All over the world ­yesterday, this birthday photograph of Prince ­William and his ­children was being studied with affection, fascination and, yes, relief.

Affection because there can surely have been no informal royal picture more ­exuberant nor radiating more happiness than this caught-in-mid-air glimpse of ­William, Prince George, Princess Charlotte and Prince Louis leaping from the sand dunes of a ­Norfolk beach.

Fascination because of what it tells us about the present and future status of the monarchy. And relief? That’s simply because the figure behind the camera ­conjuring up such a magical snapshot of her family was the ­Princess of Wales.

For his 42nd birthday, the Royal Family released this caught-in-mid-air glimpse of ­William, Prince George, Princess Charlotte and Prince Louis leaping from the sand dunes of a ­Norfolk beach

Observers will be searching for clues ­everywhere, from where precisely it was taken to its composition. But the central message would seem to ­suggest a much simpler one: after the year from hell for our most photogenic royals, things seem to be getting better.

It can be said with some certainty that the mood in the family home ­yesterday was cheerful. Even so, when William peered into his shaving mirror, he will have seen a face that has noticeably aged in the past 12 months. Still handsome, but the ­reflection will show a profile which is a ­little thinner and the lines a touch deeper.

How could it not after what even his friends acknowledge has been a nightmare year?

The double cancer blow to his wife and his father, the feud with his brother that refuses to go away and the realisation that it is on his shoulders above all that the future wellbeing of the Royal Family ­indisputably rests.

Little wonder then, that when a ­sympathetic friend recently ­gently observed that they were glad they ‘were not him’, William responded with a fleeting but rueful smile.

A year ago, life for the prince seemed blissfully content. He and Kate were ­enjoying a bucolic existence in the solitude of the Windsor estate and their children had settled quickly into a new school and had made friends.

The sadness following the death of Queen Elizabeth had smoothly given way to the optimism inspired by King Charles‘s ­coronation and a new reign.

William himself had taken up fresh responsibilities as Prince of Wales with a buoyant confidence and sent out a message that he would be doing things his way and that might not necessarily be the same as his father’s.

But as he marked his 42nd birthday yesterday, the landscape had bleakly changed. Most men his age know what direction their life is taking, but for William the future is by no means settled.

His priority remains his family, as it has been ever since he and Catherine received the ­devastating cancer diagnosis that followed her successful abdominal surgery ­earlier this year.

But the competing pressures on his time have never been more sharply illustrated than over the past seven days.

A week ago, he was on horseback at Trooping The Colour, a pageant made all the more spectacular by the first public appearance for 173 days of a beaming Kate, alongside their children George, Charlotte and Louis.

A day after the heartache revealed by her moving statement about the good days and bad days of her cancer treatment, her ­presence on Horse Guards Parade was both a tonic and a reminder of how much she has been missed.

The Princess of Wales made a glorious return to public life with her family at the Trooping the Colour ceremony

By Monday, William was flying solo once again, attending ­Windsor’s Garter parade in plumed cap and cape. Two days later, he stood in for the King — still receiving medical treatment himself — on the second day of Royal Ascot, where he shared a carriage with his stepmother.

And on Thursday he flew to ­Germany to support the England football team as it played out a lacklustre draw with Denmark in the Euros, his disappointment as visible as that of the tens of ­thousands of other English fans gathered in the Frankfurt Arena.

If there was any consolation, he was home in time for his birthday and the hand-crafted greetings cards that his children love to make for such occasions.

In a Royal Family which ­celebrates some kind of ­anniversary almost every day of the year, birthdays can sometimes be overlooked — but not in Kate and William’s home.

Indeed, the health crises in which the family has been plunged are bookended by birthdays: Kate’s 42nd in January, her ­husband’s yesterday.

William stood in for the King — still receiving medical treatment himself — on the second day of Royal Ascot, where he shared a carriage with his stepmother

It is unlikely these anniversaries will be looked back on especially fondly — certainly not by William. At times this year he has been infuriated by the global social media firestorm surrounding his wife’s health.

Her long absence from the royal front line triggered multiple ­conspiracy theories about her well-being and her whereabouts. She was subjected to a barrage of trolling that has been both ­upsetting and offensive.

The prince responded with anger and frustration. ‘In a way that has been quite a useful foil,’ says one of his circle. ‘It has added to his resilience, which he has always possessed, and I think it is fair to say it has helped him cope.’

From the death of his mother when he was 15 to the shattering of his ‘forever’ bond with Prince Harry, William has become used to personal setbacks. But nothing has presented quite such a challenge as the events of this year.

Never have the blows come quite so hard or quite so fast. While a smiling William and Kate on Christmas Day at Sandringham were a picture of youthful vitality, it was to be last time the princess would be seen in public for almost six months.

It was not until March 22 that Kate revealed in a deeply personal video recording that post-­operative tests had found cancer present and that she had begun preventative chemotherapy

Within weeks, the public was reeling from the news that this supremely fit and athletic young woman had been admitted to ­hospital for planned — but unspecified — abdominal surgery.

Within hours, Buckingham ­Palace announced that the King was to have treatment at the same private hospital as his daughter-in-law — the London Clinic — for an enlarged prostate.

Kate, it was hoped, would be well enough to resume her royal duties at Easter.

In the event, both the King and the Princess were discharged from hospital on the same day. But while Charles was photographed leaving by the front door, Kate left without being seen.

It was an ominous departure and, even after William addressed the public concern for his wife, speculation began growing online about her absence from official life.

Kate and William’s determinedly private approach contrasted sharply with that of the King. Seven days after he left hospital it was revealed by the Palace that Charles had been diagnosed with cancer and had begun treatment.

Matters came to a head when the prince, who had cleared his calendar so he could be with Kate and the children as she ­convalesced from surgery, ­dramatically pulled out of the memorial service for his godfather, ex-King ­Constantine of Greece.

Only later did it emerge that this was the day Catherine’s cancer diagnosis had been received.

But before it could be announced (and it was not until several weeks later), the couple were consumed by the frenzy that followed the revelation that a Mother’s Day picture of Kate and the children, taken by William, had been ­digitally altered.

With no wife and no brother at his side, William and his father have reinvigorated their own relationship

Instead of ending the intense speculation about her illness by showing how she was recovering, the furore over the picture ­intensified it.

It was not until March 22 that Kate revealed in a deeply personal video recording that post-­operative tests had found cancer present and that she had begun preventative chemotherapy. For any other family these ­dramatic developments would be testing enough. For William, this annus horribilis has demanded a balance between offering ­emotional support for his wife and children and continuing his role as the public face of the monarchy while his father receives treatment — a situation set to continue for several more months.

If ever William has needed the support of a brother who was once seen as vitally important to the running of the monarchy, it has been this year.

But for all the honeyed words of so-called friends that Harry is ­prepared to do his bit at a time of royal crisis, that ship has surely sailed.

While the King hankers for the day when he can see his Sussex grandchildren without the ­rancour that seems permanently to ­surround relations with his ­California-based son, William has, as a friend says, ‘turned the page’ on that chapter of his life.

‘Whatever might happen in the future, the trust that was implicit in his relationship with Harry is gone for good,’ they say. ‘Even if it is possible that some kind of ­managed reconciliation could be achieved, it will be never anything more than superficial.’

With no wife and no brother at his side, William and his father have reinvigorated their own ­relationship. Necessity may have forced them to paper over past differences but things between them have demonstrably improved.

The photograph issued on Father’s Day last week of Charles in suit and tie with a football at his feet, alongside William as a ­toddler, was a painful reminder of what an awkward and distant father the Prince of Wales then was. At the time, he was so strung up over Princess Diana and so obsessed with Camilla that he had little time or emotional energy for the boys.

Matters improved as William grew up — Charles could relate to his son’s university years and his time in the Armed Forces. He ­particularly admired the way ­William stubbornly insisted on taking up his air ambulance role.

Intriguingly, it was the arrival of Kate that was to prove the ­significant factor. He could see how good she was, not just for his son but for the House of Windsor, noting on more than one occasion that ‘we’re lucky to have her’.

The temper tantrums that once marked their relationship have passed. Like his father, William has a short fuse but one, ­according to friends, that is ‘getting longer’.

As for the King, he is grateful that he and William have been drawn closer. ‘They don’t talk about the past and Charles feels lucky that the two of them can talk about ‘the job’,’ says one old friend. ‘The illnesses have increased the bond between them, but there is also greater tolerance between the two men.’

This closeness has also given William an appreciation that has not always been evident for his stepmother, Queen Camilla, and the vital part she plays in his father’s life. She not only supports him as he fulfils his duties but keeps him cheerful.

Of course, both have very ­different approaches to duty and their roles. Charles still worries about his son’s custody of the Duchy of Cornwall, the land and property estate from which ­William derives his income. It is, along with the Prince’s Trust, Charles’ most obvious legacy — and a highly profitable one too.

When he was running the duchy, Charles was recognised as a man of the land, with not just an ­abiding love for the countryside but a deep knowledge of rural issues too, from a familiarity with rare breeds of cattle and lambing to hedge-laying and the ­maintenance of dry-stone walls.

With so much on his plate, it is hardly surprising that William has yet to find the time to develop the philosophical zeal for the duchy that his father exhibited over the decades.

The King would also like his son to take on some patronages in the world of the arts and culture, but there is a general agreement that such unresolved matters can be put to one side while Kate’s health remains the number one consideration.

Differences between monarch and heir do remain, especially when it comes to the Prince Andrew scandal. William has long held a grudge against Andrew for being unwelcoming when he first introduced the then Kate ­Middleton to the Royal Family and feels that his father has been too soft on him.

It has led to speculation that it is William who is pushing his father to evict the Duke of York from Royal Lodge, so the Waleses could move in. But, as a friend of the couple noted, taking on Royal Lodge would mean a ­transformation in the way they lead their lives.

One of the main reasons why the couple are so content at Adelaide Cottage, their current home in Windsor Great Park, is because it is a family house and there are no live-in staff. Moving into the vast Royal Lodge would mean having to accommodate domestic staff, something they have long resisted.

For years, William has wanted to be judged by what he has done, not who he is. His Earthshot Prize, the global environmental award scheme — as well as his initiative to end homelessness — is ­testimony to that.

But as he spends his birthday weekend with his family, he may reflect that his greatest achievement is making a success of his role as a father and husband.