A sternly authoritarian father, the late Bing Crosby used to lecture his seven children about the increasing "violence and porn" he found in movies. May he rest in peace. Last year Bing's only daughter, Mary Frances, 20 (whom he told Barbara Walters he would disown if she had an affair), popped up on Dallas as J.R. Ewing's sexpot mistress Kristin. Possibly even more unsettling to Dad's memory is the role lately taken by another Crosby kid. In this summer's nastiest horror film, Friday the 13th, Bing's namesake, Harry Lillis Crosby III, 21, plays a camp counselor who witnesses various beheadings, garrotings and throat slashings before he himself is bloodily dispatched by a homicidal archer after a game of strip Monopoly. The Old Man would be more aghast if he knew that the nonstop gore helped Friday earn $27 million in its first month alone. Worse, young Harry found all the mayhem "an awful lot of fun."

In other ways, though, Harry is a chip off the old Bingle. As the eldest of Crosby's three children by second wife Kathryn Grant, he was perhaps the closest to Bing, who hunted and golfed with him to atone for martinet excesses with his four older sons by first wife Dixie Lee. "I think I failed them by giving them too much work and discipline, too much money and too little time and attention," Bing once admitted. "I'm getting another chance with Tex [his nickname for Harry]." When Bing died on a Spanish golf course in 1977, it was Harry who escorted his father's casket back to Los Angeles.

Harry grew up not in Hollywood but in the San Francisco suburb of Hills-borough, "where I went to a nice, normal public school with nice, normal kids." From age 7 on, to be sure, Harry appeared with Mary Frances and his younger brother, Nathaniel, on Pop's Christmas TV specials. Yet he feels that Bing did not force them into show business: "He just opened the door a crack." Harry studied classical guitar at 14 and "became a recluse and a bookworm" after switching to private school at 16. Father set the house rules, Harry notes, but Kathryn handled the discipline. When Harry stayed out past his 10 p.m. curfew on dates, he remembers, "Mom would go to sleep in my bed until I came home."

After high school Harry toured with Bing, but decided to stay behind in England to enroll at the London Academy of Music and Dramatic Art. When Bing told him to pack and come home, his son remained. "I think he was testing me to see if I really wanted to act," says Harry. "Dad left the next day for Spain." The boy credits his mother with holding the family together after Bing's death: "She is very strong and insisted I stay in school in London." Nathaniel, now 18, is on a golf scholarship at the University of Miami. As for his half brothers—Gary, 47, twins Philip and Dennis, 45, and Lindsay, 42—Harry says, "I see them occasionally, but it's difficult." Gary has a $100,000-plus advance from Doubleday for a "Daddy Dearest" book which Harry won't discuss "until it comes out."

Last summer Harry moved to a Manhattan apartment for a Broadway play, only to have it fold out of town. He rebounded with Friday and the lead in a CBS Western pilot, Pony Express. This year he's doing Damn Yankees in summer stock. None of this leaves much time for his five-handicap golf, educated oenophilia, or Dr. Frances Jones, 27. She's a Charleston, W.Va. oral surgeon he met at last February's Bing Crosby Pro-Am golf tournament at Monterey and is still seeing. Someday Harry wants a family, and he expects to carry on at least some of Bing's legacy. "My dad had rules that worked very well," says Harry III. "I'll try to do the same for my kids."