INDIA Monitor staff writer Arthur Unger took a round-the-world trip on a frequent-flyer bonus plan recently. This article chronicles the third leg of his journey -- to Singapore and India.

Just before dawn, the tiny-meter-gauge train dubbed the Palace on Wheels pulls into the station at Jaipur. I lift the window shade next to the bed in my narrow compartment to peer out through the hazy yellow light of the kerosene lanterns. Hundreds of people in raggedy clothing seem to be living on the railroad platform -- sleeping . . . cooking . . . squatting . . . chattering. Later I climb into the howdah atop an elephant a nd ride up to the Amber Fort, then lunch on tandoori chicken at the Rambaugh Palace. For seven days, life is one long series of scenic train journeys chugging through the land of the maharajahs to cities with exotic names like Udaipur, Jaisalmer, Jodhpur, Bharatpur and Agra . . . riding elephants and camels to lunch at palaces, visiting ancient forts, shopping for silver in bustling bazaars . . . and then visiting the Taj Mahal. The `malled' city of Singapore Here we are on a new leg of our trip, which has taken us from New York City to Tahiti, then on a cruise among South Pacific atolls, on to Sydney, into remote villages in Bali, and now to this former crown colony on the southern tip of Malaysia.

For three days we experienced total luxury in the Dynasty Hotel, a high- rise owned, designed, and decorated by Chinese from Hong Kong. It's the kind of building that might be seen anywhere in the world -- except for the pagoda roof.

The Dynasty charges around $100 per night for a double room with television and all the amenities of Western-style hotels. It was a fine chance to get our laundry done, luxuriate in bubble baths, and meander through the shopping centers.

Singapore is now a modern ``malled'' city, with a shopping center on just about every thoroughfare. Some stores stock designer clothing; others are bargain-basement emporiums. You must bargain at all of them except the chic department stores like Tang.

You can find such familiar favorites as Baskin-Robbins ice cream and Kentucky Fried Chicken, or you can sample Chinese and Indonesian cuisine at the many fine local restaurants, which are kept immaculate -- by law. But don't throw a candy wrapper in the street: Singapore has well-enforced anti-litter laws, and you may be fined as much as $300.

Thus Singapore is one of the cleanest cities in the world, but not very exotic anymore, with very little left of the indigenous culture or colonial mystique. Even the famous Raffles Hotel, immortalized by Somerset Maugham, has been overpowered by a high-rise office building and shopping center. So Singapore has become a pleasant stop-over between more interesting destinations in the Far East. And we did have interesting destinations ahead, mainly India and Nepal. Bustling, bombastic Bombay

It was quite a culture shock to leave squeaky-clean Singapore and arrive in bustling, grimy Bombay at 2:30 a.m.

The first thing one must become accustomed to in the major cities of India is the sense of community. Whether you like it or not, you are part of a crowd.

It starts with your arrival at Bombay's airport, where hands clutch at your sleeve offering taxis, rupee exchanges, a peacock feather, anything you can imagine. Beggars are everywhere.

The ride from the airport to the Taj Mahal Hotel in the predawn light is a weird experience, since much of the road is lined with early risers making morning tea over bonfires. Crowds of people are preparing for the day, as the sun tries to break through the smoggy, humid air. As we approach the Arabian Sea, where the hotel is situated, the beehive of activity among the street people fades into ranks of well-dressed young men, mixed with youths in every sort of native dress. Some are hurrying to jobs in

banks, hotels, shops -- others to the streets where they will beg for money from passers-by.

The griminess of much of this city contrasts violently with the white marbled beauty of the Taj Mahal Hotel. Fortune magazine has called it ``one of the finest hotels in the world,'' and a stay in this refurbished 75-year-old establishment is, in itself, almost a mystical experience. Our room, with its triple-lacquered doors in the preferred ``Old Taj'' section, overlooks the famous Gateway of India arch. Our balcony looks down on the Apollo Bunder plaza, where sightseeing boats leave for the Elephanta caves. A central courtyard with majestic stairways gives one the feeling of being in a luxurious palace.

The lobby of the hotel serves as a kind of meeting place for local society, mainly intellectuals and artists. It is a cornucopia of exotic Indian types in a wide variety of native dress, some wearing black transparent purdah, others the tight white trousers and white tunics of the Punjab. For a Westerner, it is a bit like being at that wild saloon setting in ``Star Wars.''

Just being in frenetic Bombay is the main attraction of this city. The mix of Parsees, Punjabis, Goans, and Masha-rashtrians, among others, is extra-ordinary.

Bus tours of the city are available, but I must warn you that what Bombay calls deluxe buses would be third class elsewhere. Nonetheless, they offer an easy way to see the Victorian remnants of the British rule, such as the railway terminal and the marketplace. They also provide an easy way to see the house where Mohandas Gandhi lived for many years -- an inspiring stop for admirers of the Mahatma. And, of course, one must take one of the rickety boats across the harbor to the Elephanta caves, monolithi c rock-cut Hindu temples that were excavated in the 6th century but date to earlier times. The boat package includes a guide who explains the sculptures and the temples.

Woodlands is the name for a chain of inexpensive restaurants, where it's possible to try many typical Indian breads and curries. I highly recommend the fresh grape juice. Good Indian and Chinese restaurants, a bit pricey, are available in the Taj, the Indian one providing authentic folkloric dances with the meal. The Taj charges around $90 for a double room, and dinner for two at the Indian restaurant comes to about $24. Through Rajasthan via the Palace on Wheels

The train called the Palace on Wheels is waiting for us in New Delhi. So we jump aboard our Indian Airlines flight to the nation's capital and into a waiting taxi, which takes us to the railroad yards. We're eagerly anticipating something resembling the fabled Orient Express, but are quickly disillusioned.

A Palace on Wheels? It proves to be more a Bungalow on Wheels. But a uniquely exciting bungalow. There on the tracks are about 12 little railroad cars, headed up by a dainty-looking steam locomotive.

We are escorted to our car, which is emblazoned with the official crest of the Maharajah of Baroda. This had once been his private sleeping car. Each of the 12 cars at one time belonged to a maharajah from Rajasthan.

Two servants dressed in colorful costumes are assigned to our car, which, with its four staterooms, can accommodate eight people. On this trip, however, are only six. The car has two bathrooms, both with showers that prove very difficult to use as the train chugs along.

The staterooms are equipped with bunk beds and just about enough room for two people -- thin people, that is -- to stand properly. Besides the staterooms and the bathrooms, our car has a saloon, the benches of which are upholstered in velvet. This proves to be just about the only sign of elegance aboard, but it is a pleasant lounge area, with enough room for all of us to sit and read, chat, sip cool drinks, and look out the windows.

Some meals are served aboard the train in the narrow, crowded dining car. Fortunately, most meals are taken at palaces and hotels en route. The food is a combination of Eastern and Western delicacies with lots of good Indian chicken dishes and breads. Since it is impossible to move from one car to another while the train is in motion, the engineer stops every now and then to allow passengers to move to the dining or the lounge car. To get back to your own car, of course, the train has to stop again.

Since our companions turn out to be a hardy, charming, and amusing bunch, we spend most of our time aboard in our own saloon. We all decide to risk the dust of Rajasthan and keep the windows open so we can see everything. The joy of the trip, we all felt in the end, was in our vivid views of this scenic state. Because the train travels mostly by night, we are able, frequently by day, to explore the cities.

In Udaipur we visit the famous Lake Palace Hotel. In Jaisalmer, near the Pakistan border, we tour the abandoned mansions of the merchants who made their fortunes from camel caravans. On most days we are transported by elephant or camel or limousine to a grand palace for lunch or tea or dinner. We trudge through the bird sanctuary in early morning in Bharatpur, and, of course, we admire the Taj Mahal in Agra.

Although it is said that the best time to see the Taj Mahal is in the moonlight, we visited it with the sun reflecting off the sparkling, pristine-white marble in the pools before it. While peddlers of peacock feathers and brass ornaments are prevented from accosting tourists on the grounds of this monument to Mumtaz Mahal, nobody protects visitors from the scores of unofficial Indian ``guides'' who, for a fee, offer to lead anybody with a camera to the best angle from which to take a photograph. But th e Taj has no bad angles. It lives up to its reputation as one of the world's most beautiful buildings.

After a glorious, climactic day in Agra, the train chugs back to New Delhi early on the eighth morning, with a trainload of tired but elated tourists, ready to see more of India after having tasted but one small area.

And for us there is still Delhi to see. We find it to be a beautiful city, more on the orderly style of Washington, D.C. with its wide, planned streets and traffic circles, than a city one would expect to find in the heart of India.

We fly to Varanasi (once known as Benares), where we watch the early morning ablutions of the pilgrims in the holy Ganges and see a cremation on the river. It is said that once one sees Varanasi, one must return. After trudging along the muddy river banks, however, we felt that once was enough.

And then, before returning to Delhi for a flight to Katmandu in Nepal, we visit the tiny village of Khajuraho in north-central India. Khajuraho is noted for its sculptures in a temple complex that was, at one time, a lake. There are Hindu temples and Jain shrines, many decorated with ornately sculptured erotic statues of men, women, and gods.

The Jass Oberoi Hotel, within walking distance of the main temple complex, turns out to be one of the happiest bargains of the trip. At $40 per day for a double, we enjoy a spacious room and balcony in a marble villa, complete with swimming pool and Indian musicians, who play for us during dinner. It is the perfect ending to a joyous three-week holiday in this country.

During our return to Delhi for the flight to Nepal, we are already planning a return trip to see part of the nine-tenths of India that we've missed. For us, the Festival of India will go on for at least a decade. Tips for travel in India:

It is a good idea to use an Indian travel agency to plan the details of your holiday. But do it through your own local agent and be sure to request detailed bills from the Indian agency. The agency we used, although recommended by the Indian Tourist Office (30 Rockefeller Plaza, New York, N.Y. 10112), proved to be a bit lax in billing, although efficient in planning the trip.

Be sure at airports and hotels to arrange for transfers. We found the transfer eased the burden of travel in India tremendously, by providing a car and driver at airports to carry us to our hotel. The driver usually carried our luggage and also made certain we got seats on the Indian Airlines flights. Since Indian Airlines reservations are not computerized, there is often much confusion at departure time, and the $16 price of the transfer was well worth it.

India is probably not the best country in the world in which to economize. In some cases, what passes for deluxe here might be considered second class elsewhere. So my recommendation: Splurge your rupees.

The Palace on Wheels is run by the Indian Railways. It can be booked directly through that organization by your travel agent, or you can do it yourself. Booking is often included in package tours of India, but the cost can be inflated. The price should be around $100 per person per day, everything included, or less than $1,000 per person for the entire trip.

Third in a series. Next, in the travel section Friday, Dec. 13, the grand finale of Arthur Unger's around-the-world journey -- Nepal and Tiger Tops, where he follows white rhinos while riding an elephant. Parts 1 and 2 on this frequent-flyer bonus trip were published in the travel sections June 14 and Aug. 9.