The day was brilliantly clear, with only a few clouds drifting on the easterly wind; but the birds were so high that at first we could not see them. Then, through binoculars, someone spotted a skein coming down from the north. Again we heard the magical cry - too staccato and harsh to be called beautiful, but intensely moving, because it spoke of huge distances and changing seasons: the geese had come from the ends of the earth, and by their passage were announcing that winter is on its way.
The noise seemed to startle the deer we had been watching. Perhaps because these were the first migrants of the autumn, and their voices were unfamiliar, the hinds lifted their heads, looked about, and then ran farther up the hill.
The geese were pinkfeet, on their way from breeding sites in Greenland and Iceland to winter quarters in Britain. As always, they were flying in V-shaped formation, so that the lead bird took the brunt of the wind, and was working harder than its followers, who were coasting in each other's slipstream.
Many of their calls were probably contact notes, for families migrate together within the skeins, and like to keep in touch. But now and then a sudden outburst of cackling seemed to indicate doubts about direction: after fanning out widely, the angled lines swung back together on a new heading.
In spite of intensive study, much remains mysterious about how geese and swans navigate. Bewick swans, which nest on the Russian arctic tundra, and winter in Britain, travel mostly overland on their 2,500-mile journeys, and seem to steer by rivers, coastlines and other features that they recognise.
Species which cross oceans appear to rely on celestial information, steering by the position of sun, moon and stars, or even just by the varying brightness and direction of the light. Three years of research into whooper swans, carried out by the Wildlife and Wetlands Trust at Slimbridge on the Severn, showed that during their migration between Scotland and Iceland, whenever the sky became obscured, by day or night, the birds landed on water and waited for the cloud to clear.
Satellite tracking revealed that the routes taken by the swans were extraordinarily direct. In good weather they flew as accurately to their chosen destinations as any light aircraft could have done, and the same birds used the same tracks in both directions. Their fuel is the fat which they build up before take-off - as much as 20 per cent on top of their normal weight - and so well is their physiology organised that even if they are blown off course by gales, they have the reserves to complete the journey.
At this moment the Bewick swans are preparing to leave their summer grounds in the far north. Two factors trigger their departure: the onset of cold weather, and the shortening of daylight hours.
At the first hint of frost, any birds that have not bred take off for the warmer south. Those with broods wait as long as they dare, so their cygnets can gain strength; but there comes a cruel moment when increasing cold forces the parents to abandon any offspring too weak to fly. The timing of winter's advance is critical: if frost clamps down hard next week, many cygnets will remain earth-bound, doomed to die of starvation and cold.
The survivors will fly south in a series of hops, travelling at maybe 50 mph, touching down to feed on grass or pondweed, and starting to arrive here in three weeks' time. Between 8,000 and 9,000 of them winter at various sites in England, but the main source of information about their migration has been the 400-odd birds which come to Slimbridge.
There, every Bewick swan is known individually by the unique black-and- yellow markings on its beak, and records built up over many seasons graphically illustrate not only the birds' marital fidelity, but also the hazards which they face in transit.
Last year - as shown in the BBC's television programmes Heading South - two big males, Abelhard and Pedro, were fitted with radio transmitters and tracked by satellite as they headed for the tundra. Abelhard continued to transmit until he reached his breeding ground on Kolguyev Island, at 69.06 north, and in the autumn he returned safely to Slimbridge.
Pedro, in contrast, went off the air during his outward journey over Denmark and has not been seen again. From X-rays taken earlier, he was known to be carrying two separate charges of lead shot - so the presumption must be that he fell victim to some unscrupulous northern gunner. Fingers crossed that Abelhard has the luck or cunning to escape a similar fate.