Tampering with the status of a proud people's language - such as that spoken in Soviet Georgia - can sometimes prove too much even for a powerful central authority like the Kremlin.

The Soviet leadership discovered this anew last week when its plans to eliminate Georgian as the official language of the multi-national republic ran into stiff and potentially dangerous opposition. In an unusual reversal, the authorities backed down and restored the designation of Georgian as the republic's official language in its new constitution.

The same thing happened in Soviet Armenia, where Armenian was recently restored to that republic's new constitution in the face of similar protests.

It is no accident that the Georgians and Armenians have made an issue of their languages: as these proud peoples of the Caucasus mountains see it their culture and languages were already highly developed where the Russians, who now run things, were still living in neolithic simplicity, their tribal subsistence darkened further by the absence of a written language.

This sense of cultural superiority and identity, as well as an accompanying worry over ethnic suppression, rings forth in the Georgians' own views on the subject of their language.

"More than once (the Georgian language) has faced danger of complete eradication, of being ousted by the languages of great empires," asserts "the Georgian Language," a book published in 1969 by Tbilisi University in the Georgian capital.

"The Georgian people have for centuries preserved their heritage in fierce battles against enemies, they have preserved it intact to our day through vicissitudes of fortune, as the most cherished symbol of their national individuality," S.V. Dzidziguri wrote in that book.

The book asserts the antiquity of the written Georgian Language, a unique and appealing script of generous loops and curls that has no similarity to the Crillic writing of the Russian language. The book's tone makes clear why the philology department of the university was a strong point of anger for the protests that built through recent weeks and culminated in the march through Tbilisi Friday.

As hundreds and perhaps thousands of students gathered on the steps of the government center, Georgian Communist Party chief Eduard A. Shevardnadze appeared and reportedly shouted in his native Georgian, "My children, my children, what are you doing ?"

"We are not your children!" the demonstrators are said to have shouted back.

Whatever their ire, the notion of a large public demonstration to protest against an official government policy is virtually unheard of in the Soviet Union. No such protest ever occurred in the time of the dictatorship of Josef Stalin and his secret police boss, Lavrenti Beria, both Georgians.

The fact that they occurred posed embarrassing political questions for Shevardnadze, a former Georgian interior minister who boosted to party chiefdom in 1972 by the Kremlin to clean up widespread corruption in the previous leadership of the free-and-easy republic.

Shevardnadze has became known as a ruthless, energetic leader who has warmly embraced the spread of the Russian language in his republic. At 49, he is considered one of the new wave of tough, pragmatic leaders who are getting regional experience before trying to shove their way into the inner circle of the national party, where the average age of politburo members hovers near 70.

Russification of Georgia had indifferent results until the installation of Shevardnadze. While about 70 percent of the Soviet Union's entire population speaks Russian either as a native language or fluent second tongue, only about 20 percent of Georgia's citizens claim to have working command of Russian, according to the 1970 Soviet census.This percentage is about the same as that of Russians living in the republic, where more than 65 percent call themselves Georgians. The proportion of Russian speaker is one of the lowest to be found in any of the 15 major republics.

Shevardnadze has tried twice to press Russian over Georgian. In 1973, the leadership ordered a crash program to require virtually all children to become fluent in Russian as a condition of high school graduation. In 1975, institutes of higher education were in all subjects except those dealing directly with Georgian culture.

But these measures seem only to have sharpened resentments.

Shevardnadze himself was openly criticized for delivery a key speech to the Georgian Party in Russian instead of Georgian.

The Georgian Writers Union has been the scene of bitter tirades against Shevardnadze's policies, and a small group of human rights activists took up the issue as well. This group, including a Georgian nationalist named Zviad Gamsakhurdia, has been silenced by jailings.