On the trail of Squirrel Nutkin. If there's a bit of Peter Rabbit in your soul, be sure to visit London's Tate Gallery. Here, brought together from all of Britain's major collections, is the largest-ever show of the work of Beatrix Potter.

THE only place I have ever seen someone walking a pet rabbit down the street on a lead was in England's Lake District. Presumably, the young girl in question had been brought up on Beatrix Potter. Potter (1866-1943) was a devotee of both the Lake District and rabbits. Though London-born, she lived most of her adult life in the district as a farmer, landowner, conservationist, and breeder of Herdwick sheep. But what the world knew about this private woman was that she was witty author and remarkable illustrator of one of the most popular children's books ever published, ``The Tale of Peter Rabbit.''

A photograph still exists of her in 1891 leading her rabbit Benjamin on a string. The strange thing is that she was 25 years old that year. Thanks largely to the limited Victorian outlook of her parents towards their only daughter, her childhood lasted longer than usual. But her slow arrival at adulthood was certainly fortunate for the lovers of her little books, which increased over the years to 23. It allowed her to become a mature artist without losing a child's fantasy.

As the exhibition ``Beatrix Potter: The Artist and Her World'' here at the Tate Gallery shows, however, it was her father's encouragement of her art - and acquiescence in her and her younger brother's boundless enthusiasm for animals, birds, and plants - that fostered her determination to be an artist. He took her to art galleries. He was friendly with English painter John Everett Millais, who not only praised Beatrix's ability to draw, but also, astutely, told her that she had that much rarer gift of ``observation.'' Her father was a keen photographer (though photography was then in its adolescence, he took hundreds of photos of his family). He also drew; in fact, one of his drawings even suggests the closeness of his influence on his daughter. With a touch of English humorist Edward Lear about it, the drawing depicts birds flying. One of them is a duck wearing a bonnet - a forerunner of Beatrix's own imaginary world in which creatures became small human beings, while still remaining remarkably animal or birdlike.

Jemima Puddleduck, for instance, is the Potterized story of Little Red Riding Hood. Naturally, this scatter-brained quacker has to waddle around in a ``poke bonnet'' and shawl. Otherwise, how could we believe that she is both the daftest of ducks and the silliest of girls, so flattered by the attentions of that elegantly dressed, ``long-tailed gentleman.''

But Beatrix's wit and unsentimentality gave her an uncanny instinct about precisely the right moment in her miniature narrative for bonnets and elegant clothes to be shed. Jemima is a silly domestic duck, after all, and the ``hospitable gentleman with the sandy whiskers,'' as everyone except Jemima has known all along, is just a wild and wily fox bent on canard-icide. We don't feel particularly sorry for him when he meets his end amid ``howls, squealing, and groans.'' But the foxhound puppies that finish him off also eat Jemima's eggs. Both in her illustrations and her text, Potter usually avoids a too-soft view of nature. And if her animals can behave unrealistically like humans, there is an underlying authenticity to the obverse: that humans - even children - can behave very like animals.

The exhibition shows a good selection of original illustrations, preparatory sketches, final or unused or altered illustrations, letters, documents. Of unused pictures, one of my favorites shows Alexander (piglet) and Pigling Bland (``a sedate little pig'') dancing at sunset, intended for ``The Tale of Pigling Bland.'' Another for the same book, shows an outlined self-portrait of Beatrix shaking hands with the smartly dressed Alexander. In the final illustration she reduced herself to just a hand and a sleeve.

Many tales are looked at in depth, each given a special display. Her books have always appealed to adults as well as children, and this exhibition will do the same: Here we can learn the origins of - and the discussions with the publisher about - the stories of Jeremy Fisher, Mrs. Tiggy-Winkle, Squirrel Nutkin, the Tailor of Gloucester and others.

She was a more than competent watercolorist, who used clean color and tone to depict the minutiae of the cosy, cottagey, intimate, old-fashioned settings she preferred for her tales. She was also a straightforward painter of nature. Fine watercolors of fungi, bats, lizards, newts, mice, sheep, bean shoots, onions, hedgehogs, sheep and unclothed bunnies bear witness to this side of her talent.

The show closes with a look at ``her'' Lake District (she left over 4,000 acres of it to the protection of the National Trust) - at the way its scenery found its way into her books, but also at the way in which, after her late happy marriage, she increasingly left her storytelling and illustrating behind her to concentrate on farming and the full life of a countrywoman. She only achieved this independence, of course, because her children's books were so successful. And she never abandoned her intense, childlike affection for animals; she kept cows, sheep, horses, poultry, rabbits, dogs, a pony, and a pet pig.

``I seem to be able,'' she said, ``to tame any sort of animal.''

To Jan. 31.

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