Kate makes climbing down from a tractor look effortless and jokes with Isle of Bute locals she is going for a swim in the ice-cold sea

This is the moment the Princess of Wales effortlessly climbed down from a tractor before cheekily suggesting she was going for a swim off the Isle of Bute – despite sea temperatures dipping to a chilly 13C (55F).Kate and Prince William were enjoying their first official visit to the idyllic Scottish island, which sits off the western coast in the Firth of Clyde, to celebrate its community spirit and volunteering ethos.It came after a war of words broke out this week between William's father King Charles and uncle Earl Spencer over the latter's new memoir about Princess Diana. New footage shows the royal couple, known as the Duke and Duchess of Rothesay when in Scotland, taking in the sights and enjoying a royal walkabout with local residents on Thursday. In the latest clip, Kate can be seen emerging from the cab of a tractor, with Prince William behind the wheel, as the couple joined local residents on a beach litter pick.The Princess looked stylish in a chic autumn ensemble, with a chocolate brown trench coat layered over an olive green ribbed turtleneck sweater, topped off with an olive Bakerboy hat.After opening the door, Kate took no time to swing herself round and jump down onto the beach, before slamming the tractor door shut – without even the slightest of stumbles.It's not the first time Kate has shown off her natural athletic ability while staying chic. Kate can be seen emerging from the cab of a tractor, with Prince William behind the wheel, as the couple joined local residents on the Isle of Bute on a beach litter pick Kate took no time to swing herself round and jump down onto the beach, before slamming the tractor door shut - without even the slightest of stumbles Kate left royal fans in awe as she showed off her natural athletic ability while staying chic Princess Kate was later seen joking with the crowd: 'Next time I'm going to go for a swim' The Princess of Wales made the joke knowing that sea temperatures around the island can dip to as low as 7C during winter Kate also revealed to the crowd that Princess Anne likes to sail around the Isle of Bute Last October, the Princess of Wales left royal fans 'in awe' after she seamlessly climbed down a flight of narrow stairs after peering into a cockpit during a visit to RAF Coningsby in Lincolnshire.She amazed observers at the time by flawlessly strutting up and down an aircraft's boarding stairs in four-inch navy stilettos from Stuart Weitzman.After she had finished peering into the plane, Kate then followed the pilot, perfectly climbing the narrow stairs backwards without stumbling.Reacting to the latest video, fans applauded the royal for her natural grace.One wrote: 'Elegance, Catherine is thy name. Even getting out of a tractor.'Another drew comparisons to her visit to RAF Coningsby, adding: 'Truly. It's like going up and down the airplane stairs.'A third said the royal must have 'some serious arm strength' because tractor doors 'weigh an absolute tonne'. The couple were later seen on a royal walkabout happily chatting to dozens of residents on the Isle of Bute in Scotland and posing for selfies.In another video, Princess Kate can be seen joking with the crowd: 'Next time I'm going to go for a swim, apparently there's a sauna that appears, live music, apparently that's really good.'Onlookers laughed at her humorous suggestion, with locals acknowledging the water temperature would likely feel too cold for all but seasoned swimmers. During the winter months, sea temperatures around the island can dip to as low as 7C (45F).Referring to Princess Anne's love for the island, she added: 'The Princess Royal comes sailing around here, I can see why. She often shows us her photographs. It's really beautiful.'While on the island, the couple also visited Bute Shinty Club and watched an under-17s match from the side-lines alongside locals.When it was the couple's turn to try the sport – which like hockey is played with a curved stick and small, hard ball – they quickly learned hand-eye co-ordination is key as they practised taking penalties. The royal couple were seen driving a tractor as they joined Beachwatch Bute on a litter pick Kate looked stylish in an autumnal ensemble featuring a chocolate brown trench coast and Bakerboy hatWilliam fluffed his first shot, with the ball moving just a few inches, before making solid contact to cheers from the spectators.Kate fared little better at the start, swinging and missing – but her next shot was cheered by the crowds as it flew at the goalie.She then peppered the goal with more shots, almost hitting members of the press who were closest to the netting and saying 'sorry' in apology.The couple chatted to the crowds after their shinty display and Kate told content creator Andy McAlindon, known as Andy the Highlander, who was stood beside the goal: 'I was a bit worried I was going to take your teeth out.'Former Bute shinty player Tom McMillan said: 'I think they did very well, Kate hit the ball better than William and she really got into it and was lining the balls up.'They ended their day at the community-owned Anchor Tavern Pub and Hub in Port Bannatyne and William praised their model, where a large number of volunteers help keep the project financially viable, and Kate described it as something 'special'.William and Kate arrived on Bute at their namesake town of Rothesay, arriving by ferry from the mainland.They toured the islands of Iona and Mull in the Inner Hebrides last year. Kate and William meet people outside the Anchor Tavern Pub and Hub in Port Bannatyne Members of the public watch in Port Bannatyne during the royal visit on Thursday afternoon Prince William meets a group of schoolchildren in Port Bannatyne on the Isle of Bute Their trip came amid a public dispute between the King and Earl Spencer, who claims in a new book about his late sister Diana that Charles told him 'rest assured, we'll forget her soon enough' days after her death.Further claims from the book – serialised in the Daily Mail – said the King sounded 'giddily elated… like a lottery winner' when he rang the earl following the princess's death.In other passages of the book the earl described how his sister drove 'more than once' to the cliffs at Beachy Head in East Sussex and was 'contemplating ending it all', adding that 'her love for her sons stopped her from going further'.The excerpt went on to claim Diana told her brother 'my husband is in love with his valet' after telling him she was going to get divorced.The palace has yet to respond to the latest claims but a spokesman said on Wednesday that 'fraternal grief can cloud reason'.READ MORE: King at war with Diana's brother after astonishing response to Earl's claim that he said she would be 'forgotten' days after her death