More than eight years have passed since the completion of the great high dam across the Nile, here but Egypt's struggle to tame the river, which has been going on for millennia, has not ended.

The high dam broke forever the annual flood cycle that had been the dominant feature of Egyptian life, and it guaranteed that the people of the Nile valley between here and the Mediterranean will suffer neither flood nor drought. But a natural force as powerful as the Nile was not to be subdued without a fight, and the Egyptians are spending millions on subsidiary projects aimed at coping with the side effects of the high dam.

One of them, the Toshka Canal, illustrates how each attempt to tinker with the river creates the need for further tinkering, in what appears to be an endless cycle.

This project will, for the first time, extend the impact of the high dam out into Egypt's western desert, with eventual consequences for the environment that engineers familiar with the project admit they cannot fully foresee.

The purpose of the Toshka Canal is to get rid of excess water building up behind the high dam. Ironically, at the same time Egypt is building this canal to channel off excess water, the Sudanese are building a massive canal of their own that will increase the flow of the river northward into Egypt.

For the 40 million Egtptians, these are more than matters of abstract interest. There is probably no other country on earth so totally dependent on a single source of life as Egypt is on the Nile. The river sustains more than 98 percent of the population in a narrow green band that bisects a land that is otherwise narly as barren as the moon.

That was true in Pharaonic times as its is today. The Egyptians were even then building dams, embankments and canals to control the flow of the waters. The high dam at Aswan, which was built by the Soviet Union after the United States and the World Bank refused for political reasons to finance it, has changed the nature and the locality of the struggle to bring the river under control, but has not ended it, as the Toshka Canal project shows. Nearing the Limit

SOUTH OF THE dam, the huge artifical lake known as Lake Nasser which was created by the damming of the river has been gradually filling. It spreads over more than 2,000 square miles, reaching down to the Sudanese border. More water is flowing into Lake Nasser from upstream than is needed downstream, which means that the water is continuing to rise against the southern face of the dam.

According to figures supplied by engineers and hydrologists familiar with the dam, its top is 196 meters above sea level. The surface of the lake is approaching 182 meters. Dr. Ibrahim Asyouti, head of the Irrigation and Hydrology Department of the Cairo University School of Engineering, who has made extensive studies of the dam, said in an interview that 182 meters is the "cutoff point" above which the water would constitute a threat to the dam itself.

"You can't let it go over the top, no matter what," he said. "This is a rock fill dam, not concrete like Hoover Dam, and water going over the top could erode the earth and rock. You can't let that happen." With Ethiopia, source of the Blue Nile, reporting its heaviest rains in 50 years, the level of Lake Nasser is likely to climb higher.

The Aswan Dam has a spill way designed to let the excess water run off downstream in just such a situation. But it has been discovered that it might have serious detrimental effects downstream, in the heart of Egypt, to let large quantities of water flow through that spillway and rush to the Mediterranean.

That is because the silt that was in the water when it flowed into Lake Nasser has settled to the bottom, leaving the water clear. Hydological engineers say the clear waters, if released, would flow so much faster than the muddy waters of the annual flood used to that they might erode river banks, bridge foundations and smaller dams downstream, eventually unleashing devastation.

Fawzi Helwa, chairman of the high dam authority and an engineer, said in an interview that "even 15 years ago we could foresee these side effects. Clear water would run with a higher velocity on the whole course of the river, creating an effect called degradation, which would damage existing foundations and barrages downstream.

Faced with the need to release water from behind the dam and the danger of letting it flow at full force, he said. "The natural solution was to build new barrages to slow it down. But we found another way." Water in the Desert

THAT OTHER WAY is the Toshka Canal, described by Prof. Asyouti as a "safety valve." It will prevent the water behind the dam from rising to the danger point by channeling it out into the western desert, where it will be dumped.

Toshka is a village about 150 miles upstream from Aswan. There, construction crews are at work on a $50-million canal that will link Lake Nasser with the Toshka Depression, or valley, 25 miles to the west.

Any time the water level behind the dam reaches 178 meters, or 4 meters below the safety cutoff point, it will begin to spill over into the Toshka Canal and off into the desert. That will alleviate pressure on the dam without requiring the release of clear water to rush downstream with potentially damaging effects.

The Toshka Canal project, however, has stirred criticism from scientists who object to the way it is being carried out. One of the most outspoken is Dr. Farouk El-Baz, director of earth and planetary studies at the Smithsonian Institution in Washington. A native of Egypt, he is also science adviser to Preesident Anwar Sadat.

"Water here is our most precious resource and the river is the sole source of it. Why should we waste any?" he asked. Other scientists who object to this wastage have pointed out that because of the explosion of Egypt's population, the Nile, which at the turn of the century provided 25 cubic meters of water per Egyptian per day now provides less than 4.

El-Baz also argues that by fixing the Toshka Canal so that water will enter it only in high flood years when it reaches 178 meters, instead of installing gates that would allow periodic, controlled flows, the engineers have guaranteed that the Toshka Depression cannot be reclaimed for agriculture because its supply of water will be so erratic.

He also said that when water does run through the canal, it will become contaminated along the way by salts that it will leach out of the rocky bed and sides of the canal.

These salts in turn, he said, will filter down through the ground of the Toshka Depression into the aquifer of Nubian sandstone underneath. Not only would that destroy any reclamation potential in Toshka, he said, but also it might contaminate the underground water supply of the New Valley, one of Egypt's major reclamation areas, which lies to the north.

El-Baz argues that Egypt should install control gates at the mouth of the canal to allow Nile water to flow out to the Toshka Depression as needed for agricultural development, and line the canal with concrete to prevent salt contamination - both measures rejected by officials of the high dam authority and the Ministry of Irrigation as impractical and unnecessary.

They say there is no proof that the water in Toshka Canal will contaminate the ground water of the desert, and in any case, they say, as much as 30 years may elapse without the level of Lake Nasser reaching the 178 meters that would send water flowing into the canal. Prof. Asyouti said the question of contamination "needs more study," but said in his opinion, "it is very slight."

According to Helwa, the chairman of the high dam authority the purpose of the new canal is not to irrigate the western desert, which he regards as impractical, but to protect the dam and the channel downstream from potential damage.

It will do that, he said, even when the flow of the Nile is at a 100-year maximum and even when the waters from the flow of the massive Jonglei Canal project in the Sudan are added in.

Deep in the southern Sudan, construction has begun on the Jonglei Canal, which has been under consideration since 1904. This project, comparable in scope to the Aswan Dam, will divert much of the flow of the White Nile out of bend that carries it through the Sudd swamps. The White Nile, which contributes two-sevenths of the total flow of the Nile below Khartoum, has been losing up to half its flow through evaporation in those swaps.

By eliminating that bend through the swamp, the 220-mile canal is expected to save 47 billion cubic meters of water a year, increasing the total flow of the Nile north of Khartoum by more than 5 percent. Questioning the Benefits

DOWNSTREAM, the loss of the annual alluvial deposit from the flood has increased Egyp's dependence on chemical fertilizers. The loss of the flushing effect of the flood at the mouth of the Nile has permitted saline encroachment upon arable land. The brickmaking industry downstream has suffered from a shortage of mud.

Helwa, the chairman of the high dam authority, recites this list with the weary patience that comes of having explained it hundreds of times.

"For more than 10 years," he said, "even some Egyptians have questioned the wohole value of the high dam project, for some reason. All these side effects were known before hand. There is no question that the benefits have outweighed them."

The dam generates more than half of Egypt's electricity, cheaply, he said. "That electricity has enabled us to build our aluminum industry and expand our factories."

He said that the years 1972 and 1975 proved the dam's value to Egypt. In the earlier year, this country was totally spared the effects of a devastating African drought. And in 1975, when rainfall was heavy, the high dam prevented major floods that would have washed away farms and towns downstream.

"They say it ruined the brickmaking industry," he snorted. "Well, that's not a modern way to make bricks anyway, out of river mud. We should have new factories to make sand bricks."

Nobody in Egypt seriously questions the overall value to the country of the Aswan dam.

But it is no longer immune to scrutiny and criticism, as it was when it was the symbol of Egyptian defiance of the United States and Egyptian leadership of Third World political aspirations.

Newspapers and politicians and scientists frequently question some aspect of the way the dam and its power station are run and of the irrigation and land reclamation projects associated with it.

"No project is 100 percent right," Helwa said. "Even a medicine has its side effects."