With more than 250,000 acres, the Duke is easily the largest landowner in Britain. He is also by far the most active in inviting members of the public on to his territory, and in explaining rural activities to the urban masses. Although he was partially paralysed in a hunting accident a quarter of a century ago, his energy remains immense, and his enthusiasm for dispensing information unquenchable.
Goodness knows what the children were thinking as their coaches purred slowly up through the park and along the arrow-straight lime avenue to the 17th-century pink sandstone castle standing proud on its hillside. Most seemed temporarily struck dumb by the magnificence of their surroundings; but as soon as they set off round the series of information points, some on foot, others on trailers drawn by tractors, chatter broke out as if flocks of starlings were sweeping round the park.
The Duke sped after them, driving himself in an Argo - a tiny, eight- wheel, all-terrain vehicle - and constantly hailing groups to make sure they were enjoying themselves. "When you've been round," he called out, "will you write to me from school and tell me what you liked best of all the things you saw?"
There was plenty to see, and quite a lot to feel. On the forestry stand the estate rabbit catchers had some amazingly amenable ferrets, docile enough for young visitors to handle them without fear of getting bitten. The warreners explained that rabbits are a menace to young trees, and made no bones about the fact that they kill 40,000 a year of them above ground, besides thousands more that they gas in burrows. "A lot of them go to a dealer in Moffat," the Duke explained. "They're skinned, but have the heads and ears still on. Then they're gutted, packed and sent to Holland, where people eat rabbit all the time."
It was the teachers, rather than their pupils, who tended to blench at this kind of down-to-earth information. The children seemed to accept it for what it was - a fact of nature.
They also stared up in awe at the Douglas firs - among the estate's chief glories - and struggled to grasp the unique significance of these mighty trees. They learnt that the first one planted in England grew from a seed sent home in a matchbox from America by the pioneer botanist David Douglas to his brother, who was clerk of works at Drumlanrig, in 1832. "Practically all the Douglas firs you can see are children of that one tree," the Duke explained - and he went on to enthuse about how the estate supplies the Highland Show in Edinburgh with a pair of trunks for the annual climbing competition. "There aren't many places that can produce trees big enough," he said. "The poles are 90ft tall, with another 10ft sunk into the ground, and men wearing climbing irons and belts go up them in 15 seconds - incredible!"
At ground level one of the foresters felled a small, superfluous fir, and dispensed rounds from its trunk to one or two lucky customers so that they could count the growth rings. "Once we tried to cut a round for every child," said the head forester, Graham Booth. "All we got was a massive queue, and four men cutting wood all day."
The same robust, forthcoming friendliness was evident on every stand. The blacksmith, working red-hot metal on his anvil, proved an irresistible attraction.
The atmosphere in the farm tent, which housed a calf and some piglets, tended to make the visitors go "Phworr!", but once they had become acclimatised, they found the piglets adorable. The maintenance staff exhibited a new window they had made for the castle - one of 365 in the building - and said that it had taken 16 years to re-roof all the building's turrets with lead.
In the gamekeepers' pavilion an arsenal of traps and rifles fascinated the boys. "Me and my dad are shooting rooks," proclaimed a 10-year-old. "He's got a 12-bore, and I've got an air-rifle." When quizzed as to whether he had opened his own account yet, the budding marksman admitted, "Well - I nearly got one, but actually I shot the roof."
The adventure playground was supposed to be off limits until the formal business of the day had been completed; but shrieks of excitement betrayed the fact that some of the visitors had broken in prematurely. Then everyone congregated for the highlight of the day: the ceremonial felling of an ancient beech which had died a natural death. Even if no bets were placed, there was certainly a competition to guess the tree's age. Like a diminutive soccer crowd, the fans lined up at a safe distance along a rope, a lone chain sawyer went to work, and when the giant toppled with an earth-shaking crash, a tremendous cheer went up. The tree had been so long dead that its rings proved difficult to count, but by general consent its age was put at 170 years.
As I left, the Duke was still firing off facts like a catherine wheel. "You know we've got two herds of wild goats, one here and one at Langholm? They're quite large, and incredibly smelly... Fences? There are 5,500 miles of them on the Queensberry estate alone. They'd reach from here to San Francisco. They all have to be maintained, and they don't produce a penny..."
I cannot believe that any child left Drumlanrig without having gained some substantial benefit. Never mind that heavy showers kept sweeping over us, or that trainers got soaked in the wet grass. The vast majority of the boys and girls had been closer to the land, and to reality, than they had ever before been in their lives.