The cockerel in the backyard of our hotel in Funchal started work early, very early. But getting up early is no great hardship in Madeira -- an island of perpetual spring where man, beast, and plant show an unbounded enthusiasm for living.

It was a spur-of-the-moment decision that had brought us from the gray tedium of Scotland in early March to this sun-blessed island. And now we stood with two light haversacks as our only luggage, together with a tiny booklet hot from the printers.

It was this last item that really decided us to go. At first sight ''Landscapes of Madeira'' by John and Pat Underwood seems a typical rambler's guide to yet another island paradise, but the walks it lists are rather different. There are not many places in the world where you can find a 10-mile walk at an altitude of 3,000 feet that takes you through dramatic mountains ablaze with flowers and leads you beside chuckling water courses and into mimosa and eucalyptus forests heavy with the scent of blossom and droning with contented bees and -- wait for it -- never involves you in a gradient of more than 1 in 20.

The whole secret of the walking scene on Madeira is, like every other facet of life here, tied up in the mountains. It is their presence running across the center of the island that persuades the rain brought in from the Atlantic by northeast winds to fall on their Northern slopes. The water, coupled with the abundant sunshine and the fertile basalt-based soil, has justified the construction of one of the most sophisticated irrigation systems in the world, with over 1,300 miles of channels criss-crossing the island.

When the first irrigation channels or ''levadas'' were being hewed out of the unyielding basalt by black and Moorish slaves hundreds of years ago, nothing could have been further from their minds than the needs of sun-seeking holidaymakers of the 20th century. And the men suspended by rope in wicker work baskets over 2,000-foot drops as recently as 1970 thought only of the extra lettuces and grapes they would grow as a result of their labors. But the fact remains that the level and well-surfaced maintenance and access paths that came as an adjunct to the levadas also serve to open up for the visitor the beautiful interior of Madeira.

Because of the need to exploit every inch of the limited reserves of soil in this mountainous land, the levadas take you to remote and beautiful corners of the island inaccessible by any other means. Deep into the folds of the hills, the two-foot wide channels carry their life-giving liquid. Here where the steep slopes are terraced into tiny plots as small as 150 square feet (the average holding in Madeira is 2.5 acres) the water is meticulously metered out to each plot by the ''levadeiro,'' whose job it is to apportion the volume of water due to each landowner. Fierce feuds over water rights are easily started.

Often the levadas are swallowed into the bowels of the mountains, only to reappear miles further on in another valley. The footpath generally continues beside the levada through the tunnel, and for the adventurous a torch and protective headgear are the only passports you require to find yourself another mountain jewel in Madeira's interior.

To reach the level of the levadas needs some sort of effort but often only that of looking up a local bus timetable and being sure that you turn up at the bus stop well in advance of the scheduled departure time. Madeira has a comprehensive and very efficient bus service; it is also very, very fast. Drivers watch their clocks as if their jobs depend on them. Often they leave early, driving with great enthusiasm and flair, though some prefer to call it recklessness. For about 30 cents, you can bump and rattle round a hundred hairpin bends, all at breakneck speed, and dip and soar from the ocean to the peaks before being popped out at your destination 3,000 feet up in the silence of the mountains with the swirling dust plume of the bus plummeting toward another village in the next valley.

John and Pat Underwood's booklet gives step-by-step directions to guide you on your chosen walk, and all routes start from Funchal, Madeira's capital. Generally you will find a short climb is necessary to take you off the road to the levada, but there is so much to see you will hardly notice it. Broods of children, spotlessly clean, peer from the windows of tiny houses clinging to the hillsides. Goats and rabbits, chickens and pigs add to the volume of life. Frogs croak incessantly from warm pools of water, and everywhere flowers blossom profusely.

The sound of chuckling water heralds your arrival at the levada. From here on , while the water is beside you, the going will be easy. Within minutes you will leave the village sounds behind and enter the great quietness of the mountain world. It seems inconceivable that a matter of a few miles away sun worshippers in the concrete five-star hotels are stretching their bodies out for their daily roasting and flicking their fingers for the first refreshment of the day. Who would believe that just over the ridge in front, Funchal is teeming with its 100 ,000 inhabitants (1/3 of Madeira's total population). Here all is silence, no roads, no traffic, not even tractors can cope with these steep hillsides.

That is not to say there is no activity, but you can be sure it will be in harmony with nature. Perhaps a family of Madeirans tending their neat terraces, harvesting potatoes from beneath the vines. They will look at you with shy curiosity, but greet them with 'bom dia' (good morning) and their faces will break into a smile of welcome. They don't see many visitors up here.

Follow the paths to all quarters of the island, and one day you will be among wild hydrangeas. The next day you could be excused for thinking you have stumbled into the rain forest; and yet another day will find you among freesia and orchids.

It is Madeira's geography and associated climate that allows flora native to all parts of the world to flourish here. With its mountains rising from the sea to 6,000 feet - the second highest sea cliff in the world rears 1,800 feet at Cabo Girao - Madeira has within its 31-mile by 131/2-mile frame, scenery as varied as can be found anywhere in Europe.

In one hour you can move from the dry southern coastland through the sugar cane and banana belts to the terraced hillsides burdened with vegetables, vines, and flowers. And then above them, in areas often shrouded in mist, there are the willow plantations around Camacha, where the wickerwork industry is centered. Beautiful forests of mimosa and pine become more sparse as the altitude increases, until giant heather takes over. And finally, there are the barren peaks, where only scrub can withstand the winter storms and snow is not uncommon. There are paths to take you to them all.

To our surprise we met only a handful of tourists on the levada walks during the week we were on the island. We could only imagine that the main body of holidaymakers were following the tourist trail from wicker factory to embroidery exhibition, or maybe they didn't have a cockerel to waken them in time for the early bus!

Our companions in the mountains were indigenous to Madeira; peasant children who guided us on our way when we missed a turning, children whose Sunday afternoon entertainment was shouting at their echoes across deep-forested chasms. Often we sat alone beneath the mimosa and eucalyptus trees and sucked fresh-picked oranges.

We followed paths between houses hanging in space, tied to the hillside with the vines that covered them. We watched girls busy with their intricate embroidery, working in the only factory they would ever know, perched on the warm tiles of their houses. We ate the delicious espada (swordfish), harvested from 2,000 feet down in the ocean depths by fishermen who brave the often storm-racked seas in their small, brightly colored boats.

We came away enchanted by this beautiful island, our visit epitomized by the memory of a dark-eyed little girl to whom we waved as we descended one evening from the mountains. She waved back coyly, then disappeared. Moments later the patter of her bare feet on the track behind us attracted our attention. In her eyes shone a gentle Madeiran smile; she couldn't speak our language, but in her hands she held out a spray of red roses plucked from the pathside. Practical Information:

Madeira is administered by Portugal, and Portuguese is spoken by nearly everyone.

As Madeira's airport is not able to take jumbo jets, owing to the length of its runway, most long-haul flights land at Lisbon, where passengers change aircraft for the last leg of their journey. There are regular flights from Lisbon to Funchal.

Accommodations on the island cater to every taste and budget from ''pension'' to five-star hotel. A typical ''pension'', such as the Pension Flamenga, two minutes from the town center, costs about $7 for bed and continental breakfast. Evening dinner in a reasonable restaurant costs $7 for a three-course meal. At the other end of the scale, the world-renowned Reid's Hotel or the Hotel Sheraton offer five-star services at five-star prices. Most of the hotels are situated on the edge of Funchal, although there are one or two tourist complexes to the east at Canico and Machico.

Madeira's climate is subtropical with no dramatic variations the year round. However, if you take to the hills on a walking expedition, the cool breeze can be misleading, and it is wise to take some protection from the sun. The weather can also vary locally, and rain or mist fall suddenly, so a light anorak and a cardigan are worth taking if you intend visiting the north or west of the island. A torch and non-slip walking shoes should be taken if you are going on walks with long tunnels.

Visit the market at Funchal on Saturday, if you can, and buy orchids and freesia at give-away prices.

Try swordfish if you are eating out, and of course make the most of the beautiful fruit, sweet maypops, bananas, mangoes, custard apples, grapes, avocado, pears, and citrus.

The address of the tourist office in Madeira is Direcao Regional de Turismo da Madeira, Avenida Arriaga 18, Funchal, Madeira. The staff speaks English and will send you a list of hotels.

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