The Dancing Sun By Desmond Seward Macmillan $200 YOU do not have to be a Roman Catholic to have heard of, or even visited, Lourdes or Fatima, but what about Medjugorje, Svata Hora and Turzovka, Czestochowa, Hriushiw, Garabandal or even England's Walsingham? The common denominator in these places, and many others throughout the world, is that they have become centres of mariolatry, places where the Virgin Mary is believed to have appeared, with accompanying visual phenomena, such as the sun spinning like a Catherine wheel and multi-coloured bands of light. Some of these shrines are fervently believed in by millions of Roman Catholics and are the source of apparent miracles. The message of the Virgin is usually to warn of some impending but unspecified disaster and, given the world we live in, there is no shortage of disasters which believers can adopt to give credence to prophesies. The author, brought up a devout Catholic, was educated by the Benedictines at Ampleforth before going on to Cambridge. But doubts kept intruding. He confesses: ''I am a very unsatisfactory Christian. There have been totally godless periods in my life when I worshipped money or a woman, even briefly the bottle.'' It was certainly, at least in part, to assuage his own self-doubts that Mr Seward set out to visit seven European shrines where the sun has danced in recent years. Apart from being an experienced author (he has nine other titles to his name) he is obviously an experienced and persuasive traveller. His pilgrimage to the shrines included the Ukraine, Bohemia, Spain and Portugal. At one or two places he did experiencea certain short-lived euphoria although he never seems to have seen the Virgin Mary or the dancing sun himself. He acknowledges some of the arguments of scepticism: the fact that in most cases, the Virgin appeared first to pubescent children, the possibility of mass hysteria and mesmerism among the thousands of worshippers. None of these, he feels, can eliminate the mystery. Certainly he is an interesting travel writer and an observer of strange coincidences. ''The nuclear disaster at Chernobyl in the Eastern Ukraine sent many to their Bibles, where they read in Revelations: 'And the third angel sounded and there fell a great star from heaven, burning as it were a lamp, and it fell upon the third part of the rivers, and upon the fountain of waters: and the name of the star is called Wormwood; and the third part of the waters became wormwood; and many men died of the waters because they were made bitter.' The Ukrainian for wormwood is 'chernobyl.' '' The author does his best to distance himself from the sweatier elements of Roman Catholicism, not always with success. Catholics of all description will find something in this book to absorb them. For myself, he leaves behind an undaunted sceptic.