President Clinton was to represent the United States of America on a highly formal, orchestrated "state visit" to Great Britain. Air Force One stopped at a bright red carpet along which the President strode to join Queen Elizabeth II in a beautiful, ornate 17th-century coach hitched to 6 enormous matched white horses. The coach proceeded through the streets en route to Buckingham Palace, the President and the Queen alternating between exchanging pleasantries and waving each out their respective windows to the cheering throngs.
At one point, the right rear horse produced a thunderous, cataclysmic fart that reverberated through the air and rattled the doors of the coach. Presidents and Queens are, first and foremost, human beings. Their first reaction was to focus their attentions outside and behave as if nothing extraordinary had happened.
The Queen, steeped in decades of experience living with the mundane and bizarre together, was the first to realise that ignoring what had happened was ridiculous.
"Mr. President, please accept my regrets - - - I'm sure you understand that there are some things that even a Queen cannot control."
"Your Majesty, please don't give the matter another thought; why, if you hadn't said something, I would have thought it was one of the horses."
Update/Correction: While many versions of this joke say it was President Clinton or Bush, according to the book Secrets of the Royals by Gordon Winter and Wendy Kochman, this conversation did happen, but it was "the president of an African Country" and the discussion was slightly different.
Their version, found on page 76, goes as so:
We now turn to a subject some readers might consider rather indelicate. But to reassure them, we must emphasize that the royal family will definitely not be offended. On the contrary, it's old news to them, although we suspect that on reading it here, they will probably fall about laughing all over again. The subject concerns the passing of wind. And this brings us to the most fabulous royal joke of all - which her Majesty actually tells against herself with great relish.
It happened when the Queen was sitting in an open-topped horse-drawn carriage with the president of an African country. One of the rear horses broke wind so violently that it sounded like a thunderclap. Quite involuntarily the Queen heard herself say "I'm terribly sorry ... " Looking astonished, the African president shrugged his shoulders and, leaning toward her so the carriage driver would not hear, whispered: "If you hadn't apologized, I would have thought it was the horse."
The best part of this delectable story is that the Queen rounds it off beautifully with a mock-serious look on her face: "And, do you know, even to this day, I'm still not sure whether he was teasing me - or not."
Excerpt (c) 1990 Gordon Winter and Wendy Kochman
... Sounds like an interesting book... ~jw
Thanks to Ann Mahoney for this information.