As his friends chanted "Sanjay Gandhi, eternal life," the body of the 33-year-old son of Prime Minister Indira Gandhi was cremated today in an ancient Hindu rite.

Sanjay Gandhi, the heir-apparent to the Nehru-Gandhi political dynasty that has ruled India for most of its history as an independent nation, died in a plane crash Monday morning while doing stunts above the prime minister's official residence.

The public cremation ceremony mixed Hindu mysticism with practical politics. But it was clear that the new generation that young Gandhi brought into Indian politics as loyal supporters of his mother and himself was left without a leader.

An estimated million people stood in the sweltering 110-degree heat as Gandhi's body was carried on a flower-bedecked Army truck through the center of New Delhi to the site where his grandfather, India's first prime minister, Jawaharlal Nehru, was cremated 16 years ago. It took the cortege two hours to cover the seven miles from the prime minister's house, where the body had laid in state for 24 hours, to the cremation site.

Another 150,000 persons crowded the cremation site, named Shantivana for Nehru's great love of peace. Shanti means peace in Hindi.

It was a ceremony befitting a crown prince, which is what Gandhi had been called as he began gathering up the reins of power in India. He was his mother's confidant and chief political adviser, and generally was considered to be the man mostly likely to be India's next prime minister when Indira Gandhi, 62, decided to step down.

But since his public posts were minor -- he was a first-term member of parliament and one of four general secretaries of the Congress-I (for Indira) Party -- it was a private, not a state, cremation service.

The flags in India's capital flew at half staff today, not for Gandhi, but for V. V. Giri, a former president of India who died at 88.

Private ceremony or not, Sanjay Gandhi's cremation drew India's leading public figures, diplomats from most of the nation's of the world and hordes of this country's masses who surged past police barricades to get closer to the 15-foot-square, five-foot-high platform on which the body was placed.

Before the body was carried to it, Prime Minister Gandhi and her two daughters-in-law -- Sanjay Gandhi's widow, Maneka, and the wife of her older son, Rajiv -- inspected the flower-bedecked platform. It was their only chance to see it, since Hindu ritual does not permit women to participate in the cremation service.

The women were dressed in white, the Hindu color for mourning. After inspecting the platform, they sat together on the ground directly in front of it.

Prime Minister Gandhi, who had ridden in an open jeep the length of the cortege, appeared composed. But friends said her eyes behind the dark glasses she has worn since her son's death were red and swollen from crying.

The crowd itself displayed little of the weeping and wailng that characterized other public funerals. But there were some visible tears in a section filled with personal friends.

Six pandits, or holy men, supervised the service. They were led by Swami Dhirendra Brahmachari, the Gandhi family guru, who assisted Sonjay Gandhi's older brother, Rajiv, to sprinkle the body first with holy water and then to cover it with a mixture of incense and ghee (clarified butter).

The body was laid on a bed of sandalwood logs, and then more logs were stacked around and over it in a tent shape to make the pyre.

Although Gandhi often said he was an agnostic, he was cremated with full Hindu rites with the chanting of mantras in Sanskrit by the priests.

The last rites, known as dehsensakar, are designed to give peace to the departed soul and courage to the bereaved family.