CBS Chairman William S. Paley wrote in his autobiography a year ago: I feel we have made a wise choice in John Backe. He and I have been working well together ever since he took oiver the active management of CBS."

The abrupt firing of Backe 10 days ago brought a wave of criticism of the CBS board of directors for failing to stand up to Paley and a new round of concern on Wall Street over whether the $4 billion company is being run at the whim of a 78-year-old man unwilling to yield power.

Paley and others at CBS have spent recent days reassuring investment analysts that CBS isn't changing the direction it was on under Backe and that a successor will be found soon.

"The executive committee (of the board) will pursue the search. I think the sooner a replacement is found the better for all of us," said one man involved in the search.

CBS reportedly has approached a management talent firm to conduct a search, and the betting is that Backe's successor will come from outside the corporation. The logical inside choice would be Executive Vice President John Purcell, but insiders reason that he would have been tapped already if he were the choice.

Backe is the third heir apparent who has been dismissed from CBS. Backe, 47, and Arthur Taylor, who took the job at 37, were of a different generation from Paley. "It was like the king finding a son," one insider put it.

Paley is vague about what Backe's shortcomings were. The language is reminiscent of Paley's statement about reaching the decision to fire Taylor. "He did not have all the essential qualities to become my successor," Paley wrote in his autobiography.

Paley told Business Week that many of the qualities he demands in a successor were present in Frank Stanton who retired in 1973 after 33 years as CBS president.

But Paley never could bring himself to stand aside in favor of Stanton and, in fact, imposed mandatory retirement at 65 which forced Stanton out. Only Paley is exempt from the CBS retirement age.

Following Backe's dismissal, there was speculation that CBS might move to a different corporate structure, with its chairman on top and the heads of the various divisions reporting to him without an intervening chief executive office.

However, CBS has denied it will take this route and promises that Backe's successor will have both of Backe's titles: president and chief executive officer. Paley was forced to give up being chief executive following the ouster of Young in 1976.

The move clearly didn't diminish the power of Paley, who because of his rages and arbitrariness is referred to inside CBS as "the 400-pound gorilla," from the old joke: "Where does a 400-pound gorilla sleep? And the answer: "Anywhere it wants to."

The board of directors has closed ranks around Paley on Backe's firing despite strong criticism. Paley only owns 7 percent of CBS stock and doesn't have control of the publicly held corporation, "but the outside directors dance to his tune."

"There's no excuse for the board's line on this," said Joseph Fuchs, an analyst with Kidder, Peabody and Co.

Inside CBS, silence has surrounded the Backe firing. According to sources, none of the top executives queried Paley about what the firing meant. The chairman reportedly offered to give explanations one-on-one to any of his top managers who chose to seek one.

The presidency of CBS is perhaps less alluring after the experiences of Young and Backe, but it still is one of the most attractive spots in corporate America. (Young and Backe may have left CBS with some bruises, but they carried away some money, too. Backe has a settlement of close to $2 million which requires him to keep silent about his departure. His salary was close to $800,000 annually.)

Backe was fired although he had made CBS number one once again in TV ratings and generally was credited with setting the stage for the corporation's turnaround.

Whoever is selected to replace him will have a little more job security simply because after the turmoil this time it would be harder for CBS to engineer a third firing.

The board of directors seem to have no inclination to try to clip Paley's wings coincidentally with the installation of a new president, but even Paley has spoken from time to time of keeping his title as chairman but ceasing to work full time.

Paley and CBS board members have denied that Backe's firing was a personal decision by Paley. One insider conceded there has been a pattern at CBS. "It's a chronic disease, but this one was different. This was corporate," he said.

The corporate story is that the outside directors and Paley ordered a reassessment of Backe's performance by the board's executive committee.

Reassessments don't often end with the subject getting a pat on the back and a bonus, and this one's premise was that Backe lacked the stature to succeed Paley. Although the corporate story is that the reassessment hadn't been completed when Backe learned of it and forced a confrontation that led to his departure, there are indications that Paley was looking for a replacement before Backe knew a reassessment was under way.

Backe exploded and insisted that Paley be curbed, but the board of directors voted against him. CBS insiders insist that the general unhappiness with Backe had been building for some time, but Paley seemed unaware of any problems when he wrote in his 1979 autobiography that it gave comfort and pleasure to have his successor in place.