The price of making the parched West bloom; A River No More, by Philip L. Fradkin. New York: Afred A. Knopf. $15.95.

The next time I look at a steak I will think of the Colorado River, of our sparsely but nonetheless overpopulated West, and of Philip Fradkin's new book, "A River No More."

Fradkin begins his exploration of the Colarado at a small outcropping of meltwater which eventually becomes the Green River, the beginning of the Colorado system high in the mountains of Wyoming. From there he guides the reader down the river and back through its history. There is a map of its huge drainage area and of the vast plumbing system of dams, canals, and aqueducts that distributes the waters for man's use -- or rather, for the white man's use.

Mr. Fradkin also gives us a short but overwhelming history lesson. In culture after culture, from Sumeria to New Mexico, massive irrigation of arid lands follows a familiar pattern. First there is prosperity, and the culture expands. But rather quickly the mineral salts in the irrigation water increase the salinity of the soil, and food production drops. Farmers try to wash the salts out with even more water, and, while there is some success, groundwater levels rise, surrounding vegetable changes, and soil erodes away. Cities and pueblos are abandoned, and civilizations which once flourished by irrigation vanish.

An Indian culture prospered in Chaco Canyon in New Mexico for 600 years before the cycle destroyed the culture that had set it in motion. The ancestors of the present white population took only 10 years to destroy the native grasslands of Arizona with their cattle drives and fast-buck economics. Even the engineering marvels of their descendants, such as Glen Canyon Dam and other great high dams of the West, will be rendered useless by sedimentation in less than 100 years. The boom-bust cycles that have accompanied Western development since the 1850s may not be over, for there is just not enough water for everyone who wants it.

Most of the book deals with politics, because the history of Western development is largely the story of water politics, of who gets how much for how long and of how to get the federal government to pay the enormous construction bills. Since the division of the Colorado's waters in 1922, the states have kept each other in court over water allocation. Each party knows there is not enough water to satisfy all the demands, yet it still seems easier to wage endless legal battles than to try to separate wants from basic needs.

"When it comes to distributing water in the West," the author writes, "it has been the politically strong and aggressive who get it. To be tenacious and knowledgeable helps. Moral rights, historical priority, and legal merit count for less." The courts have routinely upheld the prior claims of Indian tribes to the river's water; but Congress, which decides which irrigation projects to pay for, has routinely ignored them. The tribes need their rightful share of the water to develop a better standard of living on their reservations. At the same time, white society still believes it must grow constantly to survive.

"The West is not an empty region," Fradkin writes. "In terms of what it can support, it is already crowded. . . ." IT seems disgraceful that the largest share of the water drawn from the Colorado system, goes not to the cities or to ranchers and their families but to their cattle. Thousands of native Americans live in poverty without the water to develop their own considerable agricultural and mineral resources, because the water goes to produce beef for those of us who can already afford it.

"A River No More" is massively researched and quite well written. It may change the way you look at rivers. It may change your attitude toward the politics of growth. It may even change the way you look at stea k.

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