following.
Rob Bath and Andrew Bleby are joint authors of "McArthur's Fart". Rob, from Adelaide, is a freelance screenwriter, occasional playwright and arts administrator. Andy is now in Melbourne where he is director of Victoria's first major youth arts festival.
Their poem has never previously been published although it has been, and is, recited throughout Australia and overseas. Keith McKenry, in a paper presented to the Inaugural National Folklore Conference in 1984, traced its progress through reciters both here and abroad.
The circumstances under which it was written take us back to 1974 in the clubroom of Adelaide University Dramatic Society. Rob and Andrew were musing over needed script for a coming revue. They had decided on a narrative poem about some wildly exaggerated superhuman effort that built to a climax. As they discussed this someone bent over their battered radiator; Rob urged them not to fart because the convection would send it all over the small room. Then one of those little light bulbs appeared in mid-air as they looked at each other and realised they had stumbled on the superhuman feat they were looking for.
And so McArthur's Fart was born.
It was first performed by Andrew Secker, then a law student, in the first night of Jumbo, June 5, 1974. Jumbo played ten performances with full houses each night. A short time later 5UV broadcast a performance recording. In July 1974 a 5UV broadcast was apparently jammed (presumably by the Postmaster General's Dept) soon after the first "fart" was mentioned. Another attempt soon afterwards made it all the way. It was performed by Andrew Secker again a few years later, and was included in a show called The Bionic Cookbook, a cabaret revue written, performed and produced by Rob, Andrew, Rob Brookman, Steve Brown and a couple of others. This semi-professional show played in the Festival Theatre bar, the Amphitheatre, the Flinders University, Adleaide University and Adelaide CAE refectories, for a season at the Box Factory in Adelaide and on a double bill program with Redgum. Its popularity is demonstrated by participation of audiences in the recurring line "On the day McArthur farted and saved the town from drought."
Rob and Andrew have given us a character in McArthur and a town (Bungadell) that have become part of our folklore, household names throughout Australia. They have inspired other writers to draw on them, in the true folk tradition.

There are some differences between the version here and the one already posted.

McArthur's Fart

Back in Donga country
there's a tale the old folks tell
'Bout a bloke whose name is famous
in the town of Bungadell

An' if youse like I'll tell ya
bit about this little town
It's a dry and dusty place to be
until the rains come down

In nineteen twenty seven
when it hadn't rained for weeks
There was bulldust in the billabongs
and dead sheep in the creeks

But the hero of our story
was soon to help them out
On the day McArthur farted
and saved the town from drought

Now no one knew too much
about this joker from the scrub
but they'd heard some yarns about him
from some drovers in the pub

Some said he came from Bunker's Run
and some from Beulah Park
But one thing that they agreed on—
he sure knew how to fart

And this was proved one day
beyond a shadder of a doubt
the day McArthur farted
and saved the town from drought

Well Bungadell was hard and dry
as a three-week stale old crust
The sheep was drinking whisky
and their piss was turned to dust

They had a dam up in the hills
a mile outside of town
which shoulda filled the water tanks
but not a drop come down

They sent a deputation up
to see what could be wrong
And found they had a problem
they hadn't counted on

Old Bert's dead horse was blocking up
the channel from the dam
You'd reckon they could shift it
but the bloody thing was jammed

Fifty blokes with crowbars
bashed it fifty days and nights
But they couldn't shift the bastard
it was stuck there good and tight

They had a stack of water
but they couldn't get it out
till the day McArthur farted
and saved the town from drought

They blasted it with dynamite
but couldn't get it loose
And even Murphy's bullock team
just wasn't any use

"There's only one hope left for us"
said Clancy's brother, Blue
"We'll have to get McArthur
and see what he can do"

The cry went up "McArthur!!
He's the bloke who knows the art
He could send that horse there flyin'
with a well-constructed fart!"

And so the townsfolk waited
for the day to come about—
for the day McArthur farted
and saved the town from drought

At last McArthur came
and all the people gathered 'round
To see the man whose fart
was gonna send the waters down

He came on two big horses
with half his bum on each
A bum so big a man could drive
a tram between the cheeks

McArthur was a quiet bloke
but thorough, through and through
He said "I'll need some food and drink
so see what youse can do."

They started preparations
and laid out a mighty spread
with forty tons of onions
and a pile of prunes and bread

They had fifty tons of blue vein cheese
and fifty kegs of stout
On the day McArthur farted
and saved the town from drought

He sat down with a knife and fork
and really knocked it back
Then finished off the kegs of stout
in thirty seconds flat

McArthur got up slowly
and he turned his bum around
The people all took cover
as they heard a dreadful sound

Like the roaring of a lion
and a chill ran through their hearts
McArthur's body trembled
and let go a mighty fart!

He farted and he farted
till the earth began to shake
The hills they started shaking
and the dam began to break

But still McArthur farted
till it made the thunder crack!
The winds they howled, the lightning flared
the sky was turning black!

They heard it up in China
where the upside-downers dwell
They heard it up in Heaven
and they heard it down in hell!

I hardly need to tell ya
it was really on the snout
On the day McArthur farted
and saved the town from drought

That was how McArthur
saved the town of Bungadell
His memory there still lingers on
and so too does the smell

And even down in Adelaide
they've heard about his Art
And every other year
they hold a Festival of Farts!