Tourists surround Machali, a Royal Bengal tiger at the Ranthambhore Tiger Reserve in northern India. (Stephen Brookes/For The Washington Post)

It’s just after dawn, our Jeep is skidding down a rocky track in the semi-darkness, and we’re hanging on for dear life. Suddenly we brake to a halt, and our guide leans over the side of the vehicle, pointing at a paw print in the dust. It’s huge and amazingly detailed; you can almost see the claw marks.

“Tiger,” the guide whispers. “Very fresh.” We peer into the twisting acacia trees around us, the shadows that stretch in every direction. The guide makes a low rumbling noise in his throat. “Tiger mating call,” he says quietly.

India’s Ranthambhore National Park, Tiger Reserve: How to get there, what to do

“Is that . . . really wise?” a woman sitting next to me asks as he makes the sound again. The guide gives us a level look, then wags his head and breaks into a grin. “Tiger is a very intelligent animal,” he says. “Hard to make him fool.”

Five of us are packed into the low, open Jeep, and for the past hour we’ve been crisscrossing the dry hills of Ranthambhore National Park in northern India in search of the Royal Bengal tiger. So far, we haven’t had much luck. Tigers have become almost impossible to find in the wild anymore; their numbers have been devastated over the past century, and fewer than 4,000 are left in the world.

But India is one of the last places where wild tigers can still be seen. About half of the planet’s remaining tigers live here, and we’ve come to the Ranthambhore Tiger Reserve because it might be the most beautiful of India’s 39 such reserves. With about 155 square miles of prime tiger country stretching over the hills of the Indian state of Rajasthan, it may, in fact, be the best place in the world to search for the splendid animals.

We’d been picked up at our hotel at 5:30 that morning by our guide, a tiger expert (and lawyer, curiously) named Mahesh Chaudhary, and a few minutes later found ourselves in a knot of Jeeps at the ancient stone gate that leads into the reserve.

You can’t get into Ranthambhore without a reservation — fewer than 500 visitors are allowed in every day — and we have to wait for the rangers to check our names and tell us which zone we’ll be allowed into.

Mahesh has been a little anxious about the zone issue. Only about a quarter of the reserve is open to tourists, he tells us, and that area is divided into six zones, some of which are virtually tiger-free. But we get Zone 4, and Mahesh gives us a relieved smile. “A very good zone!” he says. “I think we will see a tiger today.”

Maybe. But we know that the odds aren’t with us. Most visitors never get to see one of the animals; there are only about 35 in the whole reserve, and they tend to stay in a core area where humans are not allowed. Only a dozen or so live in the tourist zones, and they’re notoriously solitary beasts, spending most of their time hidden in the forest, sleeping. On the plus side, we’ve come in April; it’s the hot season, and many of the trees have lost their leaves, making tiger spotting easier. We might get lucky. But we know that at best, we’ll probably only get a distant glimpse.

The rangers wave us through, and we set off up a twisting road into the park. Tigers aside, Ranthambhore is a spectacularly beautiful place, full of plunging gorges and jaw-dropping views surrounding the ruins of a 10th-century fort. We veer down a dirt track into the forest, and animals start to appear: a delicate sambar deer with upward-curving horns, black-faced lemur monkeys in the branches of a dhok tree, a herd of Chinkara gazelles on the ridge of a distant hill.

Ranthambhore wasn’t always this Edenic. In fact, it was a battleground for 600 years, the scene of one bloody invasion after another. In the 17th century, the area passed to the Maharajas of Jaipur, who turned it into a tiger-hunting ground, and in 1955 the government made it a wildlife sanctuary. Fifty years of protection have allowed an astonishing array of animals to flourish, and as we lurch over the trails, we come across the tracks of a sloth bear, see a pair of mongooses dart across the road and watch a brilliantly colored kingfisher dive into a pond full of crocodiles. Egrets pose at the edge of a far-off marsh, and a peacock, startled by our jeep, lurches into the air with an indignant squawk.

But . . . no tigers.

It’s not too surprising that tigers avoid us, given that we’ve driven them pretty close to extinction. Of the 40,000 Royal Bengals that roamed India a century ago, only about 1,760 remain — and they’re in peril. The Sariska Tiger Reserve (less than 100 miles from Ranthambhore) lost all of its 26 tigers in 2006, most to poachers supplying markets in China and Tibet, where a pelt can reportedly fetch as much as $12,500 and the organs are sold for medicines and aphrodisiacs. The profit from a single animal can be as high as $50,000, and the risks are low; it’s a wonder any tigers are left.

We’ve spent about two hours exploring the reserve, and Mahesh has guided us into a clearing, when a high-pitched cry pierces the forest. He jumps up and stares into the trees. It’s the alarm call of a deer — a telltale sign that a tiger is around. Tigers prefer to hunt deer, Mahesh tells us, though they’ll eat monkeys and slow, easy prey such as frogs and peacocks.

“And Jeeps full of tourists?” someone asks. Dozens of people are killed by tigers every year, we’ve heard, and India has had its share of dangerous man-eaters, such as the notorious Champawat Tigress, who killed 436 people around the turn of the 20th century.

But Mahesh assures us that we’re in no danger, even though our open vehicle feels a bit like a serving tray, with us as the canapes. The tigers here have grown up with people around, he says, and if we got out of the Jeep they would probably just run away — though he urges us not to test the theory.

“We probably look like candy bars to them,” says someone in the back seat. “Crunchy on the outside, soft and chewy in the middle.” Mahesh admits that this is, in fact, sort of true. Humans can be appetizing to older tigers who have lost some of their teeth, since we lack shells, fur or fang-proof packaging of any kind. Plus, we’re slow. And not always particularly smart. Mahesh tells us that in fact someone was just killed in Ranthambhore: a local villager who went into the forest with his donkey to collect firewood. The tiger went for the donkey; the villager responded by throwing stones. The tiger took offense, and that was the end of the villager.

The deer cries again, and we follow the sound through the trees, emerging into a dry streambed where several other Jeeps and two of the lumbering, 20-seat vehicles called “canters” have pulled up, full of animal paparazzi like us. The sun is higher now and the heat is scorching, but we barely notice. Everyone has their lenses and high-powered binoculars aimed into a patch of tall grass 50 yards off the road, where one of the rangers has seen a bird fly off with a piece of meat in its mouth, a good sign that there’s been a kill.

“Machali is in there; this is her territory,” Mahesh tells us in a hushed voice. “She would have made the kill last night and returned today to eat it.” Her name is officially T-16 (all the Ranthambhore tigers have these bureaucratic labels), but the rangers have given her a nickname taken from a distinctive pattern on her right cheek. “Machali,” it turns out, means “fish.”

We creep up the dirt track, and suddenly one of the guides holds up his hand and points: Machali has appeared, gliding through the grass parallel to us about 30 yards away. She’s just a flash of stripes at first, her face a tan disk in the pale grass, and we hold our breath, expecting her to vanish into the trees. But suddenly she pauses and seems to sniff the air. And then she starts walking toward us.

It’s hard to describe the feeling — the elemental terror — of a tiger approaching you in the wild; a woman behind me has literally climbed on top of the person next to her, which gives you the general idea. Machali clears the long grass, and we can see her now in all her fearful symmetry. She’s magnificent — nine feet long and more than 300 pounds — and frighteningly powerful, gliding over the rock-strewn ground. Her eyes never leave us. Pausing by an acacia tree 30 feet away, she flicks her tail and gives us a long, cool look.

The only sound is the click of cameras and the faint whimpering of the woman behind me. Machali starts moving toward us again and in a moment is so near that with a jump she’d be in the Jeep. Even Mahesh is looking alarmed. We can see into the tiger’s pale green eyes now, trace the labyrinth of marks that run, like ancient hieroglyphics, across her face. It’s mesmerizing. No one can move — we’re caught in some kind of primal encounter, some primitive memory of being hunted in the forest before we even became human. Ten thousand years of civilization suddenly evaporate. And now, just 10 feet away, Machali stops and watches us — a cruel and unknowable god about to decide our fate.

And then. . . .

She yawns.

She yawns and strolls almost casually between the Jeeps. The god isn’t interested in us at all; she just wants to cross the road, and we are in the way. Her power, her timeless mystery seem to evaporate as she ambles tamely among the vehicles. I look down and fumble with my camera for a minute. It feels as though we’ve diminished her with our presence.

When I look back up, the tiger has vanished into the trees on the far side of the track. But a little later she reappears a hundred yards away, climbing across a rocky escarpment. Radiant in the intense morning sunlight, she makes her way down the rocks to a streambed below, and we lose her in the thick reeds where she’s gone to drink. But we catch one final glimpse as she turns and starts walking again, up the streambed and off into the distant hills. With every step away from us, she becomes more powerful, more unfathomable, more the tiger of our imaginations.

We stare after her, blinded by the glare reverberating off the hills, until she’s gone.

India’s Ranthambhore National Park, Tiger Reserve: How to get there, what to do

Brookes is a Washington-based journalist who travels frequently to Asia.