Sol Linowitz, President Carter's special Middle East envoy, sipped bitter Bedouin coffee from a little china cup, then twisted his mouth into an exaggerated stage grimace.

His gesture was meant as a joke, aimed at reporters watching the traditional Saudi Arabian ceremony of arrival coffee in the VIP lounge of Riyadh Airport, but in some ways, it raised questions about the style and method of the man Carter has assigned to conduct the difficult Palestinian autonomy negotiations between Egypt and Israel.

Linowitz, a cool lawyer and corporation executive, has showed in his first two plunges into the autonomy talks that he has little time for the ritual, symbols and principles that have governed life in the Middle East for a long time.

The emotionally charged and highly symbolic question of recognizing Yasser Arafat's Palestine Liberation Organization, for example, plays little part in his planning for step-by-step progress in the talks, according to sources familiar with his strategy, nor, they add, does the original Egyptian demand that Palestinians in Gaza and the West Bank enjoy as a matter of principle the same powers now exercised by the Israeli military occupation government.

On another level, his joking about the bitter coffee was in easy view of Saudi Foreign Ministry officials sent to welcome him to a capital that already had what it felt were good reasons to suspect his attitude and impartiality.

The Saudi rulers, according to reliable sources here, had earlier raised some eybrows at Linowitz's appointment, questioning his past activities in American Jewish groups. As if to confirm their fear, the Jerusalem Post had reported four days earlier that Linowitz exchanged pleasantries with Israeli Interior Minister Yosef Burg in such smooth Yiddish that Burg called him a 'rov' (rabbi).

Against this backdrop King Khalid found himself too busy visiting Bedouin notables in the desert to see the U.S. envoy. Fahd, the crown prince, sent word only at the last minute that he would make it back from the desert in time.

Linowitz nevertheless came away from his talks with Fahd and the foreign minister, Prince Saud, convinced his reasoned, systematic approach to the talks had evoked a new level of interest among the Saudis. But for the Saudis, saying nice things is part of the ritual of receiving a guest and there was question in the Linowitz party whether Fahd was being cooperative or just obeying the laws of Bedouin hospitality.

In any case, the Saudis and their ways seemed far removed from Linowitz's desire to escape posing and symbols and from the businesslike negotiations he had just conducted in Israel with Burg and Prime Minister Mustafa Khalil of Egypt.

The lawyerly Linowitz appeared determined in the talks to apply the reason and determination that served him so well in building Xerox into a giant and negotiating a treaty for turning over the Panama Canal. Repeatedly in describing his approach, Linowitz referred to the Panama Canal negotiations as a model and to his emphasis on system as a means of overcoming the visceral fears, suspicions and even hatred that so far have prevented swift progress in the nine-month-old Middle East talks.

In its first test, the new style seemed to work. Linowitz persuaded the Egyptians to drop their concern with principle and concentrate instead on building up a list of agreed powers to be exercised by the Palestinians. This was a major acomplishment at last week's negotiating session in Israel and helped lead to the first agreement -- admittedly only a beginning -- between Egypt and Israel on points of substance in the autonomy talks.

From here on, high U.S. officials say, Linowitz intends to add to the list of agreements point by concrete point, as much as possible in private talks with Prime Minister Khalil and Burg. His goal first is to get enough points of agreement so that neither Egypt nor Israel will risk losing the progress they have made by being stubborn on subsequent and more difficult issues, they say.

Eventually, Linowtiz feels he can amass agreement on enough Palestinian autonomy powers that Arafat's PLO no longer will be able to keep West Bank leaders from joining the talks, or that it will no longer want to try, the officials say.

State Department specialists who protest that Linowitz is forgetting the importance of emotion and longstanding principle in the Arab Israeli dispute get little attention from their new boss. He has called some of their pessimism "Pavlovian" reaction, based on shibboleth as much as analysis, and feels his stand has been vindicated by some of the agreements reached last week in Israel, according to officials familiar with his thinking.

Similary, Linowitz has appealed to other Arab leaders to drop their principled opposition to the Camp David process and watch instead what he produces. Sources present at his talks here with Fahd, with King Hussein of Jordan in London and with King Hassan in Morocco say he urged their support by asking, "What is the alternative? Violence? War? What else have you got to offer?"