Three cheers for the Big Yin and his very cheerful cheerio!

ThE lingering goodbye is a celebrity’s canniest trick. Frank Sinatra invented it with a succession of farewells and comebacks that lasted 20 years.

But even Ol’ Blue Eyes would have to admire the way Billy Connolly savoured his leisurely sign- off in Ultimate World Tour (ITV), a fond look back at the Scotsman’s travels over a quarter of a century.

Pottering near his home in Florida and harking back to adventures from the North Pole to New Zealand, the Big yin spent a happy hour composing various epitaphs for himself.

Every time he seemed to have the last word, he thought of something else to say. ‘I’ve always got hope. People are good basically,’ he said, wistfully summarising his life’s philosophy. ‘The world’s a joyous place and should be treated as such. It’s supposed to be fun,’ he added.

This was a lovely sentiment, so good that a few minutes later he popped back to preach it again: ‘People are pretty much the same everywhere you go. Tolerance is the answer.’ he signed off with a flourish: ‘From the ageing hippie.’

But if this was Billy’s last will and testament, there were another few pages to go. ‘ I’d like to die in Scotland. I’d like to be planted there eventually, in Loch Lomond.’

Just as we waved him a final melancholy bon voyage, he hove back into view, now at the wheel of a schooner. ‘Wherever you are and wherever your adventures might take you . . . cheerio!’ he cried.

Billy has been ill with cancer and Parkinson’s disease, and the evident joy he takes in everyday life must have played a great part in helping him stay so vigorously active. he’s a testament to the power of positive thinking.

he also seems to spend a lot of time studying the Florida crocodiles which, he says, have been around for 200 million years. Aeons from now, there will still be crocodiles — and perhaps Sir Billy Connolly, bidding one more elegaic farewell to the world.

The happy sadness of his curtain calls was matched by bucketloads of tearful laughter on This Is My

Song (BBC1), in which amateur singers got the chance to record with top producers in a professional studio.

They picked numbers that celebrated family bonds and triumphed over hardship, and while they poured their hearts out at the mic, mums and dads bopped in the background, wiping their overflowing eyes.

With four discs to cut and stories to tell, this was a fragmented format that suffered from the lack of a presenter. It needed one figure, such as choirmaster Gareth Malone, to mentor and coach the singers before they reached the soundbooths.

What we got instead were raw and enthusiastic performances that mostly sounded like they were at the start of a musical adventure, not the end.

This was especially true with the first duo, grandfather Ronnie and 23-year-old grandson Jordan, who took it in turns to sing solo verses of Stand By Me when, with more training, they could have harmonised much more sweetly.

The exception was a shy 13-year-old named Jasmine, who coped with anxiety by shutting herself in her bedroom and singing her heart out.

In the studio, with her parents trying nervously to give her encouragement, she clammed up. But at last she relaxed enough to reveal an astonishing natural talent, a mature voice of such purity that it brought my skin up in goosebumps.

As Jasmine lost herself in the song, this show delivered five minutes of real joy.