For Britain's Princess Anne, there is no living down her occasional lapses in horsewomanship. At a charity fund-raising evening sponsored by the Grand Order of Water Rats, an entertainers' organization, Anne and Husband Captain Mark Phillips arrived to accept a check on behalf of the Police Dependents Trust. "Have you fallen off any good horses lately?" cracked Basil Brush, a puppet fox and star of a children's tele vision show. Replied Anne coolly: "You don't fall off good horses."

The ceremony came four years late, but last week Soviet Author Alexander Solzhenitsyn finally entered Stockholm's Concert House to accept the 1970 No bel Prize for Literature. "The Swedish Academy and the Nobel Foundation have probably never had as much bother with anyone as they have had with me," said Solzhenitsyn at a Nobel ban quet. The laureate was kept from attending the 1970 ceremonies by fear that he would not be allowed to return to the Soviet Union. The prize, declared the bearded exile, "has prevented me from being crushed by the severe persecution to which I have been subjected." The prize also enabled Solzhenitsyn to be on hand for some traditional Scandinavian Christmas festivities, including a meeting with Birgitta Gahne, Stockholm's Queen of Light.

Though never known as the king of deference, Actor Rod Steiger has plaudits aplenty for the co-star and the director of his newest film, now being completed in Saint-Tropez, France. The movie, tentatively entitled Damned Innocents, features Steiger as an aging husband and Romy Schneider as his wandering-eyed wife, and is directed by New Wave Mastermind Claude Chabrol. Says Steiger of Chabrol: "He understands the necessity of allowing his actors artistic freedom. There isn't that much money to be made, and we have to use all the talent there is." Which, presumably, includes Schneider. "Working with her makes me realize how ignorant I am," concedes Steiger. "She can speak English, French, Italian and German. I have trouble getting by in English."

"I came here eight years ago with $200 in my pocket, a small child in my arms, wondering if I had any future at all," recalled Australian-born Singer Helen Reddy, 33. Now a top-ranking female pop vocalist in the U.S. and composer of the rousing feminist anthem I Am Woman, Reddy last week joined ranks with her American fans by becoming a naturalized U.S. citizen. With Bronx-born Husband-Manager Jeff Wald at her side, Reddy took the oath of allegiance in Los Angeles, then wept happily on the shoulder of Mayor Tom Bradley, who witnessed the ceremony. "This wonderful country is still the only place on earth where the boldest dreams can come true," exulted Reddy, who later celebrated by singing two concerts for women prisoners in a local jail.

"I haven't really kept track of the times I've done it." In fact, Boston Pops Maestro Arthur Fiedler has conducted Tchaikovsky's ballet The Nutcracker for a decade of Christmases, and this year's 14 performances at Boston's 5,000-seat Music Hall have been sold out for weeks. Before attending a television celebration of his 80th birthday last week, Fiedler showed that he was limber enough to teach terpsichorean twists to members of the Nutcracker cast. "I want no part in picking the dancers, and they have none in picking my musicians," the maestro said. "But it's me who puts the two together."

HOUDINI WINS TEST IN A SEALED CASKET--STAYS UNDER WATER IN AIRTIGHT CASE AN HOUR AND A HALF WITH NO ILL EFFECTS, proclaimed the New York Times headline on Aug. 6, 1926. Now, almost 50 years later, Magician Harry Houdini has surfaced again, via a long-lost letter, to explain how he pulled off his great sealed-casket trick. "I know you are doing worthwhile work, and . . . I am at your service," wrote the famous escape artist to a safety expert at the Bureau of Mines. Contending that fear, and not just lack of air, caused the death of miners trapped in airtight chambers, Houdini explained how he had kept alive for 91 minutes on a then estimated five-minute supply of air through careful breath control and by remaining absolutely still. The letter, just discovered during a drawer cleaning, revealed that even the great Houdini had a few moments of doubt: "After one hour and 28 minutes, I commenced to see yellow lights and carefully watched myself not to go to sleep."

Who better to rededicate Manhattan's Bristol Basin Memorial, a monument to the World War II bombing victims of Bristol, England, than Actor Cory Grant? "I have a deep-seated emotion about this ceremony," declared Grant, 70, who was born in Bristol and known as Archie Leach when he left more than half a century ago. His ceremonial chores for New York's English-Speaking Union completed in a blustery wind off New York City's East River, Grant then fielded a question about his film future. "Oh, I won't make more movies. I've done all that. Besides," grinned the deeply tanned, still debonair star, "I'm much too old."

The arm has been throwing better than ever, the knees haven't pulled their famous collapsing trick, and as if that weren't enough to keep Joe Namath in football, his New York Jets teammates last week voted him the club's most valuable player for 1974. Even so, Joe, 31, is conspicuously vague about his plans for 1975. Some New York sportswriters have even speculated that Quarterback Namath, who has just fulfilled his estimated $250,000-a-year contract with the Jets, is considering playing for the Rams in Los Angeles, where Actor Namath could keep near the cameras. Says Joe: "I don't know what I will do. I feel I am a better quarterback than I have ever been--able to play two more years if I want." Could money keep Broadway Joe from becoming Hollywood Joe? "Well," answers Jets Coach Charley Winner, "this is what you play for."

Only half the seats in the Club Juana near Orlando were filled on opening night, and midway through her first week the club's main attraction, Stripper Fanne Foxe, was arrested for going bottomless. No one, however, seemed willing to admit that the Tidal Basin Bombshell might be a Florida flop, least of all Club Owner Mike Pinter, who was peeling off $15,000 a week for her twelve-day run. Fanne, who immediately posted a $500 bond, claimed that her opening had unfolded "much better than I expected." She had also phoned her ailing friend, Congressman Wilbur Mills, Fanne added, to apologize for the rumors about their "engagement." Reported Fanne: "He said not to worry, that he knows how people can be."

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