The only reason these paintings are reproduced and bound together between hard covers is that they all happen to be the personal property of Queen Elizabeth II. Personal property is, of course, a rather misleading phrase since there would doubtless be numerous unpleasant repercussion were she to auction off a few at Sotheby's to plump out the privy purse, questions asked "The House," ect. Nevertheless, these pictures do hang on the walls of her private houses and castles where not many of us are asked to take tea. So books like this one do a valuable service in documenting the extent of her collection. One of the most fascinating pictures dates from the collection of the Tudor monarachis: a portrait of Elizabeth's namesake - not ferocious, bewigged and black-toothed, but a poised, slender young girl with the hands of a violinist. The Hanoverians seem to have favored Panormaic landscapes by Brueghel. Hogarth or Rubens, whole Victoria had a penchant for coy portraits by Landseer or Winterhalter. Oliver Millar, a skilled and loving annotator, has been working with the collection since 1947 and was made Surveyor of The Queen's Pictures in 1972. He organizes exhibits in the Queen's Gallery at Buckingham Palace - which is open to the public - and arranges the frequent loans made to museums from the collection. A more glorious and eclectic collection of art than that portrayed in his book is hard to imagine. (Macmillan, $35).