What does a Rhodesian poultry farmer from Scotland who thinks majority rule is coming too soon have in common with a former shipping clerk who spent five years in prison and 14 in exile for favoring majority rule? Answer: The Ministry of Transport and Mines.

What does a politician whose forebears came from the Netherlands and who thinks majority rule "does not work," have in common with a supporter of it who was a student at Indiana State University and whose parents are Zulus. Answer: The Ministry of Foreign Affairs.

These four men, two white and two black, are among the 18 co-ministers in Rhodesia's transitional government set up under an agreement signed in March by white Prime Minister Ian Smith and three black leaders. They are to rule jointly until elections at the end of this year for a black majority government.

Because of their administrative experience there is no doubt that the white continue to hold the reins of power, though decisions are supposed to be make jointly. Just before the Salisbury accord was signed. The white government's decision-making war council, which included some Cabinet ministers, was dissolved. This effectively eliminated the opportunity for the incoming black co-ministers to participate in decisions about the war against black nationalist guerrillas.

The ministerial hearth has not been peaceful in all departments, and a clash in April between the black and white co-ministers of justice sent the new government into a tailspin which almost led to its breakup. The upshot of that disagreement was the dismissal of the black minister, Byron Hove.

In most other ministries, the black-white partnership appears to be without major grievances, though friction may be kept under wraps in order not to repeat the "Hove affair."

In recent interviews with four co-ministers about how they liked working with each other, they were upbeat and uncomplaining. It is not surprising that they want to accent the positive. Their biracial experiment, threatened militarily by the guerrillas and isolated diplomatically by lack of Western support, is a precarious period of probation.

Whether this interim black-white government can hold together in the face of a rapidly deteriorating economy, intense rivalries among the three black leaders - the Rev. Ndabaningi Sithole, Bishop Abel Muzorewa and Chief Jeremiah Chirau - and most importantly, a worsening guerrilla war, remains to be seen.For the time being, it is a unique experiment that has put some strange bedfellows into top government posts.

SURROUNDED BY white civil servants, the black ministers work in plainly furnished offices, in contrast to their white counterparts whose offices are appointed with pictures of momentous events in their years of government service and other personal memorabilia.

Asked how he felt about sharing his position with a black, P. K. Van Der Byl, co-minister of information and foreign affairs, said, "I have got no difficulty about it at all. Life is full of ironies."

Co-minister Elliott Gabellah "is an extremely agreeable, constructive and competent colleague," he added. "I have no complaint, but on the contrary, considerable praise.

"We met every now and then. There are certain things we do jointly and others we don't, but we keep each other informed."

Tall and thin, Van Der Byl dresses with impeccable Victorian perfection right down to his tie pin. He puffs on long, thick, cigars during interviews in his spacious office where one photograph shows him sporting a bowler and aviation sunglasses as he inspected a military parade during his stint as minister of defense.

Van Der Byl grew up in South Africa. After his education which included a year at Harvard Business School, he went to war.He moved to Rhodesia in 1951 where he took up tobacco farming and politics.

A man known for his rightist views, Van Der Byl thinks majority rule "does not work anywhere. I think it's a disaster in America.

"But what I think about it is academic and irrelevant because now it's here. I think it's too soon, but it's inevitable and we've got to make it work," he said.

VAN DER BYL'S PARTNER, Gabellah, 55, said he finds his new job "a thrilling experience."

"I have been a politician on the opposite side condemning every inch of what the other man did, thinking I could provide better, but now I find myself in the same seat and with the same problems. It's nice to see both sides of the coin," he said.

Gabellah, a jovial stout man who waved an unlit pipe, said he was satisfied with the ministerial responsibility he has been given.

"We are equals, will you underline that? I was with [Van Der Byl] all this morning and again this afternoon."

Gabellah was a Boy Scout as a youngster in Rhodesia. After studying in South Africa, London and Dallas, he went to Indiana University where he studied theology, divinity and philosophy.

The black-white experiment has affected attitudes of blacks and whites, Gabellah has found.

"They are beginning to treat and accept each other as equals. Both complexes, the superior and the inferior, they are beginning to go fast," he said.

"THE BREAK from platform politics to ministerial responsibility was traumatic. I had no experience as a minister," said James Chikerema, 53, who returned in September from 14 years in exile because of his opposition to the Smith government.

The black co-minister of transport helped form, in conjunction with guerrilla leader, Joshua Nkomo, "the first militant Rhodesian black organization" in opposition to Smith's white minority government.

"I must be very honest, I didn't think a year ago such cooperation was possible. Most of us 'black co-minister" are using this period to work with experienced people. I have plenty to learn.

CHIKEREMA'S WHITE partner, William Irvine, 58, was asked what he thought about working with a man who once organized guerrillas to fight the Rhodesian army.

"Well, I fought against the Japanese in the last world war and they're our trading partners today," he said. "You've got to be pragmatic."

The white co-minister was born in Scotland and when World War II broke out he joined the Highland Division of the British army. Later he served in India as an army engineer, and came to Rhodesia in 1948.

Like Van Der Byl, Irvine believes majority rule is coming too soon to Rhodesia.

"One has to have some misgivings," he said, "but one hopes it will work out."