A revolutionary in education, Neill of Summerhill, by Jonathan Croall. New York: Pantheon Books. 436 pp. $20.

Apart from that famous one in 1776, revolutions tend to do no more than exchange one tyranny for another. In some ways, that is true even of A.S. Neill's loving and imaginative fight to liberate British schoolchildren. The pupils certainly needed a champion: Nicholas Nickleby would have recognized only too well the stern Scottish classrooms where Neill was first a pupil, then a teacher.

Learning was by rote, and discipline was enforced by blows from a leather strap or a cane. Neill, who passed on in 1973, could remember how grim teaching about the torments of hell and the doom of original sin in the churches were carried into the classroom, turning Scotland, Neill said, into ''a God-fearing, rather than a God-loving, nation.'' In his own case, schooldays were made grimmer by a stern father, who constantly reminded him, ''You will end in the gutter.''

In stark contrast are two stories that come some years later, after Neill had established his freedom school in 1921. One concerns a pupil, a little girl who is supposed to have asked ''Do we have to do what we like all day tomorrow as well?''

The other shows that the staff, perhaps unfortunately, had nothing to fear from their headmaster. Neill made constant attempts to fire ''Sparks,'' the odd-job man. Finally ''Sparks'' overslept once too often, and ''Neill finally said, 'Look, this is no good, you'll have to go.' To which Sparks replied: 'But Neill, I like the place, and I like you and everything about it.'' So Sparks stayed.

In his book Jonathan Croall has written a long (436 closely printed pages), carefully researched but always interesting account of how Neill bridged the gap between those two educational experiences - and managed to fight his way up from a poverty-stricken loveless childhood to become a worldwide influence on education. Mr. Croall hasn't been content to provide just a full biography of Neill: He explains the theory behind other experimental schools, fills in the background of world events, and shows how communism and psychology both effected education.

On his way up, Neill did his best to enliven those Scottish classrooms. While other state schools were calling for essays on such bland subjects as ''school'' or ''holidays,'' Neill was assigning subjects like ''the autobiography of a nose'' (''When first I began to run,'' one child wrote). Even the grimmest schools had their uses, for they persuaded Neill that there must be a better way to educate children. ''The teacher's job,'' he decided, ''is to evoke love. This he can do only by loving.''

Books Neill wrote about his ideas began to capture attention and earned him enough money first to attend Edinburgh University and then to start his own school and put his ideas into practise. Punishments were out; so were orders. Government was by a child-dominated council.

Some of Neill's ideas have become, for good or bad, catchwords, as when he says that - juvenile ''delinquency is merely misplaced social conduct.'' Nudity wasn't frowned upon, swearing was positively encouraged, and there was a degree of sexual permissiveness at Summerhill. The ropes that support had been cut along with the ropes that constrain.

There were other flaws. Freedom might have been the watchword at Summerhill, but it didn't stop Neill from dabbling in psychology - holding what were called PLs (Private Lessons) with his pupils, an invasion of privacy in a most dangerous form. Neill may have glimpsed this danger, for when he heard that his own psychologist, Homer Lane, had died he caught himself smiling. ''I was free at last,'' he recalled.

Teachers complained that Neill wasn't content simply to allow children to miss lessons: he encouraged them to skip. An ex-pupil says, ''Many stayed away from lessons for months, and in a few cases years. . . .''

Neill is said to have boasted, ''Personally I do not know what type of teaching is carried on, for I never visit lessons and have no interest in how children learn.''

At one time, to Neill's chagrin, a group of children demanded that they be given more lessons and some homework.

On the other hand government inspectors, whose visit had worried Neill no end , reported that ''initiative, responsibility and integrity are all encouraged by the system.'' And if permissiveness was carried to extremes at Summerhill, we must remember that Neill's ideas (in a milder form) have resulted in happier schools in many parts of the world.

In Vietnam during the war, a priest was running a community home for youngsters, the author writes. These children ''had lived off the pickings of war as pimps, prostitutes, and thieves, and many had themselves been severly injured.'' A visitor was surprised by ''the quiet discipline of the place and the complete openness of the children. . . . 'It was very simple, really,' the priest replied. 'I read a book by an Englishman called A. S. Neill. I just put his ideas into practice here, and, as you can see, they work.' ''