Rhodesia's white population is dwindling fast, official figures showed today.

The central statistical office reported that 1,604 Europeans left Rhodesia in August, while only 598 arrived. It was the second highest number to leave in any one month since the government of Prime Minister Ian Smith declared independence from Britain in 1965.

The largest numebr of whites to emigrate in one month was 1,754, in May.

Rhodesia has lost 54.147 whites since the 1972 outbreak of war by black nationalist guerillas seeking to topple the white minority government.

Despite the war and the uncertain future, however, 43,261 whites have arrived from other countries to settle in Rhodesia in the same period.

Latest published figures record a net loss of 7,713 whites in the first eight months of this year - 641 more than during all of 1976.

The 3,972 new immigrants in the first eght months of this year were significantly fewer than the 5,894 who arrived between January and August of 1976.

The White exodus shows no sign of slowing.

It is generally accepted here that only an end to the war between the white government and black nationalists seeking majority rule could stem the flow.

Some observers believe, however, that a settlement that brings a black government to power might, for a time, increase the white exodus.